_MG_2454

The cargo bay area presented huge artistic and technical challenges to me. Very much the 'belly of the beast' I had designed the layout of the ship so that the cargo bay would have multiple entry and exit points as well as visibility from both ground level and from the gangways and rooms that were positioned near ceiling height. My intention was for the ships interior to also present interesting opportunities for multiplayer combat game play. As with my previous galleries (unless otherwise stated) I was responsible for the design of this room and it's surrounding areas, the full concept phase for the room (as well as all machinery, doors and animating objects), modelling, textures and materials, full 'healthy' and 'damage' state lighting passes, atmospheric fog placement as well as technical setup of portal and vis-areas (cubic bounding volumes that cull unseen areas).

A plastic moth made from a shipping pallet rests on a white wall. A miniature ceramic pagoda rises out of a funerary vessel. Such tricks of scale and materiality define the topsy-turvy worlds of self-taught sculptors Heidi Lau and Leelee Chan, whose dual exhibition at Matthew Brown marks a convergence of their interests in the alchemical and the arcane. Central to both of their artistic practices is a reverence for relics, a belief that emotions and narratives can be held within objects in powerful ways. Perhaps it is their preternatural attunement to the secrets of artifacts that led Chan and Lau away from painting and printmaking—the respective mediums in which they were formally trained—and toward sculpture instead. In a sense, relics also brought the two artists together: at the height of the COVID-19 pandemic, Lau reached out to Chan on Instagram after seeing a photograph of the latter’s Celadon Weaver (2020), a swath of chainmail adorned with silver-bezeled shards of Song- and Ming-dynasty (960–1644) burial porcelain. Lau saw in this a parallel with an artwork of her own titled The Blue Robe (2018), a handmade chainmail garment modeled on traditional Chinese funerary attire and ornamented with ceramic bone fragments. The two artists developed an easy rapport, beginning a two-year-long conversation that culminated in the creation of the new works for this exhibition. Yet what the two artists do extends beyond merely referencing or utilizing classical objects and aesthetics. They are rather concerned with deeper issues of memory and myth, of how hierarchies form and how value is ascribed. More alchemy than archeology, their sculptural practices revolve around states of change, as seen in mysterious hybrid forms that straddle the boundaries between past and future, between the living and the dead. Lau often finds inspiration in Daoist mythology and Chinese folk practices—a legacy from her deeply spiritual grandfather, who escaped the religious repression of Maoist China and put down roots in the then-Portuguese colony of Macau (sovereignty was only transferred back to China in 1999, two years after the handover of Hong Kong by the British). The artist eschews romanticized notions of Eastern spirituality, however: “One of the fundamental tenets of Daoism is the return to nature, but what does it mean when this idyllic natural order might not exist anymore, or never existed to begin with?” In Lau’s retelling, the classic creation myth of Nüwa, the snake goddess who made human beings out of mud, is as violent as it is beautiful. The Primordial Molder (2018) renders the deity in serpentine segments of clay that stretch across the floor, with glistening scales in turquoise and cobalt-blue glazes. Rocky outcroppings appear to burst out of the sculpture while another section rises up to form an archway, conflating body and architecture, nature and civilization. Preferring to laboriously hand-sculpt her works, Lau herself is a kind of “primordial molder,” coaxing strange, sometimes monstrous, forms out of clay in her New York studio. “It’s like I am having a conversation with the material and letting it reveal what it wants me to do with it,” she says. If the realms that Lau envisions are mired in chaos and contradiction, it is because these conditions govern reality as she sees it. The spaces we inhabit are inexorably shaped by cycles of birth and decay, aspiration and failure. This is manifest in Lau’s home city of Macau, where traditional Chinese-style gardens and crumbling colonial architecture exist side by side with recently built casinos that house tacky simulacra of European monuments. Versions of the past are coeval with competing visions of the future—an absurd, pluralistic, and non-linear temporality that is also captured in Lau’s Spirit Vessels (2020–present). Influenced by mingqi (ancient Chinese burial objects), these sculptures merge elements of urns, architectural ruins, and fantastical landscapes. In Floating Mountains (2024), a tiered blue framework is fused atop a craggy green structure from which glistening black fingers sprout. A hand appears again in Releasing Metal in the Air (2024), holding a bronze butterfly above a ceramic construction of arches and white-glazed railings. Other recent works push further into abstraction, with orbs and orifices visible in vaguely geologic or coralloid formations. Occasionally a ghostly hand or face can be distinguished, as if otherworldly beings are struggling to escape from their ceramic confines. In the wall-mounted Rorschach Test Tile III (2024), what could be an inkblot from the eponymous psychometric exam is rendered in three dimensions as a set of green and flesh-toned ridges inlaid with silver spheres. If not for the clue in the artwork’s title, one might imagine it to be some kind of crustaceous alien. Informed by the Chinese Shanhaijing (Classic of Mountains and Seas), a millennia-old compendium of mythical lands and beasts, Lau’s new works are chimeric and ambiguous, alluding to non-hierarchical, fluctuating states of being in which the animal, vegetal, mineral, and artificial coalesce. In Leelee Chan’s practice, too, disparate elements meld in unexpected ways. Employing all manner of urban detritus, ancient artifacts, and industrial and organic materials, Chan creates sculptures with complex interlocking parts and layered constructions that reward the attentive viewer. Born into a family of antique dealers and restorers specializing in porcelain and pottery mingqi, the artist has a knack for salvaging and repurposing found objects for her practice. From polystyrene packaging and windshields to cracked slabs of asphalt, many of her materials are sourced from dumpsters and sidewalks outside the warehouses and auto-body shops that surround her Hong Kong studio. Her finds are then integrated with delicate stones and glittering metallic inlays in works that make ingenious use of the materials’ properties and activate dense networks of associations. “My practice is about making things not behave how they are supposed to behave,” she explains. “I have to abandon what I think I know about the materials I use.” One substrate that reappears in Chan’s oeuvre is the plastic shipping pallet. The humble object feels familiar to the artist, who grew up in an apartment overlooking Hong Kong’s sprawling Kwai Tsing Container Terminal, and often watched goods being loaded and unloaded. In Chan’s Lucid Formation series (2022–present), the small hollows in black shipping pallets are filled with brightly colored resins to evoke the stained-glass windows of Lingnan architecture, a Southern Chinese style that can still be found in old neighborhoods of Hong Kong. Such works not only challenge the normative distinction between trash and treasure but also bring separate material histories—vis-à-vis Hong Kong’s identity as a port city and as a distinctive cultural region—into contact. Cambium Wanderer (2024) features the addition of bronze-coated, 3D-printed wildflowers and sculpted epoxy clay corners that recall gnarled roots, as if nature is reclaiming a remnant of human civilization. In Chan’s hands, materials are always masterfully manipulated to resemble something else. Mimicry is not an end, however, but a means to invite alternative points of view. Take her wall-mounted Moth (Emperor) and Moth (Pink lined Sphinx) (both 2024), in which slabs of petrified wood and natural magnesium in triangular plastic pallets suggest the velvet flutter of lepidopteran wings. The artist has been fascinated by moths and caterpillars for some time, noting their powers of camouflage in response to both organic and anthropogenic changes in their habitats. In its interplay of nature and artifice, the Moth series prompts viewers to adopt a non-Anthropocentric perspective, considering how other species are grappling with the ways that humans have irrevocably transformed the planet. The works are inflected by the moth’s cultural associations with death and the afterlife—perhaps Chan’s creatures are harbingers of a ravaged future in which survival depends on postnatural adaptation. Chan brings her expertise in Chinese artifacts to bear on Double Passage (Verdigris) (2024), in which two discs inspired by jade bi are placed on top of a shipping pallet. The structure is flanked by vertically oriented bumper packaging, coated in epoxy clay to resemble patinated pillars. Bi were historically placed in the graves of high-status individuals, and thought to symbolize a connection between the earth and the heavens. Sans human body, Chan’s onyx bi invoke more abstract flows of energy between the artwork and its environs, which is emblematic of the artist’s belief that all objects are “alive” in ways beyond what we can perceive or comprehend. Also incorporating antiques are Chan’s Present Relics (2020–present). In these small-scale works, the artist recombines mingqi fragments with contemporary readymade objects to engage layered temporalities. In Tête-bêche II (2024), two funerary figurines face each other, separated by a piece of plastic pallet—a composition that brings to Chan’s mind the concept of parallel lives. In other pieces, abstract configurations of metal, stone, and pottery are precariously balanced. Chan imbues these works with a feeling of spontaneity, testing different arrangements of objects to see what curious patterns might emerge. According to Chan, both she and Lau favor experimental approaches over strictly outcome-directed modes of working. “When we start a sculpture, we don’t do sketches,” she says. “We’re very drawn to this sense of the unknown, trusting that the materials and the process will take us somewhere.” Dissatisfied with neat categorizations and narratives, Chan and Lau pursue the buried and the unruly. To immerse oneself in their work is to go on this journey with them, and enter anachronistic realms richly populated by specters and shapeshifters. -Ophelia Lai Heidi Lau (b. 1987, Macau) lives and works in New York. Selected solo and two person exhibitions include A Cacophony of Rocks, Sikkema Jenkins & Co., New York (2024);  Shadow Speak, with Biraaj Dodiya, Bureau, New York (2023); Gardens as Cosmic Terrains, Green-Wood Cemetery, New York (2022); Empire Recast, Grand Lisboa Palace, Macau (2021); Spirit Vessels, Matthew Brown, Los Angeles (2020); Blood Echoes, AALA Gallery, Los Angeles (2019); The Sentinels, with Rachel Frank, Geary, New York (2018); The Primordial Molder, The Bronx Museum of the Arts, New York (2017); Third Rome, Deli Gallery, New York (2016); and The Obscure Region II, Macau Art Museum, Macau (2014).   Recent group exhibitions include Shanshui: Echoes and Signals, M+ Museum, Hong Kong (2024), Cosmos Cinema: The 14th Shanghai Biennale, Power Station of Art, Shanghai; Horizons: Is there anybody out there?, Antenna Space, Shanghai (2023); And the Moon be Still as Bright, Harper’s, New York (2023); Body Without Organs, Chapter, New York (2023); River Styx, Sea View, Los Angeles (2023); Crossing, KOTARO NUKAGA, Tokyo (2023); Liquid Ground, UCCA, Beijing (2022); Concrete Spiritual, curated by Ajay Kurian, Morán Morán, Los Angeles (2022); SSSSSSSSSCULPTURESQUE, Kiang Malingue, Hong Kong (2022); Mouthed Echoes, Lyles & King, New York (2022); Recent Sculpture, Matthew Brown, Los Angeles (2022); The Hearing Trumpet Part 2, Galerie Marguo, Paris (2022); Liquid Ground, Para Site, Quarry Bay, Hong Kong (2021); Social Recession, NCECA Annual, Weston Gallery, Cincinnati, OH (2021); Earthly Coil, Magenta Plains, New York (2021).   Lau's practice has been supported by numerous residencies and awards, including the Green-Wood Cemetery Residency, Greenwich House Pottery Fellowship, NYSCA/NYFA Artist Fellowship, Colene Brown Art Prize, Emerging Artist Fellowship at Socrates Sculpture Park, Lower Manhattan Cultural Council Process Space, the Martin Wong Foundation Scholarship, and the Joan Mitchell Foundation Painters and Sculptors Grant.   In 2019, Lau presented Apparition for the Macau-China Collateral Exhibition at the 58th Venice Biennale.   Leelee Chan (b. 1984, Hong Kong) makes enigmatic sculptures that incorporate urban debris, ancient artifacts, natural materials, industrial and mundane products, generating visual paradoxes in which these objects move seamlessly between past, present and future. Reflecting the shifting urban fabric in her immediate surroundings in Hong Kong, Chan's sculptures undergo an elaborate transformation through tactile experimentation with materials and processes. The artist pushes the limits of her objects' physicality and expands the possibilities of the language of abstraction. Her sculptures provoke a particular atmosphere and feeling that conjure ambient poetry of the built environment. Chan's visceral exploration of the unknown encapsulates her interest in urbanism, architecture, material culture, craft, and antiquities. Her interplay of abstract forms, intricate details, and unexpected materials calls for a physical experience and encourages a new way of seeing and perceiving.   Chan received her MFA in painting from the Rhode Island School of Design, in 2009, and her BFA from the School of Art Institute of Chicago, in 2006. In 2020, Chan was the recipient of the ninth BMW Art Journey. Her solo exhibitions include: Silica Meadows, Capsule Shanghai, Shanghai (2023), Antinomies, Klemm's, Berlin (2022), Pallet in Repose (Resurfacer), Discoveries, Art Basel Hong Kong (presented by Capsule Shanghai) (2021); and Core Sample, Capsule Shanghai, Shanghai (2019). Her selected group exhibitions include Shanshui: Echoes and Signals, M+ Museum, Hong Kong (2024), Strange Strangers, Para Site, Hong Kong (2023); Joan Miró – The Poetry of Everyday life, Hong Kong Museum of Art, Hong Kong (2023); Poetic Heritage in Tai Kwun Contemporary, Hong Kong (2021); Liquid Ground in Para Site, Hong Kong (2021); KölnSkulptur #10 in Skulpturen Park Köln, Cologne (2020); How Do We Begin: X Museum Triennial 1st Edition in X Museum, Beijing (2020); Holy Mosses in Blindspot Gallery, Hong Kong (2019); Notes from Pallet Town in Ullens Center for Contemporary Arts Dunes, Beidaihe (2019); Hysteresis in Downs & Ross, New York (2019); Scaffolds of Meaning in Mine Project, Hong Kong (2019); Rehearsal in Tai Kwun Contemporary, Hong Kong (2018). Chan's work can be found in the permanent collections of Long Museum, Shanghai; UBS Art Collection, Hong Kong; M+, Hong Kong; Skulpturen Park Köln, Cologne; J. P. Morgan Chase Art Collection, Hong Kong and Kadist Art Foundation, Paris/San Francisco. Her work has been featured in Frieze, Artforum, Mousse Magazine, Art Asia Pacific, the Financial Times, and Ocula, among others.

Description Dec. 6, 1949 F. K. HETTINGER' ET Al. 2,490,300 LIGHTER Filed Aug. 22, 1947 2 Sheets-Sheet l 7 .n 2z 243.555 45 @1f J 463 "3- I I I I I 5 I i mn/ENTDR- Franc/s A. #eff/nge! 5y @hd/ve Jnes #WMM l ATTORNEYS Dec. 6, 1949 F.V K. HETTINGER ET AL LIGHTER Patented Dec. 6, 1949 ag. Francis K. 'I'le'ttnger and Wardwell Jones, Tucson; Application August 22., 19470,Serial No. 770,022 1 Claim. (Cl. 671-11) This invention relates to a lighter, and more particularly to a combination cigarette and pipe lighter. The lighters commonly in use are principally adapted for lighting cigarettes, and it is difficult to light a pipe with them due to the tendency of the flame to extend upwardly from the lighter instead of downwardly to the bowl of the pipe. It is, therefore, the principal objects of the present invention to provide a lighter adapted for lighting cigarettes, cigars and pipes; to provide a lighter having a main wick mechanism and a separate removable wick adapted to be lighted from the main wick for lighting a pipe; to provide a windshield guard for the main lighter mechanism; to provide the auxiliary lighting wick with a windshield which extends to the main wick windshield; to provide a removable uid container or compartment in the base of the container; to provide a compartment for an absorbing material for the lighter iiuid; to provide a wick leading from the duid container or compartment to the absorbent containing compartment; and to provide a device of this character simple, economical to manufacture and efficient in operation. In accomplishing these and other objects of the present invention, we have provided improved details of structure, the preferred form of which ls illustrated in the accompanying drawings, wherein: Fig. 1 is a perspective View of our lighter. Fig. 2 is a vertical section through the lighter. Fig. 3 is a transverse vertical section taken on a line 3 3, Fig. 2. Fig. 4 is a vertical section showing the auxiliary wick element. Fig. 5 is a transverse cross-section through the auxiliary wick element. Fig. 6 is a perspective view of the lighter showing the auxiliary wick element in disassembled relation. Fig. 7 is a perspective view of the lighter showing the duid container in disassembled relation from the remainder of the lighter. Referring more in detail to the drawings: I generally designates a lighter which is of relatively flat, rectangular shape, comprising a main case or body 2 having a closed upper end 3 and an open end i forming a compartment 5 adapted to receive an absorbent material 6, such as cotton or the like. A top 'I is provided for the main body portion 2 and is hingedly connected to an end 8 of the body member as indicated at 9 (Fig. 1). Thebottom I of the lighter consists of a con tainer II-adapted to contain a lighting fluid I2. The container II is provided with a top I3, and thevcontainer isadapted toremovably engage in Athe open lower end of the body portion 2. The " lower portion of the container I I is provided with an annular oiiset portion at its lower edge as y indicated atr I4 (Fig. 3) so that the lower edge of the'main body portion will engage the shoulderV portion when the lighter is in assembled condition. The top I3 of the uid container I I is provided with an opening for iilling the container with fuel, such as lighter fluid. The opening is made byforming a downwardly extending internally threaded boss I in the top I3 of the container II adapted to receive a threaded elongated container I6 for carrying of an extra ilint or pyro-v phoric element I1. The top of the threaded container I6 is anged and internally threaded so 'as to receive a threaded shankr I8 of a closure member I9 for preventing the lighter iiuid from entering the container, thus keeping the flint dry. The top I3 of the container II is provided with. asecond openingV as best illustrated in Fig.' 2, providedwith a sleeve 20. A wick or the like 2| isprovided to extend through the sleeve 20 into the fluid container II, and its other end A top 3 of the .main body portion 2 is provided with Van opening 22 for receiving a sleeve 23. Extending through the sleeve 23 is a wick 24, 'the' wick 24 extending a substantial distance above the top 3 of the body portion 2. `The top 3 .ofthe body 2 is also provided with an opening nearfthe end 25 of the body portion 2 andadjacent the opening 22 as indicated at 28. Adapted to engage in the opening 26 is a tube 21 for containing a iiint or pyrophoric element 28. The top of the container II is recessed as at 28 to accommodate the lower end of the tube 21 which extends through the absorbent material 6 so that the flint 28 may be removed and replaced without disturbing the absorbent material. A coil spring 29 is adapted to engage the lower end of the iiint 28, and its lower end engages the end of a threaded shank 30 of a closure member 3| engaging in the lower end of the tube 21. Rigidly secured to the top 3 of the body portion and in parallel relation to each other near the end 25 of the container of the lighter are windshield elements 32 and 33 which extend forwardly past the main lighting wick 24. The wind breaker elements are provided with a plurality of openings 35 rearwardly of the wick 24 as best illustrated in Fig. 6. The wind breaking elements 32 and 33 afford a support for a shaft 36. uMounted on the shaft 36 are knurled wheels 38 and 39, and mounted on the shaft 36 between the wheels 38 and 39 is a wheel 40 having teeth 4| adapted I to engage .the upper. end of the.,int28. The knurled wheels 38=ndf 39`fare largeiinwimeterdf than the wh'el`40and in turning' wh'el -4(1"tle "10 operators nger contacts wheels 38 and 39, but A does not contact wheel 40. This arrangement." facilitates turning the wheel 4U and prevents; soiling of the nger with partic1es.,offf 1int and., the like. It will ybe noted that tl'foiward endS"f-'15', of the wind breaking elements 32 and 33 are curved slightly inwardly around-tiravlckiufas J indicated at 42 (Fig. 6) l The top 3 of the mainbody portion 2 'ispro`' vided with an ,openingA 43 to receive atube 44 adapted to extendplnto the cotton absorbing compartm'en't'- ofjthe"'body''portiorr -bstbillisltratedi'in 2. The' ltub'e has fa ,closed upper end .45'.j Contained-in` tl1`e"tube`- isa'wick- 46hav' ing Aits 'lower' end extending outwardly -of the tube "a` sli'ght'fdistance' "indicated-at 4T and contacting tli''fab'sorbent `cotton- 6 rin thebodyv portion'2,'the"tub"being removably mounted in theb'opening in the to'pof the-bodyportion; Rig' idly secured'to the upper'v portion 'of the tube44- in anyV suitable manner is a substantially Uf:- shapd' Wind guard '48,y the`a1'ms 49 'fand' "50A" of which ex'tendto'ward the wlndshield'elements 32 and 3 3 andha've their`ends' 5'I engaging the sides i of.- the .curve'dends' 42 of the windfbreakers' 32 "35 and 33,5tliu`s forming awindbreaker-extending substantially Iacross the 'topf3`of the body'portion" 2; The "arm's' ..49 fand 'iare' 'provided with a plurality of'per'i'o'iations 52 and1`53. l Tof nu4 the, container' lliwith-jfuer the` con; tainer 'is 'disengaged 'lrornv the body.p,ortion"2; Th container 'tube l l5V i's then' removed so' that uid'm'ay be'inserted ftliroug'hthe"openirigirito the compartment andthe threadedtub replaced inthe opening. The'iluid will'b` absorbed lby the Wick 2 f andcarried to the absorbing cotton'v 6 in the m'ainbody container.' The idiwill then be absorbed by the lightingY wick 2liA extending above' the' to'p".3"of the'lbo'dy' 2'. Turning of ithe kr'irled =wheels' '38'an`cl '39 will cause'the 'teeth` 4 I engaging the end of the flint 28to emit-sparks to' contact the top of= thewickl'24ffv6r A`1ighting1 a cigarette 'or thelike'th'e elements l32"'and 33Y and arms 49 and'SUfof the 'Ushpedmmbr '48pre-4 venting 'wind:froniputting"'outfthe blaze of the wick 24. When it 'isdesiredt 'light apipe'or the like,"the"tube44 vis removedrom the'cotton absorbing montaner-'by upward pull'fonxtne uy 4 shaped member 48 and the end of the wick extending from the tube lighted from the blaze of the wick 24 for transporting of the blaze of the wick 46 to the pipe or for other use. It will be obvious from the foregoing that we have provided an improved lighter having a main and auxiliary lighting mechanism, the various partsof which are easily -accessible for replacementor materials.; It `will be obvious that changes may be made in the device without departing from the spirit of our invention. .. What we claim and desire to secure by Letters Patent, is: , Alighte'r comprising, a casing having one end conducting the lliz'luid-from said container to said absorbent material, a Awick extending from said absorbent-materialthrough the top of said body `membeig'wind breaking elements carried by said top, a shaft mountedI in said'wind breaking elementsfalfriction'device secured on said shaft, meansA for mounting' a int material adjacent sa-id"frictionl device, means for resiliently urging ^saidyint against said'friction device, an auxiliaryjwi'ck extendingv into saidabsorbent material and removably carried by said'body member, a wind breaking element'carriedby said auxiliary wick having its endsl'engagingthe rst named wind breakingel'ement to form a continuous elementA substantially across the vtop of said body member, means'in the containerfor filling the same With'igniting.iiuid,said means including arrelongated container forfiint material, 40x-. FRANCIS K. HETTINGER. WARDWELL JONES; REFERENCES CITED The following Teferencesare Vof record in the le of this patent: UNITED .STATES vPA-"JIENIS A Number Name Date 56" 1,941,8733 Aronson Jan. 2, 1934V 2,262,806 Kempf et al. Nov. 18,'1941 FOREIGN PATENTS Number Country Date 139,254 Switzerland Junel6, 1930 411.7861 Great lBritairiV June 14, 1934 519,716 Germany Feb. 11, 1932 622,094" Germany- Nov. 19, 1935

For more than fifteen years, the polychromy of ancient Greek and Roman sculpture has been captivating the public worldwide. Some three million visitors have experienced the 'Gods in Colour — Golden Edition' firsthand in the museums of cities such as Athens, Istanbul, Copenhagen, London, Malibu, Mexico City, Munich, Berlin, Rome, Vienna and, most recently, San Francisco—as well as those of renowned universities, among them Harvard and Oxford. The Liebieghaus Skulpturensammlung is now presenting a major expanded exhibition allowing a nuanced look at the disconcerting phenomenon of statuary polychromy. 'Gods in Colour — Golden Edition: Polychromy in Antiquity' features more than 100 objects from international museum collections such as the British Museum in London, the Museo Archeologico in Naples, the Ny Carlsberg Glyptotek in Copenhagen, the Archaologisches Institut in Gottingen, and the Skulpturensammlung der Staatlichen Kunstsammlungen Dresden, as well as the holdings of the Liebieghaus, which encompass 60 recent reconstructions but also some dating from the nineteenth century, along with 22 prints. Credit: Liebieghaus Skulpturensammlung “The polychromy of ancient sculpture is a fascinating phenomenon, and one that continues to surprise and astonish us despite in-depth research over the past decades and the publication of important results. The image of white marble sculpture and architecture still dominates our conception of antiquity today. The Liebieghaus Skulpturensammlung and a team of scholars around Vinzenz Brinkmann—part of an international research network—untiringly devote themselves to correcting this misconception once and for all. The expanded exhibition 'Gods in Colour—Golden Edition' at the Liebeighaus Skulpturensammlung presents the latest instructive findings as well as a resume of forty years of intensive research into the polychromy of ancient sculpture,” Dr. Philipp Demandt, the director of the Liebieghaus Skulpturensammlung, comments on the exhibition. Under the direction of Vinzenz Brinkmann, the head of the Liebieghaus antiquity collection, an international team of scientists have been researching statuary polychromy for some forty years. Their work has inspired new research projects on the polychromy of ancient Greek and Roman sculpture at universities and museums in many countries. The primary focus of these projects is the scientific analysis of the original paints. Within this context, the history of how scholars responded to polychromy in the period from the mid-eighteenth century to World War I—and their extensive accompanying reconstruction activities—have been subjects of particular interest. Since the exhibition 'Gods in Colour' was first on view in Frankfurt in 2008, the number of reconstructions carried out by the research team has doubled, and new aspects have come under consideration, for example the polychromy of ancient bronzes. In 2016, Ulrike Koch-Brinkmann and Vinzenz Brinkmann donated the reconstructions in their possession to the Stadelstiftung. Exhibition View [Credit: Liebieghaus Skulpturensammlung/ Norbert Miguletz] Prof. Dr. Vinzenz Brinkmann, the curator of the exhibition and head of the Liebieghaus Department of Antiquity, explains: “Our experimental reconstructions have proven to be our chief means of gaining insights into the colouration of ancient sculpture It is only by experimenting with the ancient painting materials and techniques on three-dimensional bodies that we can develop viable solutions to previously unknown questions. Naturally, to this end we have chosen objects whose original polychromy is well preserved. It must be added that any reconstruction always represents no more than an approximation and can never reproduce the original appearance in its entirety—nor can it achieve the artistic sophistication of the original in every detail. To the contrary, the reconstructions are the results of a scientific and thus a schematic process, but one which has the great wealth of archaeological and scientific findings of four decades of research to draw on.” Experimental reconstructions and the most recent findings on the polychromy of ancient sculpture Originally, the painted decoration of an antique sculpture not only enhanced its appearance from the aesthetic point of view and increased its lifelike impression, but also provided the ancient viewer with important information about the identity of the figure depicted. Over the past decade, research has focused increasingly on this aspect. In the process, new interpretation proposals have been developed not only in the context of large-scale Greek bronzes, but also for numerous marble sculptures. In the ancient world of the eastern Mediterranean region, the use of colour was par for the course. For the Greeks and Romans, however, the painting of sculpture was far more than superficial decoration. Rather, polychromy had means of its own for expanding the formal and narrative structure of the artwork. It was only through the dimension of colour that artists achieved the desired vibrancy of expression. Experimental colour reconstruction, Variant B, of the so-called Cuirass Torso from the Athenian Acropolis, plaster cast, natural pigments in egg tempera, gold leaf, h. ca. 62 cm, 2005, Liebieghaus Skulpturensammlung (Liebieghaus Polychromy Research Project),  Frankfurt am Main, inv. St.P 686 [Credit: Liebieghaus Skulpturensammlung/ Norbert Miguletz] The examples presented in the exhibition illustrate the different conventions that governed polychromy in the archaic (650–480 BC) and classical (480–330 BC) periods. Objects and figures were coloured in such a way as to resemble their models in nature. Where the choice of colours did not correspond to reality, it served to support the narrative content. The standing figure of a naked young man (kouros) or richly bejeweled maiden (kore) were characteristic of the Greek sculpture of the archaic period. Figures such as the Kouros of Tenea (original: Greece, ca. 560 BC, marble, Staatliche Antikensammlungen und Glyptothek, Munich) served to decorate graves and sanctuaries. The generic colour reconstruction of 2015 unites the surviving traces and details of the polychromy of several statues: the hair of the head is styled with ribbons, that on the breast and around the genitals possesses an ornamental quality, and the ear jewelry emphasizes the aristocratic origins. The colours are evidently indebted to the Egyptian tradition—the blue indicating the hair and the light brown skin colour of the skin, for example, are found on Egyptian sarcophagi and reliefs. Ancient written sources describe the wealth of colour and form characterizing the garments of the neighbors to the north and east, which fascinated the Greek artists. The splendidly colourful costume of the so-called Persian Rider from the Acropolis (original: Athens, 500/480 BC, Acropolis Museum, Athens) is especially well preserved. The diamond pattern of the trousers in the colour reconstruction of 2008/2019 exhibits sophisticated rhythmic alternations between the strongly contrasting shades of red, blue, yellow, green and brown; the tunic features an imaginative and complex tongue ornament. This clothing style of the peoples to the north and east was used around 480 BC on the west pediment of the Temple of Aphaia on Aegina to make a kneeling archer recognizable from a distance. Experimental colour reconstruction, Variant C, of an archer, the so-called Paris , wearing the costume of the horsemen of the neighbouring peoples to the north and east, from the west pediment of Aphaia Temple, artificial marble, natural pigments in egg tempera, lead, wood, h. 96 cm,  2019, Liebieghaus Skulpturensammlung (Liebieghaus Polychromy Research Project), Frankfurt am Main, inv. St.P 947 [Credit: Liebieghaus Skulpturensammlung/ Norbert Miguletz] The rich garment ornamentation of the Persian Rider and the Aeginian Archer testifies to the Greeks’ fascination with the costumes of the horse people—the Amazons, Thracians, Scythians, Trojans and Persians. Textile finds from the kurgans of the Pazyryk in the Altay Mountains now in the collection of the Hermitage in St. Petersburg show how colourful the original garments were. The third and most recent reconstruction of the archer, produced in 2019, corresponds more closely to the colour scheme and decoration techniques of these original textiles. The Greeks also adopted the use of gold sequins, examples of which have survived well intact on Scythian fabrics. The decorative elements of the garments played a key role in helping ancient viewers understand the figures depicted, as is illustrated in the exhibition by three reconstructions of female figures from archaic-period Athens: the funerary statue of Phrasikleia (original: Greece, ca. 540 BC, marble, National Archaeological Museum, Athens), the so-called Chios Kore (original: Athens, ca. 520/500 BC, marble, Acropolis Museum, Athens) and the so-called Peplos Kore (original: Athens, ca. 520 BC, marble, Acropolis Museum, Athens). Experimental colour reconstruction of the funerary figure of Phrasikleia (detail), stucco  marble on PMMA, natural pigments in egg tempera, lead tin foil, gold leaf, garnet, tourmaline, labradorite, gum arabic (iris), h. 200 cm, 2010/2019, Liebieghaus Skulpturensammlung, Frankfurt am Main (on loan from the Ludwig-Maximilians- Universitat, Munich, Leibniz Prize O. Primavesi 2007), inv. LGLH Z01  [Credit: Liebieghaus Skulpturensammlung/Norbert Miguletz] Dating from 2010/2019, the reconstruction of the Phrasikleia represents a young woman wearing sandals, a long, richly patterned dress, jewelry, and on her head a floral crown consisting of lotus buds and blossoms. The bright red gown is adorned with a red and yellow scattered pattern and decorative borders. The rosette petals of the appliques are made of gold and lead tin foil. The 2012 reconstruction of the so-called Chios Kore depicts a girl in a long skirt and a kind of undergarment made of a fine fabric forming multiple folds. The Swiss artist Emile Gillieron already painted a watercolour documenting the vestiges of vibrant blue and red paint on the original statue when it was excavated at the end of the nineteenth century. Investigations carried out in 2010 did in fact bring the pigments azurite and vermilion to light. The modern researchers moreover found the lead yellow and light-yellow ocher their predecessors had observed back in 1904. Whereas the costume of the so-called Chios Kore thus offers direct insights into the fashions of the late sixth century BC, the decorative pattern and lotus flower ornament of the Phrasikleia make symbolic reference to the cycle of life and death. The so-called Peplos Kore wears a tight-fitting outer garment without folds over an undergarment. The archaeologists equated the former with the so-called peplos (a women’s dress style in ancient Greece) and erroneously called the figure the Peplos Kore. In fact, however, the garments—and with them the figure’s true significance—only became clear with the aid of the polychromy. Recent research has enabled a complete understanding of the figure’s complex colour scheme. The exhibition presents a new, revised reconstruction of the socalled Peplos Kore. Indications of the steps preceding the painting process have now been discovered, as have weathering traces of the paint. The polychromy— in particular the animalfrieze garment (ependytes), a crown of feathers meanwhile lost (vestiges of its mounts are still visible on the head), the weapons and the immobile body—gives the figure its true identity. The statue mistakenly designated the Peplos Kore is actually a marble representation of a xoanon, an ancient wooden cult image of the goddess Artemis. Experimental colour reconstruction, Variant B, of the so-called Peplos Kore from the Athenian Acropolis, stucco marble on plaster cast, natural pigments in egg tempera, crown and weapons made of gilded and silvered wood, h. 136 cm, 2005, reworked in 2019, Liebieghaus Skulpturensammlung (Liebieghaus Polychromy Research Project), Frankfurt am Main, inv. St.P 687 [Credit: Liebieghaus Skulpturensammlung/ Norbert Miguletz] Sculptures also received a polychrome finish in the Hellenistic period (330–30 BC). In several cases, the researchers have been able to prove that the naked areas of the human figure were painted with a reddish-brown or light brown hue. As we have learned from the reliefs of the so-called Alexander Sarcophagus from the royal necropolis of Sidon (original: Lebanon, ca. 320 BC, Archaeological Museum, Istanbul), the colour scheme was determined to a decisive degree by the contrasts between radiant blue, intense red and golden ocher. Gilding played an extremely important role, occupying ever larger areas of the surfaces and serving as a painting surface itself. The precious material was used again and again to represent jewelry on humans and animals alike. Gold and silver plating and coloured stone inlays enhanced the splendor and light reflection of the ancient works. Remnants of leaf gilding on garment hems of Greek sculptures give rise to speculations that the edges of ancient garment fabrics were piped with gold threads. The traces of gold on the marble figure of the so-called Small Herculaneum Woman are an example. The late classical original of this work no longer exists, but dozens of late Greek and Roman replicas have come down to us. Experimental study of the polychromy of the so-called Treu Head, Liebieghaus Skulpturensammlung (Liebieghaus Polychromy Research Project in cooperation with the British Museum, London), Frankfurt am Main[Credit: Liebieghaus Skulpturensammlung/Norbert Miguletz] The figure of a young woman sports a hairstyle made up of several braids woven together in a tight knot. She is in the act of pulling her mantle tightly around her with both hands. The colour reconstruction of 2019 is based on examinations of the polychromy on a replica found in Delos in 1894 (original with polychromy: Delos, 2nd century BC, marble, National Archaeological Museum, Athens) and uses the cast of the eponymous replica discovered in Herculaneum in 1706 (original from which the cast was made: Herculaneum, 1st century AD, marble, Staatliche Kunstsammlungen Dresden, Skulpturensammlung). The reconstruction combines the traces of polychromy documented since the excavation. Particularly the colour scheme of the mantle reveals the sculptor’s intent: the fine greenish fabric is transparent everywhere where the mantle stretches across the body’s curves and protrusions. One section of the exhibition revolves around a three-year research project carried out in cooperation with scholars from Frankfurt’s Goethe University and concluded in January 2020. The aim was the development of physical models as well as an interactive digital publication for communicating the research and reconstruction of the polychromy of ancient Greek sculpture to specialists, students and a broader public. A statue from the Frankfurt Group of Muses was chosen as the object of this case study. This figure presumably comes from the sacred island of Delos dedicated to Artemis and Apollo (Standing Muse from the Thermal Baths of Agnano, originally from Delos, 2nd century BC). It bears a wealth of information—however difficult to see—about its original polychromy. The researchers compared it to a marble statue of the Small Herculaneum Woman type which was erected on Delos around the same time (ca. 120–100 BC) and whose polychromy has survived in better condition with a marble statue of the Small Herculaneum Woman type which was erected on Delos around the same time (ca. 120–100 BC), and whose polychromy has survived in better condition. Statue of the Muse in downscaled form with depiction of vestiges of paint (left) and downscaled Muse, Variant D (right), stucco marble on PMMA, natural pigments in egg tempera, gold leaf (right),  h. 39 cm, 2019, Liebieghaus Skulpturensammlung (Liebieghaus Polychromy Research Project), Frankfurt am Main, inv. LG 227 and 226 (on loan from the Goethe University Frankfurt, Institute of Archaeological Sciences, dept. I: Classical Archaeology, cast collection) [Credit: Liebieghaus Skulpturensammlung/Norbert Miguletz] Since the first excavations in the eighteenth century, the representation of naked skin has presented scholars with difficulties. Apart from the disapproval brought about by the then modern sense of aesthetics, the generally poor state of the skin colour has played a decisive role in scholars’ neglect of the matter. The exhibition devotes itself to this topic in colour reconstructions realized according to the latest scientific findings, for example those of the socalled Treu Head (original: Rome, 2nd century AD, marble, The British Museum, London) and the Portrait of the Roman Emperor Caligula (original: AD 37–41, Ny Carlsberg Glyptotek, Copenhagen). New examinations of the Treu Head—a depiction of a female deity—at the British Museum encompassed a large number of paint analyses that yielded precise information about the painting technique and the pigments used. For the representation of the skin, the ancient artist employed calcite mixed with not only red and yellow ferric oxides but also a small amount of Egyptian blue, which lends the skin a somewhat cooler touch. As is also the case with the Portrait of the Roman Emperor Caligula, pink madder lake was used for the space between the lips and the corners of the eyes. The Treu Head bears key significance in the current polychromy discussion. Evidently the light female skin was characterized with the aid of paint, while the precious marble served merely as the support material. Exhibition View [Credit: Liebieghaus Skulpturensammlung/ Norbert Miguletz] To date, it has not been possible to provide a conclusive answer to the question of how the polychrome enhancement of bronze statues related to marble polychromy. The research team undertook extensive initial approximations of the original appearance of bronzes, with the famous Warriors of Riace (originals: Greece, 5th century BC, Museo Archeologico Nazionale, Reggio di Calabria) and the original Bronze Sculptures from the Roman Quirinal Hill (originals: Greece, end of 4th or 3rd century BC, Museo Nazionale Romano, Rome) as examples. In the reconstructions of the two Riace Warriors, the illusion of suntanned skin was achieved with numerous layers of a much-diluted bitumen lacquer containing a bit of red pigment. The extremely lifelike impression is brought about by the elaborately made stone inlays for the eyes, nipples inlaid in copper, and lips and teeth covered with silver sheeting. Within the framework of the scientific investigations and recasts of the originals as well as the making of the reconstructions in the years 2012–2016, Warrior A turned out to be a portrayal of Erechtheus, son of the goddess Athena, and Warrior B of the Thracian king Eumolpos, son of Poseidon, god of the sea. The examinations of the so-called Quirinal Bronzes in the same years (2012–2018) confirmed the conjecture that the two figures represent heroes from the Greek Argonaut saga: Amycus, king of the Bebryces, and Polyceuces, an Argonaut and son of Zeus, who encounter one another in a boxing match. Research network and latest analysis techniques Over the past decades, information about the original ancient marble sculptures has been obtained with the aid of scientific methods, and has in turn served as the basis for the production of experimental reconstructions. The participating scholars have also reevaluated ancient written sources on statuary polychromy. Apart from precisely made plaster casts, copies of ancient sculptures have been produced in marble and, most recently, as 3D prints. These copies have then received polychrome finishes using authentic historical painting materials. In 2020, the long series of three-dimensional physical reconstructions is entering its thirtieth year. Ulrike Koch-Brinkmann and Vinzenz Brinkmann undertook their first experimental colour reconstructions on copies of originals back in 1989. This work was based on their own scientific investigations, but also and above all on the results of numerous research projects implemented on the international level. At important museums such as the British Museum in London, the Louvre in Paris, the Acropolis Museum in Athens, the Pergamonmuseum in Berlin, the Ny Carlsberg Glyptotek in Copenhagen and the Metropolitan Museum in New York, archaeologists, conservators and scientists have worked together successfully to further the research into the polychromy of their own respective holdings. What is more, a large number of extensive independent research and dissertation projects have been realized. Methods of scientific investigation have been developed further and refined. The visibleinduced infrared luminescence (VIL) imagining technique has been developed, for example, and thermographic imaging methods optimized. The researchers have also profited extensively from the new development of portable, non-invasive analysis techniques with whose aid myriad colour measurements have been carried out on the objects. Over the past years, this has led to a tremendous increase in knowledge about the pigments used in antiquity. X-ray fluorescence, a portable method for the nuanced ascertainment of a material’s metal content, has enabled the rapid identification of a large number of inorganic pigments without taking samples. UV-VIS absorption spectroscopy is capable of identifying both pigments and colourants such as plant dyes. It thus comes into play for the determination of nearly all inorganic, but also organic materials. The measurement, which amounts to an optical fingerprint, also encompasses the physical ascertainment of the antique material’s hue. Particularly in the context of reconstructing ancient polychromy, this chromatic definition permits an extremely precise approximation of the original appearance. Based on these new technical means of making light visible, but also the scientific analysis of pigment traces, the team around Vinzenz Brinkmann have arrived at detailed results and more precise forms of communication over the course of many years of work. For their work they have received support from the German Research Foundation, the Stiftung Archaologie, and the Leibniz Prize project of Prof. Dr. Oliver Primavesi, from Salvatore Settis, the government of the Republic of Italy, the Stadelscher Museums-Verein and, most recently, the German Federal Ministry of Education and Research as well as the Goethe University of Frankfurt am Main with Prof. Dr. Dirk Wicke. 'Gods in Colour — Golden Edition' will run until August 30, 2020] Source: The Liebieghaus Skulpturensammlung [November 30, 2020] Labels Exhibitions, Germany, Travel TANN you might also like Newer Post Older Post

Description CROSS-REFERENCE TO RELATED APPLICATIONS Not applicable. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT Not applicable REFERENCE TO A MICROFICHE APPENDIX Not applicable BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to trailers that can be towed by two-wheeled vehicles such as motorcycles, bicycles and the like, wherein the trailer has a single rear mounted road wheel. More particularly, the present invention relates to an improved motorcycle trailer apparatus that includes an improved configuration that includes a rear wheel, shock absorber, and swing arm assembly mounted on a frame with unique frame geometry. The present invention further relates to an improved motorcycle trailer and hitch apparatus that provides a heretofore unknown stability through locating the hitching mechanism and trailer frame below the axis of rotation of either or both of the trailer and motorcycle rear wheels. 2. General Background of the Invention There are a number of large motorcycles available in today's market that have powerful engines that propel them easily at interstate highway speeds of 70 mph. These road motorcycles are typically provided with engines that range from 250 cc to over 1000 cc in displacement. These engines are also powerfil enough to pull a substantial load in the form of a trailer. There are a number of prior art trailers that have been designed for towing behind a motorcycle. The Hawes et al. U.S. Pat. No. 3,937,489 discloses a trailer for a motorcycle that includes a hitch formed of two parallel flat plates attached to the trailer by a hinge having a transversely disposed horizontal axis. Another flat plate is sandwiched between the two parallel plates. The plates are fastened together by a pin inserted through holes in the plates to form a hinge having a vertical axis. Tubular members are mounted to the motorcycle and receive extensions adjustably mounted to the inner flat plate to thereby attach the trailer to the motorcycle. The trailer also has a resilient suspension system for the trailer road wheel which is adjustable to compensate for various loads carried on the trailer and is formed in a manner such that wind acting on the top of the trailer acts to urge the trailer downwardly to thus stabilize the trailer when in use. In the Galloway U.S. Pat. No. 4,511,155 there is provided a one-wheel trailer for a two-wheeled vehicle such as a motorcycle. The trailer includes a first and a second arm, each arm having a first and second end. The first end of each arm is connected preferably to the site corresponding to a passenger footpeg of the two wheeled vehicle or the like. A rigid frame is secured adjacent the second end of each arm. A container is secured to the bulkhead and a spring biased suspension arm is pivotally connected to the bulkhead. A castor arm is mounted adjacent the distal end of the suspension arm enabling swivelling of the castor arm relative tot he suspension arm. A wheel is rotatably mounted relative to the castor arm permitting the wheel to support the container. A trailer that is designed for either a pedal cycle or motorcycle is disclosed in U.S. Pat. No. 5,011,170. The '170 patent relates to trailers and particular to the trailers that are used with bicycles and motorcycles. The trailer may be moved 90 degrees relative to the bike when moving or parked. Locking it in such a position while parked prevents it from being wheeled away. A French patent 2 454 951 discloses an attachment for hauling a single wheeled trailer by a bicycle. The part is fixed to the bicycle frame to form a towing attachment. There is an arrangement to allow trailer movement in two planes only. The towing attachment is made of two fork pieces welded together and bolted to the rear wheeled spindle and stayed rigidly by the frame. The other part is formed by two cheeks, joined together by a pivot pin which is held at one end by a spring clip. French patent 2608-547 discloses a trailer that includes a main longitudinal bar with a rear fork for the wheel. The fork is pivoted to rear end of the bar and has a spring-loaded lever system to control the amount of movement, and a shock absorber. The upper surface of the frame bar is equipped with a plate, a transverse bar and a front bracket to support a plastics container with a lid. A trailer arrangement for a bicycle is shown in the German patent No. 868 120. These prior art designs do not provide a suitable stable towing combination of motorcycle-trailer, particularly a single rear mounted wheel with a frame that supports the wheel and a swing arm and shock absorber. With the growing popularity of motorcycle touring requiring space for carrying personal articles including, such as, camping equipment and luggage, there is growing demand for a stable towing system. All prior art devices include elements promoting instability of the combination of motorcycle and trailer, during the tow. Among these elements promoting instability are the axes of rotation and location of hitch, relative orientation of load frame and trailer wheel axle, relative location of hitch and trailer load frame, and relative location of hitch and trailer wheel axle. BRIEF SUMMARY OF THE INVENTION The present invention provides an improved motorcycle apparatus that enables large loads to be carried on the trailer with a low center of gravity. An improved frame geometry incorporates a specially configured hitch that enhances tow stability and a swing arm with an adjustable shock and, a rear fork that is supported by the swing arm to carry a single wheel behind the frame. The hitch and trailer frame is positioned well below a horizontal line that intersects the axle of the rear wheel of the motorcycle, and preferably also below the axle of the trailer wheel. The motorcycle trailer apparatus of the present invention thus includes an elongated frame having first and second end portions, the first end portion having a detachable hitch attachment for removably attaching the frame to the rear end portion of the motorcycle. The swing arm assembly pivotally attaches to the frame at the second end portion of the frame. A single wheel is carried by the swing arm assembly which includes a wheel fork that extends behind the frame. An adjustable shock absorber extends between the frame and the swing arm assembly. The arm has an upstanding portion that extends above the frame. The shock absorber is inclined, with a rear end portion of the shock absorber being higher than the front end portion of the shock absorber due to its attachment to the inclined portion of the swing arm assembly. This shock and shock mounting arrangement presents the adjustment portion of the shock at an elevated exposed position, enabling easy access. The hitch attachment includes a gimble arrangement that enables the first end portion of the frame to articulate relative to the motgrcycle during use about two orthogonal axes, i.e., the vertical axis and the horizontal axis perpendicular to the tow line. The frame can include left and right horizontal members with the wheel positioned in between the left and right horizontal members 47 and thus hitch member and is supported at the hitch and railer wheel axle relatively below the axles of the rear wheel of the motorcycle and the trailer wheel. The shock absorber can be a single shock absorber that is positioned on a transverse strut that extends between the left and right horizontal members. The frame provides a pivot at its rear or second end portion. The swing arm assembly pivotally attaches to the frame at the pivot. The swing arm includes a trailing fork portion that extends behind the pivot and carries the wheel. BRIEF DESCRIPTION OF THE DRAWINGS For a further understanding of the nature, objects, and advantages of the present invention, reference should be had to the following detailed description, read in conjunction with the following drawings, wherein like reference numerals denote like elements and wherein: FIG. 1 is an elevational view of the preferred embodiment of the apparatus of the present invention; FIG. 2 is a top plan view of the preferred embodiment of the apparatus of the present invention; FIG. 3 is an elevational view of the preferred embodiment of the apparatus of the present invention; FIG. 4 is a sectional elevational view of the preferred embodiment of the apparatus of the present invention, taken along lines 4--4 of FIG. 2; FIG. 5 is a fragmentary perspective view of the hitch attachment portion of the preferred embodiment of the apparatus of the present invention; FIGS. 6 and 7 are fragmentary elevational views of the hitch attachment portion of the preferred embodiment of the apparatus of the present invention; FIG. 8 is a fragmentary plan view of an alternate embodiment; and FIG. 9 is an elevational view of an alternate embodiment of the hitch portion of the apparatus of the present invention. DETAILED DESCRIPTION OF THE INVENTION FIGS. 1, 2 and 7 show the preferred embodiment of the apparatus of the present invention designated generally by the numeral 10 in FIGS. 1, 2 and 7. Motorcycle trailer apparatus 10 provides an elongated frame 11 that can be manufactured of welded metallic tubing such as steel, aluminum, or titanium. The frame 11 can also be constructed of composite or carbon fiber materials. Frame 11 includes a left side frame member 12 and right side frame member 12. The frame 11 has a front end portion 14 and a rear end portion 15. Transverse members 16, 17, 18 span between the left and right side frame members 12, 13. Container 46 of fiberglass, for example, can be mounted on frame 11 (see FIG. 3). A single rear wheel 19 is mounted behind the rear end portion 15 of frame 11 upon swing arm assembly 20. The swing arm assembly 20 is mounted to frame 11 using a pair of spaced apart bearings 21, 22 as shown in FIG. 2, such as pillow block bearings, for example. A pivot member 23 forms a pivotal attachment between the swing arm assembly 20 and frame 11. Swing arm assembly includes a pair of fork members 24, 25 mounted to pivot member 23 as shown in FIGS. 1 and 2. Wheel 19 is mounted at wheel axle 26 and hub 27 to fork members 24 and 25 as shown in FIGS. 1 and 2. A shock absorber 28 extends from frame 11 to swing arm assembly 20. The shock absorber 28 is inclined as shown in FIG. 1, having a forward attachment at bolted connection 30 to bracket 29. The bracket 29 can be an ell-shaped bracket that is welded to transverse member 18. The opposite or rear end portion of shock absorber 28 is at a higher elevational position than the bolted connection 30 securing front end portion of shock 28 to transverse member 18. A bolted connection 32 secures this elevated portion of shock 28 to swing arm assembly 20 at inclined pivoting shock support 31. The fork members 24, 25 and inclined pivoting shock support 31 are connected (e.g. welded) to pivot member 23 so that they define the swing arm assembly 20 as a unit. Swing arm assembly 20 rotates with respect to frame 11 during use (see arrow 44 in FIG. 1). This rotation is allowed by compression and extension of shock member 28 during use as wheel 19 encounters bumps or depressions in the road surface. Wheel 19 rotates relative to frame 11 by rotating about pivot 23 as indicated by arrows 45 in FIG. 1. A significant aspect of the present invention, contributing materially to the stability of the motorcycle-trailer combination is the relative positioning of frame 11 in respect to axle 26. By suspending frame 11 by swing arm assembly 20 and pivot member 23 below axle 26, the center of gravity of the trailer 10 is below the trailer wheel center (i.e., axle 26). Accordingly, the center of gravity of the trailer 10 and likely any load (not shown) in the trailer 10, will be at or below the pull line of the tow, i.e., between the trailer wheel 19 and the motorcycle rear wheel 80. In FIGS. 2, 4, 5-7, hitch attachment 33 is provided for joining the trailer frame 11 to motorcycle 40. Hitch attachment 33 includes a pair of bearings 34, 35 such as pillow block bearings at thefront end portion 14 of frame 11. Bearings 34, 35 rotatably support transverse pin 36. An ell-shaped plate 37 is welded at 38 to transverse pin 36 and rotates with it relative to frame 11 upon of bearings 34, 35. With the orientation of bearings 34, 35 providing rotation about transverse pin 36 about an axis horizontal to the ground and perpendicular to the tow line of the trailer, rotation is available to trailer 10 in the vertical directions. It should be appreciated by those skilled in the art that the form of ell-shaped plate is selected as a matter of convenience for the style of motorcycle and trailer combination: Plate 37 may preferably be of different configuration being dictated by relative location (in respect of the centerline of trailer frame 11) and motorcycle rear wheel 80. Likewise, a feature of the present invention is the orientation of hitch attachment 33 below a horizontal line through trailer wheel axle 26. Cylindrical pin section 43 is connected (e.g. welded) to ell-shaped plate 37. A tapered pin 39 depends from cylindrical section 43 for engaging receptacle 41 when the hitch attachment 33 is connected to the motorcycle for towing. In FIGS. 5-7, the motorcycle 40 can be provided with receiver 47 having a rectangular or square socket 48. Hitch member 49 includes a horizontal tubing section 50 that supports a vertical plate 53 that is welded or otherwise connected to horizontal tubing section 50. Receiver 47 is disposed on motorcycle 40 by means of bracket 40', being fixedly attached thereto whereby receiver 47 is disposed horizontally below motorcycle rear wheel axle 82. As with the relative horizontal location of frame 11 vis-a-vis trailer wheel axle 26, the requisite towing stability of the motorcycletrailer combination is achieved by positioning receiver 47 and thus hitch member 49, when in combination therewith, such that when the trailer is hitched to the motorcycle, frame 11 is horizontally disposed and hitched to motorcycle at or below the pull line formed between motorcycle rear wheel axle 82 and trailer wheel axle 26. In preferred embodiments of the invention ell-shaped member 37 is sized and located on motorcycle 40 (i.e., bracket 40' is located on motorcycle 40) such that transverse pin 36 is positioned from about 4 inches below the axis of rotation of the rear wheel of motorcycle to as much as about 13 inches below the wheel. The limiting factor on the lower dimension is the amount of ground clearance available below the transverse pin 36, and the upper limit is an empirical one in that the lower the transverse pin 36, the better is the stability in tow. A transverse opening 51 through horizontal tubing section 50 is aligned with a correspondingly shaped horizontal opening 52 through receiver 47 so that when the hitch member 49 is inserted into receiver 47, a transverse locking pin (not shown) can be placed through the openings 51, 52 in order to lock the hitch member 49 to the receiver 47. Vertical plate 53 supports an upper horizontal plate 54 and a lower horizontal plate 55. Each of the plates 54, 55 provides an opening 56, 57 respectively. In order to connect hitch 33 to receiver 49 and motorcycle 40, the hitch member 49 is pinned to the receiver 47 as afore described. The hitch member 33 attaches to hitch member 49 at plates 54, 55. Tapered pin 39 fits opening 57 of lower horizontal plate 55. Internally threaded opening 58 at the top of cylindrical section 43 of hitch 33 is aligned with upper opening 56 preferably including bushing 56', of upper plate 54 as shown in FIGS. 6 and 7. When the openings 56 and 58 are aligned, assembly bolt 59 can be placed through opening 56 and then into threaded engagement with the internally threaded opening 58. The assembled configuration can be seen in FIG. 7. During such an assembly, the tapered pin 39 is first placed in opening 57. Then the cylindrically shaped section 43 is rotated toward motorcycle 40 as shown by arrow 60 in FIG. 5. This aligns the internally threaded opening 58 with opening 56 so that bolt 59 can be inserted through opening 56 and into internally threaded opening 58 to be securely retained therein as shown in FIGS. 6 and 7 however readily rotate in busing 56'. As should be understood by those skilled in the art, bolt 59, or an alternative such as a securable pin may be secured in ell-shaped plate 37 to provide the vertical axis about which plate 37 may rotate in hitch member 49. Threaded opening 58 and bolt 59 (with bushing 56') provide a readily attachable and secure means in combination with tapered pin 39 and transverse pin 36 for forming the vertical axis of hitch attachment 33. The rotation available about the vertical axis of hitch attachment 33 and the rotation available about transverse pin 39 provide good tracking for the trailer in turns and over uneven ground, however offers a secure orientation with the motorcycle in the remaining orthogonal plane. This security plus the relative position of the trailer frame 11 below the axes of the trailer wheel 26 and the rear motorcycle wheel 80 are believed to provide the heretofore unavailable tow stability. In FIGS. 8 and 9, an alternate construction of the hitch is shown, designated generally by the numeral 61 in FIGS. 8 and 9. In FIGS. 8 and 9, frame 11 is shown including left and right frame sections 12, 13 and transverse member 16. A pair of bearings such as pillow block bearings 34, 35 support hitch member 62. The hitch member 62 includes a vertical plate 63 that carries a pair of spaced apart eyelets 64, 65. Motorcycle 40 carries a receiver 66 that includes upper and lower frame sections 67, 68 respectively and vertical plate 69. Eyelets 70, 71 are mounted upon plate 69. Locking pin 72 completes a connection between trailer frame 11 and motorcycle 40 when the pin 72 passes through eyelets 64, 65 and 70, 71 as shown in FIG. 9. The following table lists the parts numbers and parts descriptions as used herein and in the drawings attached hereto. ______________________________________ PARTS LIST Part Number Description ______________________________________ 10 motorcycle trailer apparatus 11 frame 12 left side frame member 13 right side frame member 14 front end portion 15 rear end portion 16 transverse member 17 transverse member 18 transverse member 19 wheel 20 swing arm assembly 21 pillow block bearing 22 pillow block bearing 23 pivot member 24 fork member 25 fork member 26 wheel axle 27 wheel hub 28 shock absorber 29 bracket 30 bolted connection 31 inclined pivoting shock support 32 bolted connection 33 hitch attachment 34 bearing 35 bearing 36 transverse pin 37 ell-shaped plate 38 weld 39 tapered pin 40 motorcycle 40' bracket 41 receptacle 42 annular shoulder 43 cylindrical section 44 arrow 45 arrow 46 container 47 receiver 48 square socket 49 hitch member 50 horizontal tubing section 51 transverse opening 52 transverse opening 53 vertical plate 54 upper horizontal plate 55 lower horizontal plate 56 upper opening 57 lower opening 58 internally threaded opening 59 bolt 60 arrow 61 hitch 62 hitch member 63 plate 64 eyelet 65 eyelet 66 frame 67 upper frame section 68 lower frame section 69 vertical plate 70 eyelet 71 eyelet 72 pin 80 motorcycle rear wheel 82 rear wheel axle ______________________________________ The foregoing embodiments are presented by way of example only; the scope of the present invention is to be limited only by the following claims.

Description BACKGROUND OF THE INVENTION The present invention is directed to a radial-hinge mechanism and, more specifically, a radial-hinge mechanism that includes a plurality of elongated interwoven elements. A variety of prior art devices have utilized elongated elements to form a structure. For example, U.S. Pat. No. 4,731,962 discloses a compression-tension unit for use in a tensile-integrity structure or in combination with similar compression-tension units in such a structure. This compression-tension unit includes elongated rigid struts of circular cross-section that each include slotted ends which receive a portion of an elastic cord to connect one strut to another. As another example, U.S. Pat. No. 3,546,049 discloses a device that includes a plurality of beams formed from sets of elongated elements. In one embodiment, the device includes four beams, each including two elements symmetrically arrayed about a geometric center or axis of the beam. These beams contact at a single common point and the elements of each beam are joined together at each end. The elements of each beam pass through a region of beam intersection and the elements of any given beam are generally parallel to each other in the region of joining and are interleaved with elements of each other beam in accordance with a uniform pattern. The beams slide within a predetermined degree of freedom with respect to each other. However, these devices do not join the ends of one beam with an end of another beam, nor are any of these designs and devices based on one continuous interweaving loop of elongated elements. U.S. Pat. No. 3,830,011 discloses a model kit for building different geometric structures and includes a plurality of struts, which are hollow tubular members, and hub connectors, which are utilized to connect an end of one strut to ends of one or more other struts. U.S. Pat. No. 4,259,790 discloses an educational device that includes a plurality of elongated sticks, rods or tubes with adhesive material mounted on both ends of a respective stick, rod or tube such that the elements can be adhered to one another to form letters, symbols, figures and geometric designs. Finally, U.S. Design Pat. No. D 238,840 discloses an ornamental design for a geometric table support structure that uses a plurality of elongated members. While the above-described patents disclose beams (also called out as struts, rods, sticks, tubes, members and elements), which may be utilized in conjunction with each other to form various structures, these structures are not capable of radial-hinge movement nor do their completed forms result in unitized continuous-loop frameworks that evenly distribute loads, transfer forces, and assist or resist with various spring-action potentials. SUMMARY OF THE INVENTION The present invention is generally directed to a radial-hinge mechanism comprised of one or more elongated members arranged and interconnected around a substantially circular inner-aperture according to specific design-parameters resulting in a unique assembly having a natural and variable propensity for radially-pivoting open upon a substantially circular, centrally-located hinge-core. In addition, these design-parameters apply to a vast family of radial-hinge mechanisms, all contingent upon having an even number of crossmembers of eight or more. Accordingly, embodiments of the present invention provide versatile mechanisms for a multitude of novel applications across a wide range of products and forms. In one particular, the mechanism provides an alternative to the conventional coil-spring by circumventing the need for curved and/or coiled members. In addition, spring-biasing techniques applied to the invention's natural properties further enhance the mechanism's usefulness as a semi-rigid framework and/or an active, flexible framework. And, in its active hinge-form, the invention also provides superior radially-pivoting motion without requiring the usual brackets and hardware of conventional hinge forms. In light of the invention's equilateral nature through its opening/closing stroke, the invention may also be interconnected with similar mechanisms along compound points of common intersection which may also be hinged, sprung, etc., and yielding a stacked configuration for two or more radial-hinge mechanisms. Along with its most common capacities to perform alone or with similar mechanisms in an active or rigid role with its elongated members mainly employed for support and/or projection motion, there are also likely opportunities for radial-hinge mechanisms interfacing with encasements and bellows, propellers, blades, fins, shafts, etc. These and other features, advantages and objects of the present invention will be further understood and appreciated by those skilled in the art by reference to the following specification, claims and appended drawings. BRIEF DESCRIPTION OF THE DRAWINGS In the drawings: FIG. 1 is a front view of a twelve-spoke radial-hinge mechanism in a fully-closed position; FIG. 2 is a side view of the mechanism of FIG. 1; FIG. 3 is a perspective view of the mechanism of FIG. 1; FIG. 4 a is a front view of a fully-closed twelve-spoke radial-hinge mechanism with six black and six white spoke-end connectors; FIG. 4 b is a side view of the fully-closed mechanism of FIG. 4 a; FIG. 4 c is a front view of the half-opened mechanism of FIG. 4 a; FIG. 4 d is a side view of the half-opened mechanism of FIG. 4 a and showing the general locale of a hinge-core; FIG. 4 e is a front view of the fully-opened mechanism of FIG. 4 a; FIG. 4 f is a side view of the fully-opened mechanism of FIG. 4 a; FIG. 5 a is a front view of a more-than-half-opened mechanism of FIG. 4 a with a hinge-core somewhat translocated; FIG. 5 b is a side view of the mechanism of FIG. 5 a and showing the general locale of the translocated hinge-core; FIG. 6 is a partial front view showing beveled ends of two spokes threaded and connected by a screw-on connector; FIG. 7 is a partial front view showing two spokes with channels configured to fit into a push-on connector; FIG. 8 is another view of the push-on connector of FIG. 7, composed of a cap and grommet; FIG. 9 is a partial front view showing two spokes connected by a double-clip connector; FIG. 10 is a side view of the double-clip connector of FIG. 9; FIG. 11 a is a perspective view of the connector of FIG. 10; FIG. 11 b is also a perspective view of the connector of FIG. 10, with one clip swiveled ninety degrees from the position shown in FIG. 11 a; FIG. 12 a is a front view of a radial-hinge spoke beveled at both ends for joining with a second spoke, as depicted in FIG. 6; FIG. 12 b is a side view of the spoke in FIG. 12 a; FIG. 13 is a perspective view of two atypical radial-hinge spokes demonstrating a variety of spoke alterations; FIG. 14 is a front view of a fourteen-spoke radial-hinge mechanism, with five arcs per chord, whose spokes are joined by couplings offset from the mechanism's peripheral points; FIG. 15 is a front view of a sixteen-spoke radial-hinge mechanism, with five arcs per chord, formed out of one elongated member and fused at one location; FIG. 16 is a front view of a sixteen-spoke radial-hinge mechanism, with seven arcs per chord, formed out of one elongated member and fused at one location; FIG. 17 is a partial chart showing twenty-six versions of a radial-hinge mechanism for spoke-counts of eight to twenty-six with a sixteen-spoke version emphasized; FIG. 18 is a graphic representation to illustrate the basic infrastructure of a sixteen-spoke radial-hinge design, with seven arcs per chord; FIG. 19 is the mirror image of the infrastructure of FIG. 18; FIG. 20 is a front view of a circle diagram that is divided into an even number of arcs and representing a first step in the design of a sixteen-spoke radial-hinge mechanism; FIG. 21 is a front view of a chord diagram derived from the circle diagram of FIG. 20, with the chord segments drawn and the outer circle removed; FIG. 22 is a front view of the chord diagram of FIG. 21, with spokes drawn in to form a spoke diagram; FIG. 23 is a front view of a partial spoke diagram derived from FIG. 22, with only foreground spoke-segments drawn in on a right-handed spiral; FIG. 24 is a front view of a diagram formed by merging the diagram of FIG. 23 into the diagram of FIG. 22; FIG. 25 is a front view of a final-resolution diagram overlaying FIG. 23; FIG. 26 is a front view of a final diagram that is formed by merging the diagrammatic resolutions of FIG. 25 into the diagram of FIG. 24; FIG. 27 is a perspective view of a radial-hinge device comprised of a radial-hinge mechanism held open by a single connecting slat, which also displaces two peripheral points; FIG. 28 is a perspective view of a radial-hinge mechanism held open by a constraining triangular jig; FIG. 29 is a perspective view of a radial-hinge mechanism held open by a constraining band around its hinge-core; FIG. 30 is a perspective view of a radial-hinge mechanism held open by a set of links constraining the full upper set of peripheral points; FIG. 31 is a perspective view of a radial-hinge mechanism held open by two sets of beams constraining all peripheral points, top and bottom; FIG. 32 is a perspective view of a partially-covered version of the device of FIG. 31; FIG. 33 is a perspective view of a fully-covered stack of two radial-hinge mechanisms, including a double constraining-band encircling both hinge-cores; FIG. 34 is a perspective view of a radial-hinge mechanism fixed between two disks with shafts attached; FIG. 35 is a perspective view of a radial-hinge mechanism fixed between two differently sized disks, with extended spokes depicted in its bottom half; FIG. 36 is a perspective view of a radial-hinge employed in a radial-hinge sink/stand apparatus; FIG. 37 is a perspective view of a radial-hinge employed in both a lamp apparatus and a table apparatus; FIG. 38 is a perspective view of a radial-hinge chair apparatus; FIG. 39 is a side view of a radial-hinge bed apparatus; FIG. 40 is a perspective view of a radial-hinge birdbath, solar-collector or other receiving-dish apparatus; FIG. 41 is a perspective view of a radial-hinge stadium or large tent structure, with a pitched roof from center; FIG. 42 a is a perspective view of a side view of a more-than-half-opened, interconnected stack of two radial-hinge mechanisms; FIG. 42 b is a side view of the fully-closed device of FIG. 42 a; FIG. 43 is a perspective view of a three-high stack of radial-hinge mechanisms employed in a G-decelerator apparatus; FIG. 44 is a side view of a standard coiled-spring employed to hold radial-hinge mechanisms together at their peripheral points to create a stack, as in FIGS. 42 a-43; FIG. 45 is a perspective view of a stack of two similar radial-hinge mechanisms with one mechanism fashioned into a hand-device for gripping and holding an object; FIG. 46 is a perspective view of a double-capped inter-hinge connector similar to the single-cap design in FIGS. 7-8, though here attached by a line hinge to create another kind of radial-hinge connector for stacking, as in FIGS. 45 and 47; FIG. 47 is a perspective view of a stack of two differently sized radial-hinge mechanisms with one being the hand-device of FIG. 45 and the other a larger mechanism whose hinge-core is translocated and equipped with a constraining band; FIG. 48 is the front view of a single butterfly-like bellows-insert interfaced within and around the radial-hinge mechanism of FIG. 4 a; FIG. 49 a is a perspective view of the bellows-insert of FIG. 48, without the accompanying radial-hinge mechanism of FIG. 48; FIG. 49 b is a side view of the single bellows-insert of FIG. 49 a; FIG. 50 is a side view of a fully-closed four-deep stack of radial-hinge mechanisms, with inter-hinge connectors of FIG. 46; FIG. 51 a is a side view of a fully-closed four-deep stack of interconnected bellows-inserts and sized to be used with the device of FIG. 50; FIG. 51 b is a side view of the partially-opened compound bellows of FIG. 51 a; FIG. 52 is a perspective view of a radial-hinge wheel apparatus; FIG. 53 a is a perspective view of a radial-hinge braking/clutching apparatus shown with an inner-aperture of the radial-hinge opened enough to allow free rotation of the shaft on an imaginary fixed axis; FIG. 53 b is a perspective view of the same apparatus of FIG. 53 a, but here shown with the radial-hinge mechanism closing its inner-aperture down upon the shaft and stopping the shaft's rotation; and FIG. 54 is a front view of a radial-hinge mechanism interfaced with fan-like blades resulting in a variably-adjustable radial-hinge fan, prop or turbine apparatus. DETAILED DESCRIPTION OF PREFERRED EMBODIMENT(S) The present invention is directed to a radial-hinge mechanism comprised of one or more elongated members arranged, formed and interconnected around a substantially circular inner-aperture into a specific closed-loop assembly which unitizes the mechanism's structure and actualizes its potential to perform similar to a scissor-hinge. Furthermore, this mechanism includes a hinge-core that can move or be translocated laterally within the framework, with crossmembers radiating out tangentially from the inner-aperture. In addition, this closed-loop assembly is based on unique geometric design-parameters, which also apply to a vast family of radial-hinge mechanisms, ranging in spoke-count from eight to infinity on the even-number scale. However, it should be appreciated that when the number of the spokes of the radial-hinge mechanism exceed a certain higher enumeration, the mechanism may not be capable of realistic implementation due to material and dimensional limitations. With reference to FIGS. 1-3, a twelve-spoke radial-hinge mechanism 100 includes a plurality of spokes 102 and an equal plurality of spoke-end connectors 104. The mechanism 100 is also defined by an outer-circumference 106, an inner-aperture 107 and a central-complex of spoke-crossings (generally located) and referred to as a hinge-core 108. In FIGS. 4 a-4 f, a twelve-spoke radial-hinge mechanism 400 (similar to the mechanism 100 in FIGS. 1-3) is shown in three positions over the full range of its movement, from totally closed in FIGS. 4 a-4 b to totally open in FIGS. 4 e-4 f, with FIGS. 4 c-4 d posing the half-opened/half-closed position (more or less). Both front and side views are shown for each position, with all views dimensionally proportional. In FIGS. 5 a-5 b, front and side views of radial-hinge mechanism 400 depict a laterally-translocated radial-hinge core 508 in FIG. 5 b, as compared to a more equilaterally-positioned hinge-core 408 in FIG. 4 d. In FIGS. 6-11, three different basic spoke-to-spoke connecting-devices are depicted. FIGS. 12 and 13 illustrate a few ideas for spoke-design from simple to extreme and FIGS. 14-16 depict three other versions and forms of radial-hinge mechanisms. A. Spokes, Peripheral Points and Parallel Planes The spokes of a radial-hinge mechanism are given their common name to best represent their posture in a circle and their resemblance to spokes on a common wheel. Alternatively, the word spokes could be replaced with struts, arms, legs, rods, sticks, spars, tubes, links, beams, poles, levers, members, etc. With reference again to FIGS. 1-3, spokes 102 of the twelve-spoke radial-hinge mechanism 100 are substantially equal in length with consistent cross-sectional dimensions. The spokes 102 are made from straight stock, though bent slightly to fulfill the requirement of achieving a three-dimensional mechanism out of a two-dimensional design-space and this bending effect invariably adds tension to the entire framework, especially when the mechanism is in its fully interconnected form. Often, a spoke material with some degree of elasticity helps keep the task of construction at a manual level. In addition and typically, radial-hinge spokes of consistent cylindrical cross-section encounter less friction than most other cross-sectional shapes for spokes. As such, the enclosed drawings predominantly employ this cylindrical form. Alternatively, specialized cross-sectional shapes may better accommodate certain applications. Furthermore, while the radial-hinge mechanism generally utilizes straight elongated members for spokes, the spokes may also be kinked, twisted, looped, jagged or erratic in various ways to achieve a desired result. FIG. 13 suggests a few forms and added features for radial-hinge spokes to achieve one or another desired application. It should also be appreciated that smooth spoke surfaces will generally more easily slide across each other to enhance radial-hinge action, which may also be improved with lubricants. Ball-bearings in tubed spokes generally also reduce friction. It should be appreciated that in some applications it may be desirable to increase as opposed to decrease friction associated with the contact of one or more spokes. The spokes of a radial-hinge mechanism may be made from rigid or flexible materials or a combination of both and made out of wood, plastic, fiberglass, appropriate metals and alloys, spring steel, composites and any other combination of matter to realize a reliable spoke-member for the desired purpose at hand. Furthermore, rigid spokes employed in radial-hinge mechanisms generally require more force to open the mechanism in contrast to the lower-resistance properties of flexible members and some rigid constructions may not open at all, though also depending on properties of their connections and/or connectors. In general, thinner spokes will also bend open more easily than thicker spokes. Reverse-biasing of the spring-action in any joint or member of a radial-hinge mechanism may also create opposite or other effects. While the radial-hinge embodiments discussed herein include elongated interwoven spokes that are generally of the same length, inconsistent spoke-lengths may be desirable in certain applications and, when implemented, this variance in framework may disrupt the radial-hinge's common feature of having its opposing peripheral points in parallel planes. A peripheral point is the specific designation for a point on the circle of a radial-hinge design and cotangent with the not-always-specific point-ends on the protrusions of conjoined spokes on the periphery of a radial-hinge mechanism. A peripheral point is thereby a loose designation for a location where the pathway of one spoke turns into the pathway of an adjoining spoke. In FIG. 16, the peripheral point includes the entire spoke-end segment 1603. Distorting one or more of a mechanism's peripheral points after its construction may just as decisively disrupt the parallel-plane arrangements (see, for example, FIG. 27). It should be appreciated that radial-hinge mechanisms have no specific requirement to limit their multi-dimensional frameworks to only parallel-plane displacements of their plurality of peripheral points, even though their initial design pattern is founded on the parallelism of two sets of an equal number of peripheral points in two planes. All embodiments of radial-hinge mechanisms generally conform to the conceptual rule of having an equal number of spokes to the number of peripheral points. However, these usually prominent protrusion points of a radial-hinge mechanism will not always be distinguished by actual points, and may rather be hidden in other variable and non-pointed transitional forms or compound curves or, conversely, be exaggerated into compound points. Spokes may also be constructed as tubes internally strung together by an elastic or inelastic cord, wire, etc., tied at both ends and, in this design, function like a modern tent-frame apparatus employing segmented, hollow tubes internally strung with elastic cord. The employment of tubes (hollow cylinders) further suggests tubes sliding within tubes, thus telescoping cylinders to constitute spokes and realizing a radially-adjustable mechanism. In addition, spokes may have protrusions of various sorts and/or be pierced with holes, flutes, notches, keyways, cavities such that other spokes can pass through, e.g., see FIG. 13. Various types, sizes, shapes, forms and specialties in spoke-design may be utilized in combination to construct a radial-hinge mechanism and the spokes may have connections made anywhere along their bodies (see FIG. 14) and/or at their spoke-ends, and these joints may be fused, fastened, formed or loosely or oddly strung, hooked, screwed, pinned, lashed, rung or otherwise joined/placed together, as determined by application. The spokes may also be carriers of other useful alterations and/or attachments, consisting of tools, fixtures, collars, levers, arms, etc. Many other creative changes in spoke-design will help to fine-tune these key members of radial-hinge mechanisms for common and special applications. As shown in FIGS. 15 and 16, radial- hinge mechanisms 1500 and 1600, respectively, are both examples of radial-hinge mechanisms each comprised of only one elongated member formed into the radial-hinge design, with a plurality of spoke-links apparent. To keep nomenclature consistent, these spoke-links will also be referred to as spokes. Hence, the radial- hinge mechanisms 1500 and 1600 are both comprised of a plurality of spokes 1502 and 1602, respectively. The mechanisms 1500 and 1600 are made complete by single fusion points 1505 and 1605, respectively. Any single elongated member constituting the full plurality of spokes of a particular radial-hinge mechanism may be made from a single length of wire, wirerope, rod, etc., which is bent or otherwise formed into the designated assembly, with its two remaining ends then joined by a connector, fused, or joined in another manner. Furthermore, the sixteen-spoke radial-hinge mechanism 1500 of FIG. 15 is fashioned with loop-end peripheral points 1503, suggesting yet another alteration in the nature of the radial-hinge mechanism to accommodate a special application. B. Connections and Connectors The radial- hinge mechanisms 1500 and 1600 are comprised of a plurality of spokes 1502 and 1602, respectively, and both mechanisms are made from one elongated member fused and/or connected at the confluence of their loose ends. It should be appreciated that there is only one connection to be made on a radial-hinge mechanism comprised of just one elongated member. However, radial-hinge mechanisms of other embodiments may require more than one connection or connector to achieve full interconnectedness and desired usefulness. As with a single connection, these multiple connections may be achieved by direct fusion, gluing, nailing, screwing, pinning, bolting, clamping, lashing, adjoining spoke-ends (or spoke-bodies) together loosely, rigidly, variably and/or by the implementation of one of a vast species of spoke-end connectors. In FIGS. 1-3, the twelve-spoke radial-hinge mechanism 100 is equipped with twelve spoke-end connectors 104. As shown, the connectors 104 are screw-on caps, each holding together two identical spokes 102. As illustrated in FIG. 12 a, ends of the spoke 102 are beveled at one-half the angle of the converging angle (where two spokes 102 come together) and their ends may be cut with a spiral thread 607, as depicted in FIG. 6, after which the spoke-end connector 104 is firmly screwed on. This type of connector will generally constitute a relatively rigid condition throughout the framework of the radial-hinge mechanism 100. Radial-hinge mechanisms employing spoke-end connectors made with the intent to impose rigidity by preventing the twist of spoke-ends will operate very similar to radial-hinge mechanisms that are welded, fused, glued or formed and expressly meant to be unyielding. Consequently, solidly-interconnected radial-hinge mechanisms will generally fail to open as far or as easily, requiring a greater applied force to overcome the constriction of the fixed joints and creating an impressed and consistent spiral-torsion from the spiral-twisting in every spoke as the radial-hinge exercises its motion opening and closing. A torsion varying in intensity depending upon many variables in materials and form. In contrast, radial-hinge mechanisms interconnected with connectors that allow twist to occur within their grasp are also mechanisms that open more easily and to a greater extent. In FIGS. 4 a-4 f, a twelve-spoke radial-hinge mechanism 400 is depicted in front and side views over three typical positions. The mechanism 400 is of similar construction to the mechanism 100 in FIGS. 1-3, except that mechanism 400 employs spokes 402, which are different from spokes 102 by not being beveled and threaded. That is, the spokes 402 are equipped with ring-around-channels 705, as shown in FIG. 7. In addition, spoke-end connectors 404 are not screw-on connectors like connector 104 but push-on connectors, as depicted in FIGS. 7 and 8. The spoke-end connectors 404 are shown in both white and black (color-coded) to enhance understanding of the balanced distribution of the peripheral points and their relationship in all views of radial-hinge mechanism 400 in FIGS. 4 a-4 f and 5 a-5 b. The twelve spoke-end connectors 404 of mechanism 400 are designed to allow the spoke-ends more freedom to twist, rather than be wedged rigidly into place, such as in the connector 104 design of FIG. 6. Consequently, with more freedom at these nexus points, the radial-hinge mechanism will generally open to its full extent, as shown in FIGS. 4 e-4 f, whereas the radial-hinge mechanism 100 in FIGS. 1-3 might only reach the half-opened position, as observed in FIGS. 4 c-4 d, and also be on the verge of breaking a spoke due to elastic limits. But, of course, in some applications, it may be desirable to limit movement to a middle range, or more, or less. Moreover, it should be appreciated that the material properties of the spokes 402 and end connectors 404 are influential in determining the extension/contraction (opening and closing) limits and powers of mechanism 400. With specific reference to FIG. 7, the connectors 404 push on to the ends of the spokes 402 and hold together pairs of the spokes 402. The ends of the spokes 402 are rounded off and, at a predetermined distance from both ends of the spokes 402, a channel 705 is cut or otherwise scribed around the circumference. The channels 705 are intended to interface with holes 808 in double-holed grommets 807, shown in FIG. 8. The grommets 807 are substantially fixed or glued into the bodies of connectors 404 and considered to be fixed parts of the connectors 404. The grommets 807 each hold two spokes 402 together as the inner-casing 801 of connectors 404 limit much of the lateral movement of the spokes 402. The grommets 807 may be made of rubber or other elasticized material or composition. In further consideration, channels 705 may fit snugly into grommets 807, thus, contributing to the whole elastic nature of the mechanism 400. Alternatively, channels 705 may have a loose fit, consequently not engaged with the elastic nature of grommets 807 and not adding to the elastic resistance of the entire framework of mechanism 400 of FIGS. 4 a-4 f and 5 a-5 b. Again, the desired application of any radial-hinge mechanism will generally help predetermine properties of its immediate components, with due recognition to the fact that certain properties achieved by spoke alteration may also be achieved by a variety of connector alterations. It should also be appreciated that a radial-hinge mechanism made with multiple spoke-end connectors will more easily allow the device to be constructed from its pattern in contrast to the more difficult methods necessary to form a radial-hinge out of a single elongated member. Spoke-connectors may also act as temporary fasteners to initially get the mechanism into its fully interconnected three-dimensional form, then to open it up to some desired position and then to remove the connectors to place spoke-ends or spoke-sections into some other temporary or permanent holding material, device, apparatus, etc. FIG. 34 depicts a spindle-like device 3400 fashioned upon radial-hinge technology, where the radial-hinge mechanism was first composed from its pattern with spoke-end connectors, then opened on its hinge to a desired degree, followed by removal of spoke-end connectors to transfer spoke-ends 3402 into retaining holes in disks 3404. Another particularly useful connector of a slightly different sort and again employed to connect just two spokes at a time is depicted in FIG. 9. Double-clip connector 900 is composed of two somewhat elongated C-clips 902. The clips 902 are again shown in FIG. 10 connected back to back with a loose fitting rivet 905, creating a point-hinge, which also acts as a fastener to hold the two C-clips 902 together. Consequently, the double-clip connector 900 may link two spoke members at any cross-location or where spoke-ends meet (as shown in FIG. 9). In FIGS. 11 a-11 b, two different views of the connector 900 illustrate the range of swivel, which may ultimately achieve 360 degrees of movement. Thus, the connector 900 is applicable to a variety of radial-hinge mechanisms with compatibly-sized spokes and, in this manner, provides a universal spoke-connector for radial-hinge mechanisms; a connector which may also be altered for special applications. The double-clip connectors 900 may be made of steel, plastic, fiberglass, composite or other materials. Typical C-clips would range in shape from fully circular to partially circular (as depicted by the clips 902 of FIG. 10) and point-hinge rivet 905 may be replaced by more sophisticated swiveling mechanisms, depending on the application. The procedures for constructing radial-hinge mechanisms may also vary and, in some situations, may not use interim connectors. In all likelihood, a high level of skill in the art of radial-hinge assembly will lead to shortcut-methodology for constructing a radial-hinge mechanism. In general, any method of connection or variety of connector best suited for any one or more applications is, of course, preferred. Many other special connectors may be utilized, some to work with more than two spokes, some to have other actions built into them, such as the double-capped inter-hinge connectors 4504 (see FIG. 46) discussed herein. C. Inner-Aperture/Outer-Circumference; Opening the Radial-Hinge With reference again to FIGS. 4 a-4 f, the twelve-spoke radial-hinge mechanism 400 is shown in three different positions, to illustrate its full and common transformational nature from its minimum to maximum range of operation. While the spokes 402 and connectors 404 generally remain the same in their material dimensions as the radial-hinge mechanism is opened or closed, the mechanism's inner-aperture 407 and outer-circumference 406 may systematically dilate or contract as the mechanism 400 is opened or closed. In a first position shown in FIGS. 4 a-4 b, the radial-hinge mechanism 400 is shown in standard front and side views with the mechanism 400 fully-closed and in the typical mode of its initial construction when first composed from the pattern of its design. In this position, the key circular parameters of the mechanism 400 are defined by its inner-aperture 407 and its outer-circumference 406. Both of these circumferences are at their maximum diameters in this position. In a second position shown in FIGS. 4 c-4 d, the circumferences have constricted considerably. In a third position shown in FIGS. 4 e-4 f, the mechanism 400 is fully-opened and the circumference 406 and the inner aperture 407 reach their minimum diameters. In this depiction, there is easily a seven-fold reduction of the diameter of the outer-circumference from the first position to the third position and a 90-degree transalignment of the mechanism 400. Specifically, the radial-hinge mechanism changes from one that can be contained in a flat disk-shaped form to one that can be contained in a long tubular form. As for the designations of opened and closed, these derive their orientation from the way the radial-hinge opens from its original two-dimensional design. This opening also correlates with the opening of the space defined by the inside volumes of a radial-hinge's double-conical-like framework, which stretches open and extends out into its opposite major axis. However, this function of opening also ignores the anomaly of how a radial-hinge mechanism physically closes down upon itself when in its fully-opened mode (as in FIGS. 4 e-4 f) along with simultaneously closing down its inner-aperture and outer-circumference. Additionally, given the perspective of a radial-hinge acting as a linkage between two generally parallel surfaces, this linkage or hinge is closed when the two surfaces are closest together. Finally, there is the hinge itself, the arrangement that makes for the radial-hinge mechanism; the provider of the radial-hinge-action and more or less centralized on the core inter-braiding of the intersection of the mechanism's plurality of spokes. Although, to be more exact, it is the entire mechanism taking part in every hinge action; thus, technically, it is the full-interconnectedness of this assembly which constitutes the singular thing called a “hinge.” Nevertheless, the radial-hinge's fulcrum location is in its core and contiguous with the inner-aperture. Here is where the spokes are levers, pivoting in an angular fashion one upon the other and like a braid forming the interwoven and interlocked radial-hinge mechanism. In addition, the hinge-core has the potential to be laterally translocated, typified in FIGS. 5 a-5 b and shown in one application in FIG. 47. This floating or fluid hinge-core also multiplies the variability of forms applicable to the many versions of radial-hinge mechanisms. But, ultimately, the present invention stands out in its cooperation of basic components to create a highly functional and economical radial scissor-hinge mechanism barring the need for extra or special brackets, fasteners or other hardware to actuate its plurality of functions and forms. D. Design and Construction of a Radial-Hinge Mechanism The current invention can be thought of as a three-dimensional mechanism composed directly off the pattern of its embodiment in two-dimensional space. The first act in designing the radial-hinge mechanism is the choosing of its spoke-count and arc-count per chord. These two parameters are cross-referenced in the chart of FIG. 17, which identifies the existence of twenty-six different versions of radial-hinge mechanisms. The chart in FIG. 17 is only a sub-chart or subset of an infinite set of radial-hinge designs theoretically reproducible in three dimensions. With further reference to the chart of FIG. 17, cross-referenced locations with dashes indicate impossible parameters for radial-hinge mechanisms, but this is also typical for all cross-referenced locations where spoke-counts are an even multiple of any applicable arc-count per chord. For the following discussion, a sixteen-spoke radial-hinge mechanism with seven arcs per chord has been chosen with its position emphasized on the chart of FIG. 17. To begin familiarization with the radial-hinge design features, an understanding of the mechanism's basic spiral form can be helpful. FIG. 18 is something of a graphic representation, specifically, a stripped-down version of the sixteen-spoke radial-hinge design in FIG. 26 and derived from FIG. 26 by removing a certain one-half of every spoke in the sixteen-spoke framework. Skeletonized as such, FIG. 18 becomes a kind of infrastructure of the full design, showing just those most forward (and leading) spoke-halves that give the best visual representation of the unique design behind a radial-hinge mechanism, with black spoke-segments 1804 a spiraling out on the backside of the hinge, white segments 1805 spiraling up in the foreground and each view from front or back distinguishing an octagon at the inner-aperture 1808, though the two back-to-back octagons are perfectly out of phase with each other. In addition, FIG. 18 reveals and clarifies a left-handedness as FIG. 19 displays a right-handedness; with both views being mirror images of each other (as are all full representations of all basic radial-hinge designs). Flipping over FIG. 18 results in FIG. 19, with the understanding that white spoke-segments depict all spokes in the foreground position in both views. Consequently, the black spoke-segments 1804 a in FIG. 18 become white spoke-segments 1804 b, when turned over 180 degrees into FIG. 19. All radial-hinge devices display this uniform double-spiral design infrastructure with left and right-handedness. FIGS. 1-5 b depict a left-handed twelve-spoke radial-hinge design, whereas FIGS. 14-16 and 26 depict right-handed designs. It should be appreciated that both design approaches lead to the same result. FIG. 20 depicts a circle diagram 2000, with a circle 2008 that is evenly divided by delineations 2006 a into sixteen arcs 2002 (with all even numbers of eight and above being eligible—see again chart of FIG. 17). Sixteen chords 2004 are then drawn between the delineations 2006 a on the circumference of the circle 2008 and, in this case, to design a sixteen-spoke radial-hinge mechanism with each chord bridging seven successive arcs on the circumference. The dashed line-segments in FIG. 20 indicate typical placements for two end-connected chords 2004 as drawn from “a” to “b” to “c”for the beginning of the continuous back-and-forth crisscrossing as depicted in FIG. 21, and where the circle 2008 of FIG. 20 has been erased from the scene, and where the delineations 2006 a become peripheral points 2006 b of the emerging mechanism. FIG. 22 illustrates the results of filling in the chords of FIG. 21 with parallel companion lines to distinguish spokes 2204 of the emerging sixteen-spoke radial-hinge mechanism, which is also defined by its outer limits, those peripheral points 2006 b, said points designating the points of the protrusions on this radial-hinge mechanism. FIG. 22 also identifies every other peripheral point 2006 b with an “F” to sort out every peripheral point in the foreground of the view. Notably, peripheral points 2006 b of FIG. 21 have been de-emphasized in FIG. 22. In FIG. 23, the “F” designated peripheral points are isolated out from the full scheme of FIG. 22 along with major consistent spoke sections 2304. The whole diagram 2300 represents the seminal step in the reconciliation of radial-hinge designs and which is again the signature spiraling-form depicted in FIGS. 18 and 19. The inner-aperture 2308 in this diagram 2300 is defined by an octagon. At this stage in the design program, all radial-hinge mechanisms display a polygon around their inner-apertures; a polygon having one-half the number of sides as the total number of spokes in the radial-hinge mechanism being planned. The diagram of FIG. 24 results from installing the pattern of FIG. 23 into the scheme of FIG. 22, or by removing line crossings in FIG. 22 to realize FIG. 24 based upon the seminal pattern in FIG. 23. FIG. 25 resolves the remaining layout necessary to complete the plan for the resultant design 2600 depicted in FIG. 26. With reference to FIG. 25 (a derivative of FIG. 23), by following the specified paths of one pair of spokes 2204, such as spokes A and B, and applying all resolutions of their pathways to all other spoke-pairs in the proto-hinge 2400 of FIG. 24, the result is the completed design 2600 depicted in FIG. 26. Specifically, the path of spoke A traveling away from its connection with spoke B is a clear run to spoke C, though having also passed over seven other spokes (not shown). Then, spoke A passes under spoke C (as is also observed in FIG. 23). From there, the path of spoke A continues over, then under, then over, then under subsequent spokes on its way to its opposite spoke-end. This over/under sequence applies to all versions of radial-hinge designs worked out with the geometric accuracy of straight spokes and equal angles, although other versions of radial-hinge mechanisms may have more or fewer crossings than what is required in this sixteen-spoke version based on seven arcs per chord. The path of spoke B also traveling away from the peripheral point 2006 b in FIG. 25 is descriptively the exact opposite of the path described for spoke A. That is, spoke B first passes over spoke D, then under the next spoke, then over the next spoke, then under the next spoke, then over, then under the remaining seven spokes. Consistently, just as the path of spoke A away from peripheral point 2006 b begins by passing over the first seven spokes, the path of spoke B ends by passing under the last seven spokes. This radial-spiral symmetry is indicative of all radial-hinge mechanisms. Furthermore, the seven spokes passed over by these foreground seminal spokes and the seven spokes passed under by the backside seminal spokes, correlate with the chart cross-reference in FIG. 17 for arc-count per chord, further revealing a seven-layered overlap of spoke crossings in this sixteen-spoke radial-hinge design keyed on seven arcs per chord. This correlation is common amongst all versions of radial-hinge mechanisms, with mechanism 100 of FIG. 1 posing as another example, being five-layered, with five arcs per chord. This aspect of layering vis-a-vis arc-count per chord suggests greater complexity and difficulty in construction as the arc-counts per chord get larger. With all spokes reconciled into their proper arrangement, depicted in FIG. 26, the design 2600 is complete. Turning this line-drawing into a radial-hinge mechanism is simply the matter of employing design 2600 as a pattern, and sizing the pattern to match with the size of actual spokes intended for the construction. Actual spokes are then placed upon the pattern and directed into the same spoke juxtapositions as the pattern depicts, spokes connected to other spokes one at a time, following the under/over pathways, sequentially building the hinge, until the last spoke meets up with the first spoke and, upon making that last connection, the radial-hinge mechanism achieves its completeness in total interconnectedness. Placing or scribing the numbers 1-16 on the spokes 2204 to correlate with spoke identification numbers on the pattern 2600 can be very helpful in this construction task. When constructing a radial-hinge mechanism out of wooden dowels, a general guideline for spoke dimensions is to figure a ratio of at least sixty-to-one for length-of-spoke in comparison to spoke-diameter and generally at most a ratio of ninety-to-one, although this relationship will also depend largely upon spoke-count and application needs. With reference to FIGS. 12 a-12 b, the spokes 102 may be cut, then crudely or expertly threaded and/or glued together one upon another, as in FIG. 6, with spoke-end connectors 104 screwed on. Similarly, the sixteen-spoke radial-hinge mechanism designed by these instructions may also follow the composition format of FIG. 6, except that the angle of the cut on the spoke-ends, as shown in FIGS. 12 a-12 b, will be different because the angle of the convergence of spoke-ends is different in different versions of radial-hinges, angles ranging between 0 to 180 degrees. These angles of convergence of spokes in a radial-hinge can be lifted with a protractor directly off the layout of the design or deduced by various mathematical operations employing spoke-count and arc-count per chord as two of the known variables. For the two versions of radial-hinge mechanism most prevalent in these specifications, the angles of spoke convergence are easy to calculate because the quotient of 360 degrees divided by the spoke-count equals the angle of convergence. For the twelve-spoke radial- hinge mechanisms 100 and 400, shown in FIGS. 1-5, this equates to 30 degrees. For the sixteen-spoke version in FIG. 26, the equated angle is 22.5 degrees. Subsequently, the angle for consistent cuts on spoke-ends are one-half the measure of the angles of convergence, i.e., cuts of 15 degrees on spokes for the twelve-spoke version and 11.25 degree beveled cuts on the spokes of the sixteen-spoke radial-hinge mechanism design 2600 in FIG. 26. Consequently, however, the end connector 104 in FIG. 6 (with an inner-thread cut to accommodate the 30 degree convergence angle on the pairs of spokes 102) may not be a good connector for the 22.5 degree convergence angle of the sixteen-spoke radial-hinge. On the other hand, off-the-shelf twist-on wire-connectors equipped with conical inner-springs will actually accomplish the task in both situations due to the amorphous nature of the springs, but which also will not result in highly rigid connections and twist-on wire-connectors are not available in an adequate variety of sizes for all situations. The resultant three-dimensional construction made from the two-dimensional single view is a radial-hinge in the purest sense, with all spokes of equivalent length, all connections identical and parallelism replete. In general, radial-hinge mechanisms with greater arc-counts per chord will have smaller inner-apertures, which, in turn, concentrate the hinge more densely, thus, allowing it to open more easily and to a greater extent. It is also expected that some versions of a radial-hinge mechanism with high spoke-count and low arc-count per chord will also result in densely packed hinge-cores and likewise perform in a less resistant manner. In addition, the unique radial-hinge mechanism design-criteria are also the most logical and viable design-criteria for bringing about the unique principles and actions characteristic of the radial-hinge mechanism. Not incidentally and to be appreciated, all radial-hinge mechanisms are based on multi-point star-designs but not all radial-hinge mechanisms resemble stars or necessarily have star-points. FIG. 16 is similar to FIG. 26, except that its peripheral points have all been truncated. Variations in the design of any and all radial-hinge mechanisms may start on paper. Other variations may occur after the mechanisms have already been composed according to pattern. Furthermore, applications for radial-hinge mechanisms may also prove to be highly variable. A brief look at the kinds and forms of products likely to result from a radial-hinge mechanism's utility in function and form comes into perspective over a range of different devices and apparatus. E. Radial-Hinge Mechanisms in Rigid/Semi-Rigid Applications Radial-hinge mechanisms of various designs can be employed as rigid and semi-rigid frameworks for a vast number of radial-hinge devices and apparatus, with many of the resultant forms interfacing with an external sheathing or covering. The sheathing or covering may be used merely to enclose the radial-hinge mechanism and/or elastic sheathing materials may be used to influence the dynamic properties of the radial-hinge mechanism therein employed. A sampling of radial-hinge mechanisms interfaced and interconnected with various coverings and attachments are depicted in FIGS. 27-54. These devices and apparatus are based on the twelve-spoke radial-hinge mechanism(s) 400. It should be appreciated that this format of using just one version of the radial-hinge mechanism is strictly intended to keep the forms simple, consistent and not meant to represent finished products and not intended to represent the full plurality of likely or potential radial-hinge devices and apparatus across the range of the numerous versions of radial-hinge mechanisms. In regard to the end-connectors 404, these may actually be functional in the range of devices and apparatus depicted. In practice, however, a wide assortment of other kinds of radial-hinge body-connectors and end-connectors, some discussed herein, may work better, depending upon the application. The spokes 402 may also be replaceable by other more or less sophisticated spoke designs. Starting with FIG. 27, a radial-hinge device 2700 is shown and similar to radial-hinge mechanism 400 in FIG. 4, except for where a slat 2702 supplants the connectors 404 at two of the spoke-end connecting positions, consequently resulting in a device 2700 whose radial-hinge mechanism displays an example of peripheral points no longer confined to only two parallel planes. Overall, this is not a stable radial-hinge device for loading purposes, nor are the variably-constrained mechanisms 400 in FIGS. 28-30. Altogether, these four views (FIGS. 27-30) illustrate some typical methods of propping open a radial-hinge mechanism against the mechanism's naturally resisting closed position. Essentially, in FIG. 27, an elastic or rigid slat 2702 holds open its radial-hinge mechanism. In FIG. 28, a rigid triangular jig 2806 holds open radial-hinge mechanism 400. In FIG. 29, an elastic or rigid band 2902 holds open the mechanism 400. FIG. 30 depicts elastic or rigid links 3002 holding open the mechanism 400. Various other performances of action may be realized from these modified radial-hinge mechanisms, which are only partially load-bearing radial-hinge frameworks. For example, the constraining band 2902 of FIG. 29 may be particularly useful and very easily installed in some situations by fully opening mechanism 400, then slipping on the band 2902. Consequently, within this mode and when the band 2902 has some elastic give, the entire device 2900 becomes reverse-biased in its elastic nature, thus, requiring force to close its springiness rather than its normally common characteristic of needing force to be opened. The elastic properties and force-characteristics of the radial-hinge mechanism are extremely diverse, depending on construction methods and material variations. In general, the radial-hinge mechanism may be sprung either way or not sprung at all, or it may have timely and variable elastic properties due to changes in temperature, changes imposed by electric or magnetic influence or other known ways to artificially influence the properties of the materials of the mechanism. Some applications may utilize the catalytic assistance of some sort of constraining band and, overall, this exemplifies the dual nature of the radial-hinge mechanisms. That is, the radial hinge mechanism is able to hold together two parallel surfaces of which it is attached to and able to push apart these surfaces when a reverse bias is created by a constraining band or other reverse-spring-biasing method. In addition, as the band 2902 acts to constrain movement toward the closing of device 2900, the band 2902 also helps to fix the core of the radial-hinge mechanism into a desired position along its fluid range (see FIG. 47, which includes a band 4702 similar to the band 2902). FIG. 31 shows beams 3102 constraining radial-hinge mechanism 400 at both ends, thus, creating a much stabler and fixed framework for device 3100 in comparison with those forms in FIGS. 27-30. A constraining band 2902 around the center of this device 3100 would further increase its load-bearing capacity, as would other types of constraining devices and methods, and including the employment of the double-clip connectors 900 depicted in FIGS. 9-11 b. FIG. 32 shows one approach to covering the radial-hinge device 400, with a fascia material 3205, to then convert it to a container or chamber 3200. FIG. 33 shows another approach to external dressing-up, also built upon the framework of FIG. 31, though herein showing a stack of covered-over or encased radial-hinge mechanisms affixed with plates or fabric 3301 and bound further by central bands 3303 and given top covers or plates or fabric 3305. This finished encasement may also be the prototype for artificial (i.e., decorative) building columns or that of an unusual design for a drum with surface 3305 then being a drum-skin. In addition, FIG. 31 may be a framework for a basketball basket; moreover, a stacked-basket for basketballs or any-sized balls; or a ball basket with an adjustable inner-aperture 408, as explained in connection with FIGS. 4 a-4 f; and other permutations of similar apparatus for basketing balls and the like. FIG. 32 may also be seen as a style for columnar designs, or the likes of a stacked raceway for wires, pipes, etc. Various different drum versions may also be achieved with this form. FIGS. 34 and 35 express two alterations in comparison to previous FIGS. 27-33 and yet both FIGS. 34 and 35 also represent generally fixed-in-form radial-hinge devices. In FIG. 34, spoke-end connectors have been removed and spoke-ends 3402 are affixed into disks 3404 and the disks at both ends of this radial-hinge device 3400 are further attached to shafts 3405. In addition, peripheral points 3406 in FIG. 34 are designated to directly correspond to peripheral points 3406 in FIG. 35. In FIG. 35, radial-hinge device 3500 is similar to device 3400 in FIG. 34, except that shafts 3405 have been removed and spokes 402 have been extended divergently from peripheral points 3406, creating yet another arrangement characteristic of radial-hinge versatility and suggesting yet further designs for radial-hinge devices and apparatus incorporating disks and wheels, shafts and axles, turning and spinning, functioning in various rotary applications, including the transferring of differential rotational forces. In addition, cages, spools, spindles, and sheaves may be achieved with the radial- hinge devices 3400 and 3500. In FIGS. 36-41, the radial-hinge mechanism 400 is involved within the familiar fixed apparatus of a sink-and-stand 3600 in FIG. 36, table and lamp 3700 in FIG. 37, chair 3800 in FIG. 38, bed 3900 in FIG. 39 (with its radial-hinge fully-closed), a birdbath, solar oven, radiowave-collector 4000 in FIG. 40 and one likely building scheme 4100 in FIG. 41, e.g., a small stadium or circus tent. In addition, frameworks for benches, tables, decks and scaffolding around trees, around swimming pools and other central themes can be conceived out of radial-hinge designs (see the mechanisms in FIGS. 14 and 15). Basically, anything that stands on legs may be accommodated by these radial-hinge designs, which also includes docks, towers, teepees, circular fencing, coat/hat-racks, bag-holders, drum-stands, platter/plate-holders, cup-holders, any cylindrical-type standing-up holders, etc. and each of these aforementioned implementations generally express at least one unique quality over their counterpart conventional form. But caution should also accompany implementation due to the scissor-hinge-like action which may be a hazard requiring consideration in most radial-hinge productions. Of course, radial-hinge mechanisms employed in trap and snare apparatus are intended hazards. With regard to the stationary forms depicted in the various prototype devices of FIGS. 36-41, some may have an elastic give to them, a kind of bounce and/or some may be intentionally collapsible for portability or adjustability and/or intended for shock-absorbing applications. Thus, usual parameters for solid-structure-design may not exactly apply to many of these common, familiar, radial-hinge devices and apparatus and may require designed-in safety factors based on probable loads, torques, angles of radial-hinge-openings, etc.; to, essentially, design around inter-dimensional stresses to sufficiently reduce fatigue in all component materials such that even in extremely high-stress situations elastic limits can be avoided. F. Radial-Hinge Mechanisms in Active Applications The radial-hinge mechanism multiplies its potential usefulness when put into an active role in active devices and apparatus and, though many of these productions will only entail the inclusion of a single radial-hinge mechanism, the greater variety of these active forms will be composites of two or more radial-hinge mechanisms variously connected together into a stack. The first indication of the radial-hinge's intrinsic design-feature of “stacking” is shown in FIG. 33 as a fixed object. In a similar fashion, a stack of radial-hinge mechanisms may also be interconnected to operate cooperatively in active roles of extension and retraction. With reference to FIGS. 42 a-42 b, a device 4200 is comprised of two radial-hinge mechanisms 400 connected end to end by six straight coiled-springs 4203 (shown in original form in FIG. 44, enlarged) joined to spoke-end connectors 404. As with an elastic constraining-band 2902 around radial-hinge mechanism 400 in FIG. 29, these connecting springs 4203 also encourage this stacked radial-hinge device 4200 to assume an “opened” mode (again becoming reverse-biased in its elastic nature, i.e., reversing its first tendency to be “closed”). The arrows in FIG. 42 b indicate that a force is required to keep this radial-hinge device closed down. In FIG. 43, a G-decelerator apparatus 4300 has a framework based on a three-high-stack of radial-hinge mechanisms 400, which are interconnected with coiled-springs 4203. In addition, the apparatus 4300 is also interfaced at both ends with further components 4301 on the top and 4303 a on the bottom. The component 4301 is a kind of pouch variably composed but generally incorporating soft, strong, elastic fabric to catch a delicate object 4308 and effectively prevent the object from bouncing back out when this apparatus 4300 recoils after it has collapsed or closed down (similar to device 4200 in FIG. 42 b) and due to the force of the mass of falling object 4308. Base component 4303 a is here shown as a disk with spoke-end connectors 404 plugged into slide-tracks 4306 a to guide and hold the connectors 404 in a stable, planar semblance, as apparatus 4300 is activated by a falling object 4308. This base component 4303 a also aids in the stability of the entire radial-hinge apparatus 4300 by helping to prevent toppling. Object 4308 may also be other than an acrobat or person leaping from a burning building and pouch-component 4301 may be other than soft and yielding. Similar useful apparatus will resemble this apparatus 4300 in the guise of weight-scales, vertical-lifts of various sorts, trampolines, radial-catapults, gantry-arms on space vehicles, landing-pods for various airborne vehicles, etc. Again, it should be noted that constraining bands 2902 (or similar rings, hoops, straps, lashes, belts, etc.) may also be incorporated or retro-fit to increase resistance in these stacked, active devices and apparatus and the bands 2902 may also act as break-bands, to actually self-destruct (or release) when stresses reach a specific threshold. With regard to FIGS. 45 and 47, two similarly stacked radial- hinge apparatus 4500 and 4700, respectively, are shown. The apparatus 4500 and 4700 each include two radial-hinge mechanisms, which are interconnected by double-capped inter-hinge connectors 4504 instead of utilizing coiled-springs 4203 (depicted in FIGS. 42-44). The connectors 4504 (depicted in FIG. 46) are comprised of two push-on cap-connectors 4601 similar to caps 404 in FIGS. 4 a-4 f, except that caps 4601 have a flat side 4606 formed into their conical lateral dimension, with a line-hinge 4609 that attaches the caps 4601 in a pivotal configuration. Unlike coiled-springs 4203, double-capped inter-hinge connectors 4504 pivot freely, without elastic resistance. In FIG. 45, the stacked radial-hinge apparatus 4500 is comprised of a typical radial-hinge mechanism 4506 (similar to mechanism 400 in FIG. 4) and a radial-hinge mechanism 4507, which is slightly atypical with its free set of peripheral points depicted as fused or formed and subsequently bent in toward an imaginary central axis of apparatus 4500, thus, creating a kind of mechanical hand of six fingers 4508. As is shown, a ball 4509 has been picked up by apparatus 4500 and remains firmly held until released by the action of this prototypical arm and hand apparatus 4500. FIG. 47 depicts an apparatus 4700 similar to apparatus 4500 in FIG. 45, except that radial-hinge mechanism 4506 in FIG. 45 is supplanted by a larger radial-hinge mechanism 4706 in FIG. 47 and the larger mechanism has necessarily translated the location of its radial-hinge core to reasonably interconnect with its smaller counterpart mechanism 4507. Constraining band 4702 (similar to band 2902 in FIG. 29) is also attached to modify the forces throughout this arm and hand apparatus 4700. Stacked, active radial-hinge devices and apparatus may be useful in many applications beyond the few so far mentioned and variably depicted. In the medical field alone, single and stacked radial-hinge mechanisms may bring innovations to instruments, such as retractors, forceps, hemostats, etc., as well as improvements in splints, stents, casts and so forth. It should also be appreciated that radial-hinge mechanisms may be interconnected in a similar manner to coiled-springs arrayed to form cushions for beds, for other furniture and other cushioning and related applications. And not to be overlooked, a radial-hinge toy-set apparatus also comes to mind and already appears well represented in the forms and components herein discussed and depicted in the drawings. Also to be included in the mix of properties so far discussed, there is again the aspect of handedness previously defined and, though only a minor aspect of a single radial-hinge mechanism or device, the feature of handedness is apparently a significant feature in the act of stacking, wherein one radial-hinge mechanism may be interconnected to a second radial-hinge mechanism in two opposite ways. That is, by connecting a like-handed side of one radial-hinge mechanism to the like-handed side of an adjoining radial-hinge mechanism or by joining a left-handed side to a right-handed side. The active nature of radial-hinge mechanisms also takes on the range of apparatus used to inhale and exhale gases and fluids in the form of bellows interfaced externally or internally with the framework of single or stacked radial-hinge mechanisms. As an example, FIG. 48 depicts a single bellows-insert 4800 interfaced within and around radial-hinge mechanism 400 and the insert 4800 is attached to connectors 404 of mechanism 400 at attachment points 4803 (although a similar radial-hinge apparatus may not require attachment points or positioning posts of any sort, depending on the application). FIGS. 49 a-49 b show the single bellows-insert 4800 in a perspective view in FIG. 49 a and in a side view in FIG. 49 b. This particular bellows design and insert 4800 is a combination of two identical concave umbrella-like forms 4902, each composed of six triangular-shaped facets with each form 4902 stitched together back-to-back around an inner-aperture 4905. Notably, forms 4902 are also exactly out of phase with each other in keeping with the phase-shift inherent in all standard radial-hinge mechanisms where peripheral points on one side are typically out of phase with peripheral points on the opposite side. In FIG. 50, a stack of four radial-hinge mechanisms is attached end-to-end by double-capped inter-hinge connectors 4504 to create radial-hinge device 5000. As is shown in FIG. 51 a, a composite of four single bellows-inserts 4800 are stitched together along their outer peripheries to make one compound bellows 5100 intended to be fixed or loose within the framework of the device 5000 in FIG. 50. FIG. 51 b depicts multiple bellows 5100 in a partially opened view, thus, inhaling and assuming that bellows-inserts 4800 are composed of partially or totally impermeable material, which is also pliable and/or elastic in nature. In a much simpler fashion, regular balloons and/or compound balloons standing in for the custom bellows 4800 would function similarly, though probably less effectively or compactly, and bellows-forms of many other conceivable configurations are likely to be abundant. Used in bellows applications, radial-hinge mechanisms involved in pneumatic and/or hydraulic systems may be useful in pressure relief, pressure maintenance and flow-control functions for valves, nozzles, gauges, etc, including the pushing of air in organs, concertinas and various pumps for various purposes. In FIG. 52, a radial-hinge apparatus 5200 is comprised of radial-hinge mechanism 400 ensconced within the two wheel-forms 5202 and each form 5202 is also connected with six co-planar peripheral points of the mechanism 400 and the connections may be elastic or rigid. The apparatus 5200 suggests applications for a more road-worthy or off-road-worthy wheel apparatus, though also assuming its inner-cavity is suitably isolated within a membrane to keep debris from corrupting the inner-works. Radial-hinge wheel-apparatus 5200 may be designed to open on its radial-hinge mechanism or be designed to follow a more rigid stance with negligible give. Either way, the force variables will differ from the conventional and single wheel/tire forms and likely be superior in certain applications. In FIGS. 53 a-53 b, a twelve-spoke radial-hinge mechanism 5301 is implemented within a clutching/braking apparatus 5300. The apparatus 5300 is also comprised of a circular disk 4303 b (similar to base component 4303 a in FIG. 43) on one side of mechanism 5301, with a fixed clevis 5304 on the other side. Both disk 4303 b and clevis 5304 are endowed with slide-tracks 4306 b to facilitate the opening and closing of mechanism 5301. Through the central openings of clevis 5304 and disk 4303 b and through the inner-aperture of the radial-hinge mechanism 5301 runs a shaft 5305 on a fixed axis. An arrow in FIG. 53 a shows the shaft 5305 in rotational motion. An arrow in FIG. 53 b shows a lateral force upon the disk 4303 b, which subsequently opens the hinge mechanism 5301 and simultaneously closes down the inner-aperture of mechanism 5301 (as illustrated in FIGS. 4 a-4 f), consequently grabbing onto shaft 5305 and actualizing functions of clutching and braking and, in this figurative example, the shaft 5205 is brought to a halt in FIG. 53 b. A wide variety of forms of this application will be feasible, including arrangements using stacked radial-hinge mechanisms. Similar devices and apparatus employing radial-hinge mechanisms may also serve in bearing-stabilization, shock-absorption, axle-protection and axle-support, as well as in roles to transfer and transmit power. Another plurality of potential applications for radial-hinge mechanisms resides in the natural juxtaposition of spoke-crossings in all versions of radial-hinge mechanisms where attachments, such as plates, props, fins, blades, etc. automatically assume an equivalent oblique angle to the plane upon which the radial-hinge mechanism is common. FIG. 54 depicts a fan apparatus 5400 showing one such arrangement of blades 5403 attached to the radial-hinge mechanism 400 at points 5405, indicating three attachment points 5405 per blade 5403. In this particular arrangement, the apparatus 5400 may also open its mechanism 400 to regulate the angle of incidence of blades 5403 with the medium that the apparatus 5400 is interacting with, be it a gas or a liquid. Other applications of such devices and apparatus will range from boat props to windmills, including the likes of cutting-blades positioned around the inner-aperture and employed for radial-cutting operations, as in a radial-hinge circular-planer apparatus to cut, hone, grind or otherwise finish dowels and posts, rods and columns of wood, plastic, metal, fiber, etc. Special drill-heads, even turbines, may also evolve out of this modified radial-hinge device, whose radial-hinge action may also be adjustable and result in a more controllable and variable tool or machine apparatus. G. CONCLUSION The advantages of a radial-hinge mechanism constructed according to specifications are due to its general simplicity and variable nature, both of which emphasize its uniqueness and versatility and probable application in roles and functions currently and formerly monopolized by more complex, costly devices and apparatus which generally produce the same result. In addition, irrespective of whether the radial-hinge mechanism is constructed of separate spokes or segments, or including an intervening medium to realize other important radial-hinge configurations, or whether the spokes are formed as a continuous member, a radial-hinge mechanism, device or apparatus may be achieved. The above description is considered that of the preferred embodiments only. Modifications of the invention will occur to those skilled in the art and to those who make or use the invention. Therefore, it is understood that the embodiments shown in the drawings and described above are merely for illustrative purposes and not intended to limit the scope of the invention, which is defined by the following claims as interpreted according to the principles of patent law, including the doctrine of equivalents.

Money is the most dominant human transaction tool in modern human life, even human life is always in contact with money both in communication and in association because money demands value and form of authority of a person or family, when money is used as a tool for transactions money has value added by the rotation of regional and national and international money transactions, money for individuals and groups and countries shows the ability and legitimacy of those who have it that a person or group and country has the ability to develop and move forward for innovation and research in various fields of technology. the velocity of money is faster, the development of money and interest from the quality of money is also more beautiful and quality. money in the practice of human life has its own place in our lives from the past to the present, where now money has a faster turnaround speed and is more transparent and accountable than when it used currency and demand deposits or more backward that is barter (barter = where money has no advanced meaning yet). electronic money allows more money and faster technological developments in various fields, but there are obstacles when it comes to the regulation of life in various countries on earth. movement of money economy because the people who are still not ready to move quickly. Today's humans live without money like side dishes without salt and without lighting where we do not know what is served and do not know how to process it and enjoy it from all that God has given to us all on earth. we should thank the Father who belongs to heaven that he gives us the resources that we can manage well and with good added value and good transaction tools that are faster and more precise and accurate so that technological developments can be achieved appropriately as well as prosperity evenly distributed in all places and changing human mentality to be more solid that cannot be swayed by the flow of dramatic life                                           LOVE  ( Line On Victory Endless )                                                        Gen. Mac Tech Zone e- speed of rotation of electronic money                                      A. XO Transforming Money  finance was transformed from a clubby world of cozy relationships to a mathematical one of complex securities, abstract formulas and computing power.  Now, a generation later, the financial industry is about to be remade once again, except this time, it is not obscure financial securities that are being transformed, but very nature of money itself. What is Money? Money : It was a much more efficient way to transact business than bartering one good for another.  Money was also a useful store of wealth, certainly more convenient than livestock or grains.  These two core functions—a medium of exchange and a store of value—still define money today. Many people object to the concept of fiat money because of the control governments have over it.  Central banks can increase or decrease the money supply at will, giving them enormous control over economic activity. In extreme cases, hyperinflation can ensue, debasing the currency and wreaking havoc. So it’s not surprising that innovating the concept of money through a digital currency has been a recurring theme in technology circles.  Intuitively, it seems that the global financial system should be based on more than the judgments of a small group of central bankers. Yet only recently has digital money actually become possible. Another solution would be to create unforgeable signatures, which is what digital technology makes possible (digital signatures have been around for some time).  Moreover, in digital form, these signatures can be distributed—both instantly and ubiquitously—making it an ideal vehicle for an alternative currency to fiat money. It works through a widely distributed digital ledger, which makes it not only super secure, but also incredibly efficient because payment processing is automatic. Further, it is unlikely that a digital currency will ever displace national ones like the dollar.  As long as governments have the power to tax, they have the power to demand payment in whatever form they choose.  Invariably, that will be a national currency.                  Facilitating Transactions While digital currencies are unlikely to impact national currencies’ role as a store of value, there is vast potential in using vehicles like Bitcoin as a medium of exchange.  Consider that Visa and Mastercard make over $30 billion per year in interchange fees and you can see the possibilities.  Bitcoin can do a far better job at a much lower cost. Remember that Bitcoin has a widely distributed ledger, so it’s much more impervious to attack than a centralized institution like a bank.  It also transacts business instantaneously, so there is no “float” (i.e. the bank can’t keep your money in limbo while it earns interest on it) and because processing is automated, fees can be lowered substantially. TechCrunch describes another interesting aspect of digital currencies, the ability to program currency to create new financial products with functionality built in.  Imagine being able to set up an automated escrow account or a trust on your smartphone, with no lawyers involved. Digital currency is still a very new concept and these are merely initial ideas.  Surely, as the market and technology matures, more useful applications will arise. Money has always been intertwined with centralized power.  Only governments could issue it and only banks had the resources to facilitate transactions.  That model worked well enough, but had obvious drawbacks.  Many were shut out of the system while others earned fortunes as gatekeepers. The revolution underway in finance going on now has the potential to be even more consequential than the one that happened back in the 70's.  While financial innovation transformed many practices in the industry, its institutions remained intact.  The financial world today is still lorded over by a relatively small collection of bankers, clearing houses and regulators. Digital technology, however, is making finance exponentially more democratic. Crowdfunding and microlending have made it possible for people to acquire financing who never could before.  New payment systems like Square, Paypal and Apple Pay have made it easier for merchants to accept electronic payment.            SYSTEM AND METHOD FOR PROTECTING ELECTRONIC MONEY TRANSACTIONS Yet digital currency is something else altogether because it represents a decentralized form of money that is more secure, more fungible and more functional than anything we’ve seen before.  More than a mere store of value or medium of exchange, digital money has the potential to be more transformative than anything we’ve seen before.     B. XO  Transforming Aspect Real MONEY  To  e- MONEY   The value of money at the moment is experiencing a significant shift where the amount of wealth that can be owned by individuals can increase and increase all because of the availability of financial transactions in instrumentation and measurement in the method of financial electronics. when we are in the real money era, namely currency and demand, we always have a variety of physical evidence of the value of money, either in the form of whole or in the form of checks, can go forward or check backwards, and withdrawals are limited and require space and the place also takes a lot of time in making the value of money as a transaction tool which of course greatly nullifies a business in a mega project that requires fast and limited cash flow in times and times that are fast and appropriate in disbursing the value of money to customers, owners and founders also every member of the community who is competent in the business of value money. in the era of industry that is growing rapidly, especially the attraction of pure technology for industrial processes that are prolonged and developing continuously, transaction tools are needed that can move the economic rotation on a macro and cash basis in a micro manner quickly, precisely and easily and credibly can also be accountable. makes it easy for us to develop new and renewable industrial methods and techniques for excavating techniques on planets outside the earth and the solar system.  some comparative tool for the value of money that is now on earth as we know it is NPV, where the NPV value in the era of financial electronics transactions will accelerate and slow down which is more measurable and controlled and reduces human error both intentional and incidental: 1. The NPV in the micro sense is the difference between disbursed expenditure and income by using the social opportunity cost of capital as a factor discount, or in other words a cash flow that is expected to be discounted in the future.  2. NPV in the sense of macro is money in the present is worth more than the same as inflation, and earnings from alternative investments that can be made during the intervening time. In other words, a dollar earned in the future won't be as much as one earned in the present.                                                                                                                 the main difference between the profitability index and net present value                                                   how in the era of real money when people or individuals could hoard money such as hoarding rice and wheat barns and corn that needed a place, moths and rust could damage it and require up-to-date maintenance and maintenance costs and this raises the value of money which drops dramatically. our tendency to return to the era of the Barter era in which without proper management of the value of money but in the era of financial electronics all did not need to be stockpiled such as hoarding rice, corn and wheat but kept in the place of financial electronics which were also more private and safe to manage without super tight guard because it has been protected by a system of qualified financial electronic instruments and measurements. of course the value of money transactions are more useful and efficient are also effective and penetrate the value of money for better and more effective prosperity as well as energy for all of us.            C.  XO   Discounted Cash Flow and the Time Value of Money Aspect  Time value of money concepts are the cornerstone of modern finance. finance. What are "Discounted Cash Flow" and the "Time Value of Money?" Discounted cash flow DCF is an application of the time value of money concept—the idea that money that will be received or paid at some time in the future has less value, today, than an equal amount collected or paid today. The DCF calculation finds the value appropriate today—the present value—for the future cash flow.The term "discounting" applies because the DCF "present value" is always lower than the cash flow future value. In modern finance, "time value of money" concepts play a central role in decision support and planning. When investment projections or business case results extend more than a year into the future, professionals trained in finance usually want to see cash flows presented in two forms, with discounting and without discounting. Financial specialists, that is, want to know the time value of money impact on long-term projections. Two Central Terms: Present Value and Future Value In discounted cash flow analysis DCF, two "time value of money" terms are central: Present value (PV) is what the future cash flow is worth today. Future value (FV) is the value that flows in or out at the designated time in the future. A $100 cash inflow that will arrive two years from now could, for example, have a present value today of about $95, while its future value is by definition $100. For each cash flow event, the present value is less than the corresponding future value, except for cash flow events occurring today, in which case PV = FV). The further into the future before a cash flow event occurs, the more discounting lowers the present value below its future value. the total of all of the cash flow present values for the cash flow series, across a timespan extending into the future, is the net present value (NPV) of a cash flow stream.  DCF is center stage when decision makers and investors evaluate potential investments, action proposals, or purchases. Looking forward in time, the analyst projects cash inflows and outflows (cash flow streams) the investor can expect from each of these. Other things being equal, analysts will recommend the action or investment with the more substantial cash flow NPV, as the "better business decision." When first hearing the definition of discounted cash flow, many people understandably react with comments like these: "It sounds like fiction" or "The time value of money cannot refer to real value because DCF does not measure real cash flow" or "It's an interesting calculation, but there's no tangible value involved." However, business professionals recognize that the results of discounting calculations do represent real tangible value, readily seen when they state the time value of money concept like this: Having the use of money for some time has a value that is tangible, measurable, and real. Discounted cash flow (DCF) is one application of this concept, while interest paidfor a loan is another. With DCF, the discounting lowers the present value PV of future funds below the future value FV of the funds for at least three reasons: Opportunity. Funds you have now could (in principle) be invested now, and gain return or interest between the present and the future time. You cannot use now funds that you will not have until a "future" time.  Risk. Funds you have now are not at risk, but funds arriving in the future are uncertain. A well-known proverb states this principle more colorfully: "A bird in the hand is worth two in the bush." Inflation. A sum you have today will very likely buy more than an equal amount you will not have until years in future. The buying power of money decreases over time due to inflation.  What future money is worth today is called its present value (PV) and what it will be worth in the future when it finally arrives is called not surprisingly its future value (FV). The right to receive a $100 payment one year from now (the future value) might be worth to us today $95 (its present value). Present value, in other words, discounts to a value below future value. Present Values for a Cash Flow Stream When the analysis concerns a series of cash inflows or outflows coming at different future times, the series is called a cash flow stream. Each future cash flow has its value today (its present value). The sum of these "present values" is the "net present value" for the cash flow stream. Consider an investment today of $100, that brings net gains of $100 each year for six years. The future values and present values of these cash flow events might look like this: One 6-Year cash flow stream, as Future Values (FV) and Present Values (PV) at two discount rates. All three sets of bars represent the same investment cash flow stream. Black bars stand for cash flow figures in the currency units when they arrive in the future (future values). Green and Blue bars are values of the same cash flows now, in present value terms. The net values in the legend show that after five years, the net cash flow expected is $500, but the Net present value (NPV) today is discounted to something less. The next section explains the role of the discount rate (a percentage) and time periods in determining NPV. Interest Rates and Time Periods in Discounting The size of the discounting effect depends on two things: the amount of time between now and each future payment (the number of discounting periods) and an interest rate called the discount rate. The example shows that: As the number of discounting periods between now and the cash arrival increases, the present value decreases. As the discount rate (interest rate) in the "present value" calculations increases, the present value decreases.  Whether you will or will not calculate present values yourself, your ability to use and interpret NPV / DCF figures will benefit from a simple understanding of the way that interest rates and discounting periods work together to create DCF. If you Many if not most business people outside of finance, are unfamiliar with "time value of money" terms and calculations. The subject becomes approachable, however, if the explanation begins by noting that DCF mathematics are very closely related to that is familiar to most people:calculations for interest growth and compounding. Remember briefly how interest calculations work. The FV formula looks into the future and might ask, for instance: What is the future value (FV) in one year, of $100 invested today (the PV), at an annual interest rate of 5%? FV1  = $100 ( 1 + 0.05)1 = $105 When the FV is more than one period into the future, as most people know, interest compounding takes place. Interest earned in earlier periods begins to "earn interest on itself," in addition to interest on the original PV. Compound interest growth is delivered by the exponent in the FV formula, showing the number of periods. What is the future value in five years of $100 invested today at an annual interest rate of 5%?. FV5  = $100 ( 1 + 0.05)5 = $128 The same formula can be rearranged to deliver a "present value" given a "future value" and "interest rate" for input, as shown.  Now, the formula starts in the future and looks backward in time, toward today. The formula now asks: What is the value today of a $100 payment arriving in one year, using a discount rate of 5%? PV1 = ($100) / (1.0 + 0.05)1          = $100 / (1.05)         = $95  You should be able to see why PV will decrease if we either (a) increase the interest rate, or (b) increase the number of periods before the FV arrives. What is the present value of $100 we will receive in 5 years, using a 5% discount rate? PV5  = $100 / (1.0 +0.05)5          = $100 / (1.276)          = $75.13 When the FV is more than one period into the future, as most people know, interest compounding takes place. Interest earned in earlier periods begins to compound, in addition to interest on the original PV. Compound interest growth is delivered by the exponent in the FV formula, showing the number of periods. What is the future value in five years of $100 invested today at an annual interest rate of 5%?. FV5  = $100 ( 1 + 0.05)5          = $128 When discounting is applied to a series of cash flow events, a cash flow stream, as illustrated in the graph example above, net present value for the stream is the sum of PVs for each FV:   Year-end discounting for a stream of n future cash flow events (FVs). Should You Use Mid-Period (or Mid-Year) Discounting? What Difference Does it Make? Finally, note two commonly used variations on the examples shown thus far. The cases above and most textbooks present first the "Period-end" (or "Year-end") discounting. Period-end discounting is the more frequently used DCF approach. The approach, moreover, usually turns up as the default approach for spreadsheet and calculator DCF functions. Period-End Discounting With the period-end approach, discounting works as though all cash flow occurs on the last day of each period. When periods are one year in length, of course, analysts call this the year-end approach. With year-end discounting, all of the period's cash flow is assumed to occur on day 365 of the year.  Mid-Period Discounting Some financial analysts, however, prefer to assume that cash flows are distributed more or less evenly throughout the period. For them, discounting should, therefore, be applied when the cash flows during the period. Calculating present values this way is mathematically equivalent to saying that all cash flow occurs at mid-period.  For this reason, this approach is called mid-period discounting. And, of course, the name mid-year discounting applies when periods are one year in length.  What Are the Differences Between the Two Approaches? Period-end discounting is more severe (has a more substantial discount effect) than the mid-period approach. Period-end calculations are more severe than mid-period versions because they impact all of the period's cash flow for the full period. You can see how this works mathematically from the formulas in the next section. The period-end approach divides each FV value by a more substantial discount factor than do mid-period calculations. Some analysts prefer to describe the difference between approaches by saying the "period-end" discounting is the more conservative approach. Those preferring the other approach say that discounting mid-period is more accurate. Remember that the discount rate recognizes the values of opportunity, risk, and inflation—values that can change as time passes. Mid-period discounting comes closer, they say, to applying the discounting effect precisely when cash flows. Formulas for Mid-Period Discounting The methods below show NPV calculations for the mid-year approach (at panel top) and for discounting with periods other than one year (at mid-panel). The first NPV formula shows how the present value formula applies for mid-year discounting. And, the second NPV formula shows the calculation for periods other than one-year. In any case, the business analyst will want to find out which of the above discount methods is preferred by the organization's financial specialists, and why, and follow their practice (unless there is justification for doing otherwise). Choosing a Discount (Interest) Rate for Cash Flow Analysis The analyst will also want to find out from the organization's financial specialists which discount rate the organization uses for discounted cash flow analysis. Financial officers who have been with an organization for some time, usually develop good reasons for choosing one discount rate or another as the most appropriate rate for the organization. In private industry, many companies use their own cost of capital (or a weighted average cost of capital) as the preferred discount rate. Government organizations typically prescribe a discount rate for use in the organization's planning and decision support calculations. In the United States, for instance, the Office of Management and Budget (OMB) publishes a quarterly circular with prescribed discount rates for Federal Government use. Financial officers may use a higher discount rate for investments or decisions viewed as risky, and a lower discount rate when expected returns from a proposed action come with less risk. The higher "discount rate" is a hedge against risk, because it puts relatively more emphasis (weight) on near-term returns compared to distant future returns.  Comparing Competing Investment Proposals with DCF and NPV Consider two competing investments in computer equipment. Each calls for an initial cash outlay of $100, and each returns $200 over the next five years making for a net gain of $100. But the timing of the returns is different, as shown in the table below (Case Alpha and Case Beta), and therefore the present value of each year's gains is different. The sum of each investment's "present values" is called the discounted cash flow (DCF) or "net present value" (NPV). Using a 10% discount rate again, we find:   Timing CASE Alpha CASE Beta Net Cash Flow "Present Value" Net Cash Flow "Present Value"   Now – $100.00 – $100.00  – $100.00 – $100.00   Year 1 $60.00 $54.54 $20.00 $18.18   Year 2 $60.00 $49.59 $20.00 $16.52   Year 3 $40.00 $30.05 $40.00 $30.05   Year 4 $20.00 $13.70 $60.00 $41.10   Year 5 $20.00 $12.42 $60.00 $37.27   Total Net CFA =  $100.00 NPVA = $60.30 Net CFB = $100.00 NPVB = $43.12 Comparing the two investments, the larger the early returns in Case Alpha lead to a better net present value (NPV) than the later large return in Case Beta. Note especially the Total line for each present value column in the table. This total is the net present value (NPV) of each cash flow stream." When choosing alternative investments or actions, other things being equal, the one with the higher NPV is a better investment. What Roles Do DCF and NPV Play in Business Case Analysis? In brief, an NPV / DCF view of the cash flow stream should probably appear with a business case summary when: The business case deals with an "investment" scenario of any kind, to compare different uses for funds. The business case covers a long period (two or more years). Inflows and outflows change differently over time. For example, the most substantial "inflows" come at a different time from the most substantial "outflows." Two or more alternative cases for comparison differ concerning cash flow timing within the analysis period.                  D. XO   Net Present Value (NPV) as a Capital Budgeting Method  What is net present value and how is it used in capital budgeting? Companies often use net present value as a capital budgeting method because it's perhaps the most insightful and useful method to evaluate whether to invest in a new capital project. It is more refined from both a mathematical and time-value-of-money point of view than either the payback period or discounted payback period methods. It is also more insightful in certain ways than the ​profitability index or internal rate of return calculations.​​ What Is Net Present Value? Net present value is one of many capital budgeting methods used to evaluate potential physical asset projects in which a company might want to invest. Usually, these capital investment projects are large in terms of scope and money, such as purchasing an expensive set of assembly-line equipment or constructing a new building. Net present value uses discounted cash flows in the analysis, which makes the net present value more precise than of any of the capital budgeting methods as it considers both the risk and time variables. A net present value analysis involves several variables and assumptions and evaluates the cash flows forecasted to be delivered by a project by discounting them back to the present using information that includes the time span of the project (t) and the firm's weighted average cost of capital (i). If the result is positive, then the firm should invest in the project. If negative, the firm should not invest in the project. Capital Projects Using Net Present Value Before you can use net present value to evaluate a capital investment project, you'll need to know if that project is a mutually exclusive or independent project. Independent projects are those not affected by the cash flows of other projects. Mutually exclusive projects, however, are different. If two projects are mutually exclusive, it means there are two ways of accomplishing the same result. It might be that a business has requested bids on a project and a number of bids have been received. You wouldn't want to accept two bids for the same project. That is an example of a mutually exclusive project. When you are evaluating two capital investment projects, you have to evaluate whether they are independent or mutually exclusive and make an accept-or-reject decision with that in mind. Net Present Value Decision Rules Every capital budgeting method has a set of decision rules. For example, the payback period method's decision rule is that you accept the project if it pays back its initial investment within a given period of time. The same decision rule holds true for the discounted payback period method. Net present value also has its own decision rules, which include the following: Independent projects: If NPV is greater than $0, accept the project. Mutually exclusive projects: If the NPV of one project is greater than the NPV of the other project, accept the project with the higher NPV. If both projects have a negative NPV, reject both projects. Example: Calculation of Net Present Value Say that firm XYZ Inc. is considering two projects, Project A and Project B, and wants to calculate the NPV for each project. Project A is a four-year project with the following cash flows in each of the four years: $5,000, $4,000, $3,000, $1,000. Project B is also a four-year project with the following cash flows in each of the four years: $1,000, $3,000, $4,000, $6,750. The firm's cost of capital is 10 percent for each project, and the initial investment is $10,000. The firm wants to determine and compare the net present value of these cash flows for both projects. Each project has uneven cash flows. In other words, the cash flows are not annuities. Following is the basic equation for calculating the present value of cash flows, NPV(p), when cash flows differ each period: NPV(p) = CF(0) + CF(1)/(1 + i)t + CF(2)/(1 + i)t + CF(3)/(1 + i)t + CF(4)/(1 + i)t Where: i = firm's cost of capital t = the year in which the cash flow is received CF(0) = initial investment To work the NPV formula: Add the cash flow from Year 0, which is the initial investment in the project, to the rest of the project cash flows. The initial investment is a cash outflow, so it is a negative number. In this example, the cash flows for each project for years 1 through 4 are all positive numbers. Tip: You can extend this equation for as many time periods as the project lasts. To calculate the NPV for Project A: NPV(A) = (-$10,000) + $5,000/(1.10)1 + $4,000/(1.10)2 + $3,000/(1.10)3 + $1,000/(1.10)4 = $788.20 The NPV of Project A is $788.20, which means that if the firm invests in the project, it adds $788.20 in value to the firm's worth. NPV Disadvantages Although NPV offers insight and a useful way to quantify a project's value and potential profit contribution, it does have its drawbacks. Since no analyst has a crystal ball, every capital budgeting method suffers from the risk of incorrectly estimated critical formula inputs and assumptions, as well as unexpected or unforeseen events that can affect a project's costs and cash flows. The NPV calculation relies on estimated costs, an estimated discount rate, and estimated projected return. It also can't factor in unforeseen expenses, time delays, and any other issues that come up on the front or back end, or during the project. Also, the discount rate and cash flows used in an NPV calculation often don't capture all of the potential risks, assuming instead the maximum cash flow values for each period of the project. This leads to a false sense of confidence for investors, and firms often run different NPV scenarios using conservative, aggressive, and most-likely sets of assumptions to help mitigate this risk. Alternative Evaluation Methods In some cases, especially for short-term projects, simpler methods of evaluation make sense. The payback-period method calculates how long it will take to earn back the project's initial investment. Although it doesn't consider profits that come in once the initial costs are paid back, the decision process might not need this component of the analysis. The method only makes sense for short-term projects because it doesn't consider the time value of money, which renders it less effective for multiyear projects or inflationary environments. The internal rate of return (IRR) analysis is another often-used option, although it relies on the same NPV formula. IRR analysis differs in that it considers only the cash flows for each period and disregards the initial investment. Additionally, the result is derived by solving for the discount rate, rather than plugging in an estimated rate as with the NPV formula. The IRR formula result is on an annualized basis, which makes it easier to compare different projects. The NPV formula, on the other hand, gives a result that considers all years of the project together, whether one, three, or more, making it difficult to compare to other projects with different time frames.            D. XO    Aspect NPV on The Next-generation digital payment technology                                    Use Due Cash payment system with anyone You can make, share, or receive payments from anyone in the U.S. who has a phone number or email account regardless if they are actually using the Due Cash payment system and digital wallet. All they need to do is create a Due account to claim or make their payment. Find others you know with a Due account simply by syncing your smartphone contacts. All personal and financial data is encrypted and protected on Due’s secure servers. We work tirelessly to ensure that our security system meets or even exceeds the current security industry standards.            Our next-generation digital payment technology guards against any type of unauthorized transaction. If you believe that there has been unauthorized activity on your Due digital wallet .    If you have lost your phone or believe it is being used in an unauthorized way, you can protect your Due digital wallet by visiting Passwords & Authorizations within your online account settings. Here, you can revoke access from your phone so it will log out of any active sessions within your Due digital wallet.    Only use your Due digital wallet and eCash payment system with people you know. We don’t permit merchants to make sales via Due or offer buyer or seller protection.                                                E-CASH INDUSTRY The advancement of technology has helped electronic payments grow significantly. For example, in 1968 the exchanging of electronic data became commonplace for anyone looking to transfer money. In 1974, Robert Moreno patented technology for smart cards, which was followed by the first ATMs in the United States. Before the decade was over, electronic terminals called, “EFTPOS” (meaning, for non-cash bank payments) were being used in the United States. Five short years later in 1984, email was being used by enterprises everywhere in the financial sector to communicate with customers.  Cash without acknowledging the release of the first PC by IBM in 1981. The PC made it possible to develop microelectronics, which would quickly allow for microprocessors to be installed in a credit card.  David Chaum, a U.S. citizen and brilliant mathematician, became the head of cryptography at the Dutch national research center CWI. Dr. Chaum was responsible for the invention of secure digital cash, along with the idea of blind signatures for untraceable payments. This resulted in the founding of the first electronic payment system in the world, DigiCash. Unfortunately, DigiCash went bankrupt in 1998 and sold its assets to eCash Technologies. However, DigiCash had already left an impact everywhere in the eCash world. At one American bank, the customers had already embraced the eCash idea, with 90% of its depositors using the system. At the “Real World Crypto” conference held at Stanford University January 6, 2016, Chaum was back with information on a new plan for encryption, called PrivaTegrity which he is working on with a whole team of experts from other universities. This group of academic partners hopes to allow a system that will fully allow secret and anonymous communication, including eCash capabilities, to be totally secure and be fast enough to work as a smartphone app. It is unknown if the project is fully coded and tested. Particularly compelling was Dr. Chaum’s claim that we may be able to have a “civil society electronically without the possibility of covert mass surveillance.” Dr. Chaum’s DigiCash wasn’t the only company exploring the electronic cash industry .  The 2000’s saw impressive gains in the use and acceptance of eCash as a result of advances in technology. Some of the most notable occurrences have been: Bitcoin, a digital asset and a payment system, was invented in 2009. Google’s mobile payment system, Google Wallet, is released in 2011. Following in the steps of Google, Apple, Android, and Samsung release mobile payment and digital wallets services in 2014 and 2015. The United States makes the switch to EMV cards – which stands for Europay, MasterCard, and Visa – in 2016. HOW DOES ECASH WORK? How exactly does eCash work? To have a better understanding, let’s first familiarize ourselves with how money traditionally flows using eCash. Withdrawal. Users have the ability to convert money from their eCash accounts into eCash coins. However, access can only be granted to the eCash account if the user can sign the withdrawal request. The signature is checked against the public key that has been registered with the ecash account since the coins are accessed using a password-encryption. Payment. In order to pay a specified amount, a set of coins that equal the desired amount must be selected. If you were using the on-line ecash system, the set of coins would be encrypted for the bank through the bank’s unique public key. The shop then deposits the payment at their bank, who then credits the merchant’s eCash account, as long as all coins are valid. The accepted coins are added to the database of spent coins to prevent them from being spent again. Payment deposit. Again, using the on-line ecash system, this protocol would be completed by the shop or merchant. The most important component of the payment protocol is that the payment deposit will be made specifically to the payee. Coin redemption. Coins can be directly returned to the mint without using them in a payment if they’ve expired, need to be refreshed, or need improved distributions. Recovery. If coins that have been lost they can be recovered through a protocol carried out between the user and the mint. Now that we’re aware of how the money flows, it’s time to realize that the money flow can only be accomplished through the cooperation of the following four components: Issuers. These can either be financial institutions, or non-bank institutions. Customers. These are the individuals who spend eCash. Merchants or traders. These are the vendors who receive eCash. Regulators. Authorities or state tax agencies. Once all of the parties are involved, the basic idea of an eCash transaction involves at least one of the components; the issuer, customer, and merchant who will accept the eCash in exchange for the products or services rendered. There are then three general stages for the transaction to be completed. Account Setup The Consumer has to open an account with a bank that provides eCash accounts. The merchant who is willing to participate in eCash transactions must have access to these accounts with a number of banks in order to support the transaction of the consumer who may use any of these various bank accounts. However, the banks will manage both the consumers’ and merchants’ accounts. Purchase Once the consumer decides to purchase a good or service, he or she will transfer the eCash amount from their bank account to either their electronic purse (on-line system) or eCash token (off-line system). The eCash payment will then be transferred to the merchant so that they are compensated for the goods or services provided. The eCash payment will be either a softcopy (via software) or token based. For most transactions through the Internet, the process will be encrypted. Authentication After receiving the electronic payment from the consumer, the merchant will receive a confirmation from the bank. The bank will then authenticate the electronic transaction. During this same step, the bank will debit the consumer’s account for the amount that was agreed upon. Finally, the merchant delivers the products or services and will inform the bank to deposit the payment into their bank account. Although these stages may sound complicated if you’re new to eCash, digital cash actually acts very similarly to physical cash. The obvious difference is that electronic is digital. Here’s an example of how an eCash system would work: A bank creates a unique digital bank note that includes a message which issues a serial number (with a primary or public key) and value of the note. This is sent to Person A. Whenever Person A withdraws this note, it will use Chaum’s Cryptographic technique. This will alter the serial number. As a result, the bank will not recognize the note when it is withdrawn. The note will be returned to the bank with a new serial number. Person A will then pay Person B electronically by sending the bank note to him or her. Person B will check the note’s validity by decrypting it through the bank’s public key to check its signature, a.k.a. the new serial numbers validity. Person B ships the note off to the bank, which checks the serial number to confirm that this specific bank note has never been spent before. The serial number, which is different from the note number that was withdrawn by Person A, will prevent the bank from linking the two transactions. The final phase includes the enabling bank checking the new serialized key account for the amount of the transaction. If validated, the amount will be transferred via a depository notice. Person B, who is using the same encrypting technique, will return the depository notice with the new serialize account. Again, the enabling bank will be aware of who the merchant is. The bank will only know that that money is available and can be used as a payment. In other words, think of this eCash transaction as a debit card transaction except that there is no other information besides the amount of the transaction, making the process secure. WHAT IS CRYPTOCURRENCY AND HOW IS IT OBTAINED? You simply can’t have a discussion involving eCash and not mention cryptocurrency. Ever since Bitcoin launched in 2009, the cryptocurrency has captured the minds of lawmakers, financial institutions, and the general public as a whole. But, what exactly is cryptocurrency and how can it be obtained. Cryptocurrency Explained In it’s simplest form, cryptocurrency is a digital or virtual currency that uses cryptography for security purposes to prevent counterfeit. Cryptography, for those who are unaware, means the science of coding and decoding messages so that they remain secure. During the coding process, a key is used which is known to only the sender and the recipient. What makes cryptocurrency unique is that it is not issued by any type of authority figure, such as a central bank. Because of this, cryptocurrency is in theory, immune to interference from bodies of government. Another feature that cryptocurrency is known for is that users can remain anonymous. The issue with anonymity is that it can be used for illegal activity like money laundering and tax evasion. In most cases, cryptocurrency works simply when two parties transfer funds between each other. Since this involves cryptography, either a public or private keys like an RSA signature must be used to complete the transaction. Each transaction is recorded on a public ledger, also called either a distributed ledger or a blockchain, that is visible to anyone in the network. Personal information is not shared, though. Besides security and anonymity, cryptocurrency is appealing to users because there are only minimal processing fees, as opposed to the expensive fees that most banks and financial institutions charge for transfers. The major concern involving cryptocurrency is that because it’s a virtual or digital currency, an individual’s balance can be erased if there is a security breach or computer crash. In most instances, however, this information can be easily backed-up on the cloud. Finally, the price of cryptocurrencies is that the value can fluctuate sporadically. A Quick Word Regarding Bitcoin While the idea behind cryptocurrency existed years before, cryptocurrency came to the forefront in 2009 when Bitcoin was released. Bitcoin was created by a computer programmer going by the pseudonym Satoshi Nakamoto. Bitcoin is an open-source, peer-to-peer digital currency that is completely decentralized. Today, Bitcoin is accepted by more than 6,000 companies that include Overstock and Virgin Galactic. As explained by the Congressional Research Service, “Like the U.S. dollar, the Bitcoin has no intrinsic value in that it is not redeemable for some amount of another commodity, such as an ounce of gold. Unlike a dollar, a Bitcoin has no physical form, is not legal tender, and is not backed by any government or any other legal entity, and its supply is not determined by a central bank.” (In part of this Congressional Research Service report it states that the dollar is a legal currency, yet doesn’t specifically say the Bitcoin isn’t legal, it just eludes that it isn’t traceable, and therefore a concern to governments.) Through cryptographic techniques “special users on the bitcoin network, known as miners, to gather together blocks of new transactions and compete to verify that the transactions are valid—that the buyer has the amount of Bitcoin being spent and has transferred that amount to the seller’s account. For providing this service, miners that successfully verify a block of transactions are rewarded by the network’s controlling computer algorithm with 25 newly created Bitcoins.” How to Obtain Cryptocurrency Whether it’s Bitcoin or one of the hundreds of alternatives on the crypto-current market, (called Altcoins, meaning an alternate cryptocurrencies – which basically means an alternative to Bitcoin) you must first download the free and open-source software. After that, there are two basic ways to obtain cryptocurrencies, according to Forbes; “mine them using a powerful computer and buy them through a crypto exchange.” Mining Bitcoins and Altcoins, as described in PCWorld, “involves writing a short script to run in the command prompt. It’s only a few steps, which you must follow exactly to ensure success.” However, this can put a lot of stress on your computer because it must “solve complex problems that keep the respective cryptocurrency’s peer-to-peer infrastructure secure.” In exchange for their work, miners are given pieces of Bitcoins. If you prefer to purchase Bitcoins or Altcoins, you can only do so through select and limited markets. This includes currencies on major exchanges like VaultofSatoshi, Kraken, Coinex, and BTC-e. What makes cryptocurrencies like Bitcoin interesting is that they can be used as an investment tool and a transactional platform. PROPERTIES OF ECASH For electronic payments to be as effective and efficient as paper and coin currency, electronic payments should include the following properties: Security One of the main concerns surrounding eCash is how secure it is. When the determined amount is being transferred between consumers, merchants, and banks the prevention of any unauthorized individuals like hackers intercepting, or even changing, the content of the messages, such as the dollar amount, should be addressed. This is commonly addressed through encryption and special serial numbers that give the bank the power to verify the authenticity of the transaction. Besides online security, physical security should be taken into account. For example, if a hard drive crashes or a smart card is stolen, the eCash could also be lost. Thanks to advances in technology, eCash can be stored on secure cloud databases so that it can be easily recovered. Privacy Privacy, in regards to eCash, is the anonymity of the consumers who have made the payment. As with coins and paper notes, the payee should not be able to be linked or be traced during transactions. Privacy is important because consumers’ privacy should be protected from being monitored by financial surveillance. Anonymity, however, does present a number of concerns like counterfeiting, money laundering, and blackmailing in extreme circumstances. Keep in mind that the more anonymity that is offered the less security there will be. Portability One of the benefits of electronic cash is that it’s portable and can be taken with you no matter where you are in the world. In fact, the portability of eCash could replace traditional wallets since it can be stored on your smartphone on in the cloud. Transferability Another advantage of eCash is that it can be transferred from the payee to the payer without being referred to a bank. The ability to transfer between parties should be easy and convenient, just as with traditional paper and coins. Parties should also be able to exchange funds electronically to each other no matter where they are in the world. Divisibility When discussing divisibility, eCash denominations should be able to be divided into small amounts. This makes smaller transactions possible between parties. Arguably on the main challenges for divisible systems having the ability to divide the value into smaller amounts that will eventually be equal to the original value. Previously, divisibility systems were solved by Eng, and Okamoto’s scheme, Okamoto’s scheme and Okamoto and Ohta’s scheme. More recently, International Association for Cryptologic Research shared a system by Patrick Märtens that is based on bounded accumulators and “a new technique to prove that several revealed values are inside an accumulator.” As a whole, eCash payments do not just have to contain the features listed above. To truly replace traditional money transfers, electronic payments have to be more convenient, easier-to-use, and ubiquitous – meaning that eCash networks must work with each other. ECASH SYSTEMS It’s common practice for eCash systems like PayPal, eCash, WebMoney, and Payoneer to sell their electronic currency directly to the end user. However, it’s not uncommon for other systems to sell their currency through third-party digital currency exchangers. For example, the M-Pesa system transfers money via mobile devices in third world countries like Africa, India, Afghanistan, and Eastern Europe. In some situations, community currencies, such as local exchange trading systems (LETS) and the Community Exchange System, work with electronic transactions. In the above examples, these systems are known as centralized systems where the user’s real identity is still known. This has raised privacy concerns over centralized systems, however, it has also been argued that being able to identify users is a benefit if they need to be contacted or identified. Decentralized Systems You can’t talk about decentralized systems without discussing how cryptocurrencies play a part in these systems. Cryptocurrencies, as noted previously, are not regulated by any governing body that can verify the peer-to-peer transaction, which occurs anonymously. Because these systems are decentralized, the value of the currency can fluctuate quickly and often. Besides Bitcoin, are here some other examples of cryptocurrencies that use decentralized systems: Monero launched in 2014 and “is built on principles of privacy, decentralization, and scalability.” Litecoin was founded in 2011, Litecoin is “a peer-to-peer Internet currency that enables instant, near-zero cost payments to anyone in the world.” Dogecoin is an open-source peer-to-peer currency that allows you to easily send money online. Peercoin claims that it’s more energy efficient and the world’s first proof-of-stake coin that was created in 2012. Primecoin is an innovative cryptocurrency that uses as “unique form of proof-of-work based on prime numbers.” Ripple doesn’t rely on the Bitcoin code and focuses on improving cross-border payment offerings. Nxt also uses its own code that was developed from scratch. Contactless Payment Systems These are credit cards, debit cards, smart cards, or mobile devices that rely on radio-frequency identification (RFID) or near field communication (NFC) to make secure transactions that do not require signature or PIN verification. The most common examples are contactless payment systems are mobile subsystems and digital wallets. Examples include: The ‘electronic purse’ that was introduced by Mondex and National Westminster Bank in 1994. The payment system called Mobipay that was implemented by Telefónica and BBVA Bank in Spain in 2005. Venmo originally launched as a mobile payment system through SMS in 2010. It became a social app where friends could pay for small purchases like a cup of coffee. Google Wallet, which launched on September 19, 2011, allows users to store all of their credit card and debit card online. Easytrip was initiated in 2012 in Ireland as a way to pay road tolls. The tolls were charged to the user’s mobile phone account or prepaid credit. The O2 Wallet was introduced in 2012 and could be loaded with regular bank accounts or cards. The service shut down in 2014. In October 2014 Apple Pay was released and is similar to Google Wallet, except it’s exclusive to iPhone users. Samsung Pay debuted in 2015 to rival Apple Pay. It has similar features but is available for Samsung devices. GNU Taler is an anonymous and open source electronic payment system that will be available to the public in 2016. THE BENEFITS OF ECASH The greatest benefit with eCash is that allows individuals to make financial transactions online in real-time. Because financial information is stored electronically, consumers no longer have to carry cash, only mobile devices or smart cards to complete a transaction. eCash also gives merchants more opportunities to partake in commerce. Those are a just a few of the benefits of eCash. Here’s a closer look at the advantages that users and merchants can enjoy. Users Instead of waiting for a bank to approve a transaction, such as for a check to clear, users can send and exchange funds instantly without ever having to step inside of a bank. In fact, you can use electronic payment systems anywhere in the world, as long as you can get online. Furthermore, eCash prevents consumers from having to pay withdrawal fees that are commonly by banks whenever you visit the ATM or the interest rates that incur with credit cards. In fact, people can exchange money directly to each other without the involvement of a third party. Merchants Merchants also have a lot to gain by embracing eCash systems. For starters, these systems can become a marketing tool for their eCommerce business. When a merchant uses a payment system, whether it’s PayPal, Apple Pay, or Primecoin, the consumer can feel secure in making a purchase of the site since the online marketplace uses a trusted payment system. Some payment systems also provide merchants with coupons to help entice consumers. Another perk is that the fees charged by eCash payment systems are usually lower than what credit card companies charge. eCash also gives merchants from anywhere in the world to partake in the global marketplace. For example, an online merchant in India can sell their products to anyone in the world and accept payments with just one-click of a button. Family members in Uganda can exchange funds between each other, even if none of them have a traditional bank account. Finally, both merchants and customers can enjoy the security, and if needed the anonymity, that eCash provides. Since each transaction still needs to be verified, the chances of fraud are greatly reduced. International Exchange This was touched upon earlier, but one of the greatest advantages of eCash is that it’s going to increase the opportunities for international exchange. No matter where you live in the world, you can sell your product to international consumers and receive a payment in real-time. For example, you could be a record shop in Germany that sells a $20 vinyl to a customer in Australia or a clothing manufacturer in America who sells products to customers in Brazil for $15 a shirt. Not only are the fees cheaper, it makes it easier to sell items to a global marketplace by using a fast, secure, and convenient eCash system. DISADVANTAGES OF ECASH While electronic payment systems have been improving their security features, this is one area that remains a concern for users and merchants. Despite needing to verify transactions, fraud is still a common occurrence, thanks to hackers. For example, a hacker can find their way into the bank accounts of unsuspecting victims which could lead to instances of identity theft or having your funds stripped away. Hackers could also attempt to counterfeit the money by recreating the eCash form. Additionally, there is a concern that eCash can become easily available to criminal and terrorist groups if they use a decentralized system. This makes it harder for governments to track these types of organizations since it’s more difficult to find a paper trail. eCash also makes it more challenging to monitor and collect both income and taxes, so it’s possible for people to easily transfer funds and hide assets in offshore accounts. One of the troubling limitations of eCash is that while it has the chance to be used by low-income individuals or those in undeveloped countries, it will be an uphill battle for these groups to use an eCash system since a computer, mobile device, and internet connection are required for eCash transactions. Until this problem is addressed, which is an area that organizations like the Bill and Melinda Gates Foundation are working on, not everyone can enjoy the benefits of eCash. Finally, there are concerns about what happens when you can’t access your funds, such as during a power failure. Or, what happens when your records or coins are lost because of a security breach. These are rare occurrences and have been considered as more and more information is stored in the cloud. ECASH REGULATIONS In 1996, Patrick G. Goshtigian discussed the regulations of eCash in a paper published at the Anderson Graduate School of Management at UCLA. In regards to security, Goshtigian stated; “The legal challenges of E-cash entail concerns over taxes and currency issuers. In addition, consumer liability from bank cards will also have to be addressed (currently $50 for credit cards). E-cash removes the intermediary from currency transactions, but this also removes much of the regulation of the currency in the current system. Tax questions immediately arise as to how to prevent tax evasion at the income or consumption level. If cash-like transactions become easier and less costly, monitoring this potential underground economy may be extremely difficult, if not impossible, for the IRS. The more daunting legal problem is controlling a potential explosion of private currencies. Large institutions that are handling many transactions may issue electronic money in their own currency. The currency would not be backed by the full faith of the United States, but by the full faith of the institution. This is not a problem with paper currency, but until the legal system catches up with the digital world, it may present a problem with cybercash.” For over twenty years we are still facing numerous legal questions surrounding eCash since it not only can cross borders but also because it’s difficult to track. These issues, especially the governmental oversight of currencies, will continue to be an issue with eCash use. To have a better understanding of the laws and regulations regarding eCash, here are how several different countries are handling cryptocurrencies like Bitcoin: The United States Bitcoin is legal in the United States and was classified as a convertible decentralized virtual currency by the U.S. Treasury in 2013. In 2015, the Commodity Futures Trading Commission, CFTC, started to classify Bitcoins as a commodity. Currently, New York state is the only state to have granted a license to a Bitcoin exchange in 2015. The company, itBit, now has a bank-like status in the U.S. Canada According to the Library of Congress, “Canada does not have a specific law or regulation that regulates bitcoins.” However, Bitcoin is not considered legal tender in Canada and has been briefly mentioned during anti-money laundering and anti-terrorist financing regulations for virtual currencies. Germany Germany considers Bitcoins like foreign currency. While not recognized as legal tender, Bitcoins “are units of value that have the function of private means of payment within private trading exchanges, or they are substitute currencies that are used as a means of payment in multilateral trading transactions on the basis of legal agreements of private law. ” The United Kingdom While Bitcoins are not regulated in the UK, it’s been reported that “Her Majesty’s Revenue and Customs has classed bitcoins as “single purpose vouchers,” rendering any sales of them liable to a value-added tax of 10–20%.” Japan As of this writing, Japan has no laws regarding the use of Bitcoins. Haruhiko Kuroda, the governor of the Bank of Japan (BOJ), has said that the BOJ was “researching issues of bitcoins, but I have nothing to say regarding bitcoins at the moment.” China China is one of the few countries in the world where Bitcoins are essentially illegal. In fact, the country announced the “Notice on Precautions Against the Risks of Bitcoins,” in 2013 stating that it prohibits banking and payment institutions from dealing in Bitcoins. India While there doesn’t appear to be any legal framework that regulates, restricts, or bans the use of Bitcoins in India, the country’s banking institutions have warned customers about the potential hazards that Bitcoin can present. This was most evident with the 2013 release of the Reserve Bank of India’s public notice. Russia Bitcoin is currently in dispute in Russia. In 2014, Legislation was introduced by the Ministry of Finance that would view Bitcoin transactions as a misdemeanor and would impose fines for dealing with cyber currencies and monetary surrogates. Brazil As noted by the Library of Congress, “On October 9, 2013, Brazil enacted Law No. 12,865, which created the possibility for the normalization of mobile payment systems and the creation of electronic currencies, including the Bitcoin. The Law provides, among other things, for the payment arrangements and payment institutions that comprise the Brazilian Payment System.” Overall, most central banks across the world are cautioning individuals from using virtual currencies like Bitcoin. In most cases though, most authorities are allowing citizens to use virtual currencies, even though they’re not accepted as legal tender. THE FUTURE OF ECASH Jerry Kuch, Yacov Yacobi, and Paul England, cryptography researchers at Microsoft, proclaimed that eCash will be the future of money. According to these researchers “we’ll carry little cards with computer chips called e-wallets and exchange encrypted bits of information for things we need.” They also predicted that we’ll be able to: Make one-click micro-payments online. Have anonymous payments online. Use non-traditional devices like a smartphone to make payments. Does any of this sound familiar? It should. Because those predictions have already come to fruition to make this an exciting time for electronic payments. But, where are we headed next? Dan Schutzer, Senior Technology Consultant, BITS, believes that the future of digital cash could go in four different directions: Digital cash would be replaced by an alternative, such as a pre-paid or debit card, or a new start-up payment processor that meets the security and privacy needs of customers. Digital cash will continue to grow and may even get embraced by governments and banks. This could already be in happening. In 2012 the MintChip was introduced by the Royal Canadian Mint. The chip was attached to SD cards and contained a private key that was signed by the mint. Digital cash will only exist in niche markets, similar to how PayPal started because it was the preferred payment gateway for eBay users. Bitcoin and other blockchain alternatives will be replaced by improved financial platforms. For the purpose of this guide, this is where we expect eCash will bring to the future of the payments industry. Bitcoin Will Be Replaced By the Blockchain One interesting development that has occurred is the work that IBM has contributed to the blockchain that could have serious implications. In March 2012. Reuters reported that IBM was working on a way to create a digital cash and payment system for major currencies. While this would use the blockchain idea, the “transactions would be in an open ledger of a specific country’s currency such as the dollar or euro.” In December 2015, this became a reality when it announced that the Open Ledger Project had been created. This new blockchain was supported by IBM, Intel, JP Morgan, the Linux Foundation, and several big banks. As stated in Fortune, “The Open Ledger Project isn’t proposing another cryptocurrency, but rather it wants to use blockchain technology to create tools to allow businesses to build a distributed ledger for anything they can dream up–from exchanging automotive titles in seconds to paying retail suppliers when a sale is made.” Because this new ledger is connected and distributed, the changes that have been made in the database will be easy to track, as well as be more difficult to forge. Currently, Honduras is using this technology to keep tabs on land titles and musicians are able to let fans pay them directly for their music. There won’t be just one blockchain. There were be several versions that could bring an end to Bitcoin, primarily because these specific blockchains will be more exclusive. Unlike Bitcoin, which basically allows anyone in, the blockchain will be a part of a limited community. Besides the Open Ledger Project, there are a number of innovative companies embracing the blockchain. Bitwage uses the blockchain to make international payroll cheaper. Voatz is aiming to make elections cheaper and more transparent through smartphones and the blockchain. And, Chronicled has merged RFID tags with the Blockchain in order to validate luxury goods which will curb counterfeit items. Mobile Payments Will Go Mainstream This shouldn’t come as a surprise. With more than 6 billion in the world having access to a mobile device, and that figure expected to grow, electronic payments via mobile devices will become more common. This will be accomplished with near-field communication. With NFC chips already installed in most mobile devices, the transfer of electronic payments is already taking place. Users simply have to download an app and will be able to transmit banking and payment data when placed near readers. And, unlike debit cards, mobile devices are capable of displaying the payment details in real-time. Mobile devices, however, are only a part of the potential that NFC chips present. NFC chips can be installed in wearable devices, like a watch, wristband, or ring. Instead of using plastic or even pulling out our phones, we’ll be able to tap or swipe or use a wearable device to complete a purchase. On top of NFC chips, the use of proximity beacons will enhance the growth of mobile payments. Companies will be able to target customers based on their location. For example, as a person approaches a store that they are already a customer of, the store will send you a coupon. The customer can then make the purchase through their mobile device and pick-up their item in swift motion. The convenience of making electronic payments with your mobile device isn’t the only benefit. As noted in Forbes, “Ridding ourselves of cash will require new thinking on customer interaction, crime, value, and even cars.” For example, you could take the EZ Pass idea and apply that to drive-throughs at fast food restaurants where payments are collected from a device located on your vehicle. Without cash registers and physical cash, the amount of robberies and pickpockets could be reduced. Governments could track how money is moved in real-time and use that information to solve problems like poverty. Check-out lines and transaction costs will also decrease. Beyond the blockchain, mobile devices, and wearables, we may even experience digital currency exchanges by using biometrics. Companies like Apple and Samsung are already using fingerprints to verify transactions. But, don’t be surprised if someday soon people will have chips implanted in their hands that will contain payment information. That’s not to say that cash will be completely eradicated. There may still always be a need for physical cash, however, digital cash will continue to evolve quickly.          E. XO  NPV TO Object in What Is an E-payment System?        An e-payment system is a way of making transactions or paying for goods and services through an electronic medium, without the use of checks or cash. It’s also called an electronic payment system or online payment system. Read on to learn more. The electronic payment system has grown increasingly over the last decades due to the growing spread of internet-based banking and shopping. As the world advances more with technology development, we can see the rise of electronic payment systems and payment processing devices. As these increase, improve, and provide ever more secure online payment transactions the percentage of check and cash transactions will decrease. Electronic payment methods One of the most popular payment forms online are credit and debit cards. Besides them, there are also alternative payment methods, such as bank transfers, electronic wallets, smart cards or bitcoin wallet (bitcoin is the most popular cryptocurrency). E-payment methods could be classified into two areas, credit payment systems and cash payment systems. 1. Credit Payment System Credit Card — A form of the e-payment system which requires the use of the card issued by a financial institute to the cardholder for making payments online or through an electronic device, without the use of cash. Still, one of the most popular e-payment methods are credit and debit card #payments E-wallet — A form of prepaid account that stores user’s financial data, like debit and credit card information to make an online transaction easier. Smart card — A plastic card with a microprocessor that can be loaded with funds to make transactions; also known as a chip card. 2. Cash Payment System Direct debit — A financial transaction in which the account holder instructs the bank to collect a specific amount of money from his account electronically to pay for goods or services. E-check — A digital version of an old paper check. It’s an electronic transfer of money from a bank account, usually checking account, without the use of the paper check. E-cash is a form of an electronic payment system, where a certain amount of money is stored on a client’s device and made accessible for online transactions. Stored-value card — A card with a certain amount of money that can be used to perform the transaction in the issuer store. A typical example of stored-value cards are gift cards. Pros and cons of using an e-payment system E-payment systems are made to facilitate the acceptance of electronic payments for online transactions. With the growing popularity of online shopping, e-payment systems became a must for online consumers — to make shopping and banking more convenient. It comes with many benefits, such as: Reaching more clients from all over the world, which results in more sales. More effective and efficient transactions — It’s because transactions are made in seconds without wasting customer’s time. It comes with speed and simplicity. Convenience. Customers can pay for items on an e-commerce website at anytime and anywhere. They just need an internet connected device. As simple as that! Lower transaction cost and decreased technology costs. Expenses control for customers, as they can always check their virtual account where they can find the transaction history. Today it’s easy to add payments to a website, so even a non-technical person may implement it in minutes and start processing online payments. Payment gateways and payment providers offer highly effective security and anti-fraud tools to make transactions reliable.  E-commerce, as well as m-commerce, is getting bigger year after year, so having an e-payment system in your online store is a must. It’s simple, fast and convenient, so why not have one? Still, one of the most popular payment methods are credit and debit card payments, but people also choose some alternatives or local payment methods. If you run an online business, find out what your target audience needs and provide the most convenient and relevant e-payment system. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++                                                   The Examples NPV concept in Energy Industries                                               E.XO  e- Money and working capital Turn Over  Working capital turnover ratio :   we examine the working capital turnover ratio. The working capital turnover ratio is an activity ratio that measures how many times working capital is used to generate sales, ie revenue, during a specific time period. As such, the ratio is a good indicator of company growth and liquidity and is calculated as follows: Working capital turnover  =  net sales working capital The ratio is sometimes known as the capital turnover ratio, as net sales to working capital, or by the acronym WCTO. Working capital is generally calculated as the company’s current assets less its current liabilities. Current assets include inventory and accounts receivable together with all other assets that will be held for less than 12 months. Current liabilities include accounts payable and payroll as well as any other liabilities, eg taxes, due in under a year. Example Company XYZ’s net sales year-to-date are €189,445, its current assets are €85,361, and its current liabilities are €43,262. Using the above equation, company XYZ’s working capital turnover is: 189,445 85,361  –  43,262 = 4.5 This means that during the period, the company has used (and of course replaced) its working capital 4.5 times to generate sales. Interpretation of results As with the majority of turnover ratios, the results should be interpreted on an industry sector basis to provide an accurate benchmark. However, in general, a high working capital turnover ratio usually indicates that the company is actively generating sales from its working capital, which is a positive indicator of future prospects. If the ratio increases significantly over the years however, or seems excessively high in relation to sector peers, this could indicate that the company is overtrading, ie taking on large orders that it does not have the resources to fulfil, and/or that a high proportion of the business’s assets are fixed assets (ie long-term assets such as buildings and machinery that are not easily converted into cash). Being top-heavy on fixed assets brings the available working capital down and means that the company lacks liquidity. This lack of liquidity could mean that the company would struggle to pay all of its debts. Meanwhile, a low working capital turnover ratio could point to inefficiencies as the company is not generating a significant return on its assets, which can signal financial difficulty. Some companies, particularly those that are going through periods of rapid growth, do however run with negative working capital as they are able to generate cash extremely quickly. This is often the case in the food outlet or restaurant industry as customers pay for the goods up front. If the company’s working capital turnover is negative, this may be a sign of an efficient business strategy, particularly if inventory is tactically low, ie just sufficient to meet demand. A well-known organisation that has operated using this business model is McDonalds. Many companies on the verge of bankruptcy also have negative working capital turnover though, so it is important to make sure that a company with negative working capital turnover has both low inventory and accounts receivable. If the company has high accounts receivable, this may indicate that it is not collecting its debts efficiently and that products have not been paid for up front. This, combined with a low inventory, would mean that the company is owed money and yet has no stock to sell to cover these debts. What is working capital? One of the most common needs for working capital occurs when a business must increase its inventory and accounts receivable in order to grow its customer base and revenues. Let’s first be clear on what the term ‘working capital’ really means. From an accounting standpoint, working capital = current assets – current liabilities. Current assets are short term in nature and can be converted quickly to cash, primarily accounts receivable and inventory. Current liabilities are obligations that come due within one year, primarily accounts payable and short term debt. The term “working capital” is often used incorrectly when talking about the financing needs of a business, especially for a start up business. For example, if a start up business is looking to finance typical operating expenses like an advertising budget and salaries for new employees, what it really needs is “long term capital” or equity. If a business is unable to support the expenses for advertising and salaries then most likely it is under-capitalized. If the company is projecting losses for the first year then most likely “equity” is what is needed, not “working capital.” Money used to fund growth in short term assets like inventory and accounts receivables is correctly considered “working capital” financing.  you need to understand how money flows through your business. In other words, you need to understand your “working capital cycle.” The cycle consists of: How quickly current assets (e.g. accounts receivables & inventory) are turned into cash How quickly that cash is used to pay current liabilities (e.g. accounts payable).  The working capital cycle is also referred to as the “Turnover Rates” for accounts receivables, inventory, and accounts payable. Turnover Rates.  Your business’s historical turnover rates are the first step in forecasting your growing working capital needs. You need to analyze your actual income statement and balance sheet to find out the following information:  How many days of inventory do I keep on hand (called inventory turnover)?  How many days do customers take to pay me (called accounts receivable turnover)? How many days do I take to pay my vendors (accounts payable turnover)?  The chart below shows how to calculate your annual turnover ratios.  Now that you have calculated your turnover rates, you are ready to forecast your working capital needs based on your plan for growth.  This growth will require carrying higher levels of inventory and accounts receivable, which will require additional working capital financing.  But how much is the question.  To do that calculation, you need to have a projected income statement, which includes both projected sales and cost of goods sold figures.  Using these figures and the working capital turnover ratios (see calculations above), you can get an estimate of how much additional working capital is needed to grow your business.  See the example below. Using these projected balances, you can figure out the changes to working capital by simply calculating the difference between your projected and historical balances for accounts receivable, inventory, and accounts payable. So what does this all mean?  Simply, your new working capital needs equals the change in Accounts Receivable plus Inventory minus Accounts Payable. For our example, if you project to grow your sales from $500,000 to $700,000, you will need additional working capital of $21,496.  How to fund additional working capital needs For small businesses who have been in operation and generating profits, you will most likely have reinvested some of the profits back into the business (this is called retained earnings). You reinvest your profits into your inventory, use the profits to carry increased levels of receivables or you use the profits to pay down your trade suppliers.  In essence, the retention of these profits increases the working capital that enables you to grow.  If you did not earn or retain sufficient profits to finance your own growth, however, you need to turn to borrowings for your increased working capital needs.  Generally speaking, small businesses find it difficult to obtain working capital financing from traditional banking sources. As a result, you might be tempted to turn to non-bank lending sources such as factoring, merchant cash advance, and online lenders. You should know that these sources of working capital financing charge annual percentage rates (“APR”) of 50% or more! What are alternative sources of working capital financing? Small business owners needing to finance inventory and accounts receivables may be eligible for financing from community lenders, such as Community Development Financial Institutions (“CDFIs”). CDFIs are nonprofit, private financial institutions that provide affordable lending to small business owners who are not being served by the banking community. Conclusion When growing your small business, you will need to make an additional investment in inventory and accounts receivable.  How much working capital you need can be estimated by creating projections that use your historical “Turnover Rates” for inventory, accounts receivable, and accounts payable as shown in the example above. Working capital is the difference between a company’s current assets and current liabilities. It is a financial measure, which calculates whether a company has enough liquid assets to pay its bills that will be due in a year. When a company has excess current assets, that amount can then be used to spend on its day-to-day operations. Current assets, such as cash and equivalents, inventory, accounts receivable and marketable securities, are resources a company owns that can be used up or converted into cash within a year. Current liabilities are the amount of money a company owes such as accounts payable, short-term loans and accrued expenses, which are due for payment within a year. Positive vs negative working capital Having positive working capital can be a good sign of the short-term financial health for a company because it has enough liquid assets remaining to pay off short-term bills and to internally finance the growth of their business. Without additional working capital, a company may have to borrow additional funds from a bank or turn to investment bankers to raise more money. Negative working capital means assets aren’t being used effectively, and a company may a liquidity crisis. Even if a company has lots invested in fixed assets, it will face financial challenges if liabilities come due too soon. This will lead to more borrowing, late payments to creditors and suppliers and, as a result, a lower corporate credit rating for the company. When negative working capital is ok Depending on the type of business, companies can have negative working capital and still do well. Examples are grocery stores like Walmart or fast-food chains like McDonald’s that can generate cash very quickly due to high inventory turnover rates and by receiving payment from customers in a matter of a few days. These companies need little working capital. Products that are bought from suppliers are immediately sold to customers before the company even gets a chance to pays the vendor or supplier. In contrast, capital-intensive companies that manufacture heavy equipment and machinery usually can’t raise cash quickly, as they sell their products on a long-term payment basis. Since they can’t sell fast enough, cash won’t be available immediately during tough financial times, so having enough working capital is desirable. Adjustments to the working capital formula While the above formula and example are the most standard definition of working capital, there are other more focused definitions. Examples of alternative formulas: Current Assets – Cash – Current Liabilities (excludes cash) Accounts Receivable + Inventory – Accounts Payable (this represents only the “core” accounts that make up working capital in day-to-day operations of the business)  MANAGING WORKING CAPITAL Working capital management has an impact on the liquidity, profitability and financial health of the organization. If the following main components of Working Capital are managed, working capital as a whole can be managed: INVENTORY MANAGEMENT A balanced inventory should be maintained to optimize working capital requirements. Inventory should not remain idle nor should the company lose out on sales / production because it does not have sufficient inventory in hand. cash conversion cycle (CCC)  A higher, or quicker, inventory turnover decreases the cash conversion cycle (CCC). A lower, or slower, inventory turnover increases the CCC. The CCC measures the number of days it takes a company to generate and collect revenue from its inventory assets. Stated differently, the CCC measures the time it takes a company to purchase its inventory and then collect cash from its sales. Cash conversion cycle = days inventory outstanding + days sales outstanding - days payables outstanding A company's inventory turnover affects the CCC in that it is used in the calculation for days inventory outstanding: Days inventory outstanding = average inventory / cost of goods sold per day When a company's inventory turnover is high, meaning it cycles through inventory quickly, it reduces the average inventory, and therefore decreases the days inventory outstanding. When a company's inventory turnover is low, meaning inventory sits on its books for an extended period of time, it increases the average inventory, and therefore increases the days inventory outstanding. When the days inventory outstanding is low, it reduces the CCC. This means a company is able to collect cash from revenues quickly; the business is able to use its working capital in other areas. When the days inventory outstanding is high, it increases the CCC. This means it takes a company longer to collect its cash from revenues, which causes potential cash flow issues to arise when it company needs working capital.  What is a Working Capital Cycle? The Working Capital Cycle for a business is the length of time it takes to convert net working capital (current assets less current liabilities) all into cash.  Businesses typically try to manage this cycle by selling inventory quickly, collecting revenue from customers quickly, and paying bills slowly, to optimize cash flow.  the influence of e-money can change the value of accelerating cash on the turnover of working capital and investment and continuous innovation Steps in the Working Capital Cycle For most companies, the working capital cycle works as follows: The company purchases, on credit, materials to manufacture a product (for example, they have 90 days to pay for the raw materials). The company sells its inventory in 85 days, on average (days payable outstanding) The company receives payment from customers for the products sold in 20 days, on average. In the first step of the process, the company get the materials it needs to produce inventory but doesn’t initially have any cash expense (purchased on credit under accounts payable).  In 90 days’ time, it will have to pay for those materials.  Eighty-five (85) days after buying the materials, the finished goods are sold, but the company doesn’t receive cash for them initially (sold on credit under accounts receivable).  Twenty (20) days after selling the goods, the company receives cash, and the working capital cycle is complete. Working Capital Cycle Formula Based on the above steps, we can see that the working capital cycle formula is: Working Capital Cycle Sample Calculation Now that we know the steps in the cycle and the formula, let’s calculate an example based on the above information. Inventory days = 85 Receivable days = 20 Payable days = 90 Working Capital Cycle = 85 + 20 – 90 = 15 This means the company is only out of pocket of cash for 15 days before receiving full payment. Positive vs Negative Working Capital Cycle In the above example, we saw a business with a positive, or normal, cycle of working capital.  Sometimes, however, businesses enjoy a negative working capital cycle where they collect money faster than they pay off bills. Sticking with the above example, imagine now that the company decides to become a “cash only” business with its customers.  By only accepting cash (no credit cards or payment terms), its accounts receivable days become 0. Let’s use the same formula again and calculate their new cycle time. Inventory days = 85 Receivable days = 0 Payable days = 90 Working Capital Cycle = 85 + 0 – 90 = –5 Now, this means the company receives payment from customers 5 days before it has to pay its suppliers. Financing Growth and Working Capital Businesses with normal/positive cycles often require financing to cover the period of time before they receive payment from customers and clients.  The is especially true for rapidly growing companies, and hence the idea that it’s possible to “grow the company out of money.” To solve this problem, companies often arrange to have financing provided by a bank or other financial institution.  Banks will often lend money against inventory and will also finance accounts receivable. For example, if a bank believes the company is capable of liquidating its inventory at 70 cents on the dollar, it may decide to provide for 50% of the cost of the inventory (to give the bank a buffer in case the inventory has to be liquidated). Additionally, if a company sells products to businesses that have high creditworthiness, the bank may finance those receivables (also called “factoring”) by providing early payment. By combining one or both of the above two banking solutions, a company can reduce the capital required to finance their operations. Working Capital Cycle in Financial Modeling In financial modeling and valuation, one of the key set of assumptions that are made about a company is its accounts receivable days, inventory days, and accounts payable days. When building a financial model, it is important to clearly lay out these assumptions and understand their impact on the business. Operating working capital needs to be kept as low as possible, even down into negative values, in order to improve the cash position. To control the stock level, the purchasing volume needs be fine tuned to the latest sales trend and forecast. When you’re working on reducing the capital locked up in inventory, start by keeping inventory on hand levels low and ordering just-in-time inventory to meet your customer demands. Ideally your customers should be paying you before you need to pay your suppliers. The advantages are obvious: When your working capital is negative, you do not need to tap into your bank account when procuring inventory. As long as you’ve not paid your suppliers for the inventory on hand, you can cash in when it’s sold to the customer. Finally, you only pay the supplier only after you receive the cash from the customer. This way, you would receive a cash benefit from the supplier and have a positive cash balance. In this scenario, a growing business would not feel the strain of pre-financing a larger inventory level, as the inventory would be pre-financed by the suppliers. To unlock capital tied up in your inventory, you need: Supplier payment terms that are longer than the payment terms of the customer Inventory turnover that is faster than the payment term difference An effective way to control your inventory levels is to introduce maximum stock levels that keep the working capital low or even negative while balancing the benefits of lower cash-out with the potential reduction of some supplier discounts. Reducing Stock Levels Inventory management plays an important role in reducing working capital, as the goal is to sell out the inventory to the minimum stock level before the supplier needs to be paid. However, you also need to be careful of overselling, as this can cause you to end up in an out of stock situation. With an inventory management solution like TradeGecko, you’ll have access to sales intelligence reports that can help you decide on the optimal inventory levels for your product based on your sales history. Once you’ve set your optimal stock levels after taking customer demand and safety stock into account, the next step is to calculate your reorder points to ensure you’ll always have enough stock on hand for your customers. There is always the temptation for wholesalers to increase their order sizes for a supplier discount or rebate, which is why it’s important to set maximum stock levels for your products. To measure the benefits of the available cash, you have to look at your financing situation. Let’s assume that you have a company loan of $1 million. If you can reduce the stock level on average by $100,000, you can reduce the loan to $900,000. That way, you save the interest rate on the $100,000 as you do not need to finance the stock. If you keep the loan at $1 million or have no loan at all, you have just increased your cash position by $100,000. You can now use this money to invest in other opportunities for growing your business that will earn you more profit. In case you have an attractive investment opportunity but financing resources are used to the limit, you can look into freeing up cash from careful stock management to finance these investments. However, if you choose to maintain high inventory levels, you’ll face the opportunity costs of losing out on these growth opportunities. At the same time, additional side effects may complicate the assessment. For example, reducing the order size may result in higher handling costs even as it reduces the warehouse costs. As a business owner, you need to evaluate your specific business case and make sure the benefits outweigh the additional costs when deciding. Reducing Order Size Some suppliers require a minimum order quantity and this quantity could already be more than needed. In this case, you should start negotiating better terms to improve your cash flow management. When faced with a minimum order quantity, try to negotiate longer payment terms for this specific order or splitting payments in line with the expected sales of the product. A side note on negative working capital Negative working capital has many benefits to a business in stable times and times of growth, but it can become a risk when customer demand is shrinking. If sales are declining dramatically and aren’t anticipated in a reduced order size, you will face an increase in working capital and an increase to your expenses. At the same time, slow sales also result in a cash drain, leaving a business stuck with little available cash due to capital locked up in stock. For a B2B business, the absolute amount of working capital can be huge and the potential outflow of cash, significant. So as a business owner, you need to be prepared for this risk and have alternative financing options ready to minimize the impact to your business. Conclusion It is essential to manage your stock level according to your individual sales cycle and financing capabilities. If you place large orders to cash-in supplier discounts it might not be to your overall advantage. The best starting point is to find out the stock level that really supports your business at minimal cash out. Only afterwards you might consider extending an order and receive a supplier discount, because now you are aware of the extra cash required to get this discount. With this preparation you are in the position to reduce the working capital and improve your cash flow. That way, you can put yourself in a better position to control your spending - get discounts or expand the business.         F. XO  cash money rotation system in micro finance  Resources, events, agents (accounting model) Resources, events, agents (REA) is a model of how an accounting system can be re-engineered for the computer age. REA was originally proposed in 1982 by William E. McCarthy as a generalized accounting model, and contained the concepts of resources, events and agents (McCarthy 1982). REA is a popular model in teaching accounting information systems (AIS), but it is rare in business practice. Most companies cannot easily dismantle their legacy data warehouse systems or are unwilling to do so. Workday, Inc., IBM Scalable Architecture for Financial Reporting, REATechnology, and ISO 15944-4 are exceptions.[1] Fallon and Polovina (2013) have however shown how REA can also add value when modelling current ERP business processes by providing a tool which increases the understanding of the implementation and underlying data model. The REA model gets rid of many accounting objects that are not necessary in the computer age. Most visible of these are debits and credits—double-entry bookkeeping disappears in an REA system. Many general ledger accounts also disappear, at least as persistent objects; e.g., accounts receivable or accounts payable. The computer can generate these accounts in real time using source document records. REA treats the accounting system as a virtual representation of the actual business. In other words, it creates computer objects that directly represent real-world-business objects. In computer science terms, REA is an ontology. The real objects included in the REA model are: goods, services or money, i.e., resources business transactions or agreements that affect resources, i.e., events people or other human agencies (other companies, etc.), i.e., agents These objects contrast with conventional accounting terms such as asset or liability, which are less directly tied to real-world objects. For example, a conventional accounting asset such as goodwill is not an REA resource. There is a separate REA model for each business process in the company. A business process roughly corresponds to a functional department, or a function in Michael Porter's value chain. Examples of business processes would be sales, purchases, conversion or manufacturing, human resources, and financing. At the heart of each REA model there is usually a pair of events, linked by an exchange relationship, typically referred to as the "duality" relation. One of these events usually represents a resource being given away or lost, while the other represents a resource being received or gained. For example, in the sales process, one event would be "sales"—where goods are given up—and the other would be "cash receipt", where cash is received. These two events are linked; a cash receipt occurs in exchange for a sale, and vice versa. The duality relationship can be more complex, e.g., in the manufacturing process, it would often involve more than two events (see Dunn et al. [2004] for examples). REA systems have usually been modeled as relational databases with entity-relationship diagrams, though this is not compulsory. The philosophy of REA draws on the idea of reusable Design Patterns, though REA patterns are used to describe databases rather than object oriented programs, and are quite different from the 23 canonical patterns in the original designs pattern book by Gamma et al. Research in REA emphasizes patterns (e.g., Hruby et al. 2006). Here is an example of the basic REA pattern shown as an E-R diagram: The pattern is extended to encompass commitments (promises to engage in transactions, e.g., a sales order), policies, and other constructs. Dunn et al. (2004) provide a good overview at an undergraduate level (for accounting majors), while Hruby et al. (2006) is an advanced reference for computer scientists. Here is a diagram of an extended REA pattern (from Hruby et al. 2006) REA is a continuing influence on the electronic commerce standard ebXML, with W. McCarthy actively involved in the standards committee. The competing XBRL GL standard however is at odds with the REA concept, as it closely mimics double-entry book-keeping. REA is now recognised by The Open Group (OG) within the TOGAF® standard (an industry standard enterprise framework), as one of the modelling tools which is useful for modelling business processes.                                         The model Money Creation  We consider a closed economy that is composed of  N agents, one central bank and one commercial bank. The central bank is in charge of determining the amount of money base and the required reserve ratio. Agents are endowed with a certain amount of money at the very beginning of the model and then trade with each other randomly. The commercial bank provides depositing services to savers and lending services to borrowers. The economy is considered to be in an insufficient demand situation where extra supply of goods can be realized as long as there is extra demand.                                                                  Money Creation         money creation and money circulation in a credit economy. Our special attention is paid to the role of debt in the two processes. With the agent-based modeling approach, macro phenomena are well founded in micro-based causalities. A hypothetical economy composed of a banking system and multiple traders is proposed. Instead of being a pure financial intermediary, the banking system is viewed as the center of money creation and an accelerator of money circulation. Agents finance their expenditures not only by their own savings but also through bank loans. Through mathematical calculations and numerical simulation, we identify the determinants of money multiplier and those of velocity of money. In contrast to the traditional money creation model, the money multiplier is determined not only by the behavior of borrowing but also by the behavior of repayment as well. The velocity of money is found to be influenced by both money-related factors such as the expenditure habits of agents with respect to their income and wealth and debt-related factors such as borrowing and repayment behaviors of debtors and the reserve requirements faced by banks. Theoretical analysis The economic processes described above include two types of interactions: the interaction between agents and the banking system which constitutes the money creation process and the interaction among agents themselves which constitutes the income–expenditure process. Thanks to those debt-related behaviors, these two processes are not independent from each other, but intertwined with complicated feedback loops. For example, the behavior of lending of the banking system does not only changes the stocks of money and debt through the money creation process, but also enables borrowers to make debt-financed expenditure in addition to those financed by their own income or wealth, which then results in changes in the flows of income for others. On the other hand, the behavior of repayment, which is constrained by the income flow for indebted agents in the income–expenditure dynamics among exchanging agents, also affects the money creation process by annihilating money and debt simultaneously. Therefore, when we study the determinants for money multiplier and those for velocity of money circulation, we cannot isolate the two processes. In addition, we should be aware that there exist two different types of equilibrium where the artificial economy eventually falls into: the stock equilibrium where the stocks stop changing and the flow equilibrium where the flows stop changing. When we simulate the model under the initialization and follow the evolution of the stock variables (the money aggregate and the total amount of debt) and the flow variable (aggregate income/expenditure) as shown in Fig. 2 and Fig. 3 respectively, we can find that the stock equilibrium and the flow equilibrium are not reached at the same time. Fig. 2    Fig 3 With this in mind, we next calculate the equilibrium value for the money multiplier and velocity of money by employing the mean-field approximating approach.   The Conclusion   the behavioral foundations of the money creation and money circulation processes with an agent-based model. The role of debt is taken into special consideration, and the banking system is characterized as the center of money creation and the accelerator of money circulation. With the mean-field approximation method, we obtained the theoretical expressions of the money multiplier and the velocity of money and studied the dependence of these two variables on different parameters through computer simulation. As a result, three major conclusions can be drawn from these analyses. First, we found that the expenditure habits of the public determine the extent to which the economy relies on debt. A clear phase transition between a credit economy and non-credit economy is observed when people vary their propensity to spend. It is also proven that unlike the traditional money creation model, the money multiplier is influenced not only by the borrowing behavior that creates money but also the repayment behavior that destructs money as well. Finally, both money-related and debt-related factors, namely the expenditure habit of agents, the borrowing and repayment behavior of debtors and the monetary policies the banking system is subject to, are found to be the determinants of the velocity of money.                              Money supply Money supply data are recorded and published, usually by the government or the central bank of the country. Public and private sector analysts have long monitored changes in the money supply because of the belief that it affects the price level, inflation, the exchange rate and the business cycle.  The business cycle, also known as the economic cycle or trade cycle, is the downward and upward movement of gross domestic product (GDP) around its long-term growth trend.[1] The length of a business cycle is the period of time containing a single boom and contraction in sequence. These fluctuations typically involve shifts over time between periods of relatively rapid economic growth (expansions or booms), and periods of relative stagnation or decline (contractions or recessions). Business cycles are usually measured by considering the growth rate of real gross domestic product. Despite the often-applied term cycles, these fluctuations in economic activity do not exhibit uniform or predictable periodicity. The common or popular usage boom-and-bust cycle refers to fluctuations in which the expansion is rapid and the contraction severe.  In recent years economic theory has moved towards the study of economic fluctuation rather than a 'business cycle' – though some economists use the phrase 'business cycle' as a convenient shorthand.  The explanation of fluctuations in aggregate economic activity is one of the primary concerns of macroeconomics. The main framework for explaining such fluctuations is Keynesian economics. In the Keynesian view, business cycles reflect the possibility that the economy may reach short-run equilibrium at levels below or above full employment. If the economy is operating with less than full employment, i.e., with high unemployment, Keynesian theory states that monetary policy and fiscal policy can have a positive role to play in smoothing the fluctuations of the business cycle. Beside the Keynesian explanation there are a number of alternative theories of business cycles, largely associated with particular schools or theorists in heterodox economics. A common alternative within mainstream economics is real business cycle theory. Nowadays other notable theories are credit-based explanations such as debt deflation and the financial instability hypothesis. The latter two gained interest for being able to explain the subprime mortgage crisis and financial crises.  This theory explains the nature and causes of economic cycles from the viewpoint of life-cycle of marketable goods. The theory originates from the work of Raymond Vernon, who described the development of international trade in terms of product life-cycle – a period of time during which the product circulates in the market. Vernon stated that some countries specialize in the production and export of technologically new products, while others specialize in the production of already known products. The most developed countries are able to invest large amounts of money in the technological innovations and produce new products, thus obtaining a dynamic comparative advantage over developing countries. Recent research by Georgiy Revyakin proves initial Vernon theory and shows that economic cycles in developed countries overrun economic cycles in developing countries.[29] He also presumes that economic cycles with different periodicity can be compared to the products with various life-cycles. In case of Kondratiev waves such products correlate with fundamental discoveries implemented in production (inventions which form the technological paradigm: Richard Arkwright's machines, steam engines, industrial use of electricity, computer invention, etc.); Kuznets cycles describe such products as infrastructural components (roadways, transport, utilities, etc.); Juglar cycles may go in parallel with enterprise fixed capital (equipment, machinery, etc.), and Kitchin cycles are characterized by change in the society preferences (tastes) for consumer goods, and time, which is necessary to start the production. Simultaneous technological updates by all economic agents (as a result, cycle formation) would be determined by highly competitive market conditions: in case if a manufacturing technology at an enterprise does not meet the current technological environment, – such company loses its competitiveness and eventually goes bankrupt. If we consider two consumption paths, each with the same trend and the same initial level of consumption – and as a result same level of consumption per period on average – but with different levels of volatility, then, according to economic theory, the less volatile consumption path will be preferred to the more volatile one. This is due to risk aversion on part of individual agents. One way to calculate how costly this greater volatility is in terms of individual (or, under some restrictive conditions, social) welfare is to ask what percentage of her annual average consumption would an individual be willing to sacrifice in order to eliminate this volatility entirely. Another way to express this is by asking how much an individual with a smooth consumption path would have to be compensated in terms of average consumption in order to accept the volatile path instead of the one without the volatility. The resulting amount of compensation, expressed as a percentage of average annual consumption, is the cost of the fluctuations calculated by Lucas. It is a function of people's degree of risk aversion and of the magnitude of the fluctuations which are to be eliminated, as measured by the standard deviation of the natural log of consumption. Lucas' formula Robert Lucas' baseline formula for the welfare cost of business cycles is given by (see mathematical derivation below): {\displaystyle \lambda ={\frac {1}{2}}\sigma ^{2}\theta } where  {\displaystyle \lambda } is the cost of fluctuations (the % of average annual consumption that a person would be willing to pay to eliminate all fluctuations in her consumption),  {\displaystyle \sigma } is the standard deviation of the natural log of consumption and  {\displaystyle \theta } measures the degree of relative risk aversion.[6] It is straightforward to measure  {\displaystyle \sigma } from available data. Using US data from between 1947 and 2001 Lucas obtained  {\displaystyle \sigma =.032}. It is a little harder to obtain an empirical estimate of  {\displaystyle \theta }; although it should be theoretically possible, many controversies in economics revolve around the precise and appropriate measurement of this parameter. However it is doubtful that  {\displaystyle \theta } is particularly high (most estimates are no higher than 4). As an illustrative example consider the case of log utility (see below) in which case  {\displaystyle \theta =1}. In this case the welfare cost of fluctuations is {\displaystyle \lambda ={\frac {1}{2}}(.032)^{2}=.0005.} In other words, eliminating all the fluctuations from a person's consumption path (i.e., eliminating the business cycle entirely) is worth only 1/20 of 1 percent of average annual consumption. For example, an individual who consumes $50,000 worth of goods a year on average would be willing to pay only $25 to eliminate consumption fluctuations. The implication is that, if the calculation is correct and appropriate, the ups and downs of the business cycles, the recessions and the booms, hardly matter for individual and possibly social welfare. It is the long run trend of economic growth that is crucial. If  {\displaystyle \theta } is at the upper range of estimates found in literature, around 4, then {\displaystyle \lambda ={\frac {1}{2}}(.032)^{2}4=.002} or 1/5 of 1 percent. An individual with average consumption of $50,000 would be willing to pay $100 to eliminate fluctuations. This is still a very small amount compared to the implications of long run growth on income. One way to get an upper bound on the degree of risk aversion is to use the Ramsey model of intertemporal savings and consumption. In that case, the equilibrium real interest rate is given by {\displaystyle r=\rho +\theta g} where  {\displaystyle r} is the real (after tax) rate of return on capital (the real interest rate),  {\displaystyle \rho } is the subjective rate of time preference (which measures impatience) and  {\displaystyle g} is the annual growth rate of consumption.  {\displaystyle r} is generally estimated to be around 5% (.05) and the annual growth rate of consumption is about 2% (.02). Then the upper bound on the cost of fluctuations occurs when  {\displaystyle \theta } is at its highest, which in this case occurs if  {\displaystyle \rho =0}. This implies that the highest possible degree of risk aversion is {\displaystyle \theta ^{Max}=r/g=.05/.02=2.5} which in turn, combined with estimates given above, yields a cost of fluctuations as {\displaystyle \lambda ={\frac {1}{2}}(.032)^{2}2.5=.0013} which is still extremely small (13% of 1%). Mathematical representation and formula Lucas sets up an infinitely lived representative agent model where total lifetime utility ( {\displaystyle U}) is given by the present discounted value (with  {\displaystyle \beta } representing the discount factor) of per period utilities ( {\displaystyle u(.)}) which in turn depend on consumption in each period ( {\displaystyle c_{t}})[4] {\displaystyle U=\sum _{t=0}^{\infty }\beta ^{t}u(c_{t})} In the case of a certain consumption path, consumption in each period is given by {\displaystyle c_{t}^{cert}=Ae^{gt}} where  {\displaystyle A} is initial consumption and  {\displaystyle g} is the growth rate of consumption (neither of these parameters turns out to matter for costs of fluctuations in the baseline model, so they can be normalized to 1 and 0 respectively). In the case of a volatile, uncertain consumption path, consumption in each period is given by {\displaystyle c_{t}^{vol}=(1+\lambda )Ae^{gt}e^{-{\frac {1}{2}}\sigma ^{2}}\epsilon _{t}} where  {\displaystyle \sigma } is the standard deviation of the natural log of consumption and  {\displaystyle \epsilon } is a random shock which is assumed to be log-normally distributed so that the mean of  {\displaystyle ln(\epsilon _{t})} is zero, which in turn implies that the expected value of  {\displaystyle e^{-{\frac {1}{2}}\sigma ^{2}}\epsilon _{t}} is 1 (i.e., on average, volatile consumption is same as certain consumption). In this case  {\displaystyle \lambda } is the "compensation parameter" which measures the percentage by which average consumption has to be increased for the consumer to be indifferent between the certain path of consumption and the volatile one.  {\displaystyle \lambda } is the cost of fluctuations. We find this cost of fluctuations by setting {\displaystyle \sum _{t=0}^{\infty }\beta ^{t}u(c_{t}^{cert})=\sum _{t=0}^{\infty }\beta ^{t}u(c_{t}^{vol})} and solving for  {\displaystyle \lambda } For the case of isoelastic utility, given by {\displaystyle u(c_{t})={\frac {c_{t}^{1-\theta }-1}{1-\theta }}} we can obtain an (approximate) closed form solution which has already been given above {\displaystyle \lambda ={\frac {1}{2}}\sigma ^{2}\theta } A special case of the above formula occurs if utility is logarithmic,  {\displaystyle u(c_{t})=ln(c_{t})} which corresponds to the case of  {\displaystyle \theta =1}, which means that the above simplifies to  {\displaystyle \lambda =.5\sigma ^{2}}. In other words, with log utility the cost of fluctuations is equal to one half the variance of the natural logarithm of consumption.[6] An alternative, more accurate solution gives losses that are somewhat larger, especially when volatility is large.[7] Risk aversion and the equity premium puzzle However, a major problem related to the above way of estimating  {\displaystyle \theta } (hence  {\displaystyle \lambda }) and in fact, possibly to Lucas' entire approach is the so-called equity premium puzzle, first observed by Mehra and Prescott in 1985.[8] The analysis above implies that since macroeconomic risk is unimportant, the premium associated with systematic risk, that is, risk in returns to an asset that is correlated with aggregate consumption should be small (less than 0.5 percentage points for the values of risk aversion considered above). In fact the premium has averaged around six percentage points. In a survey of the implications of the equity premium, Simon Grant and John Quiggin note that 'A high cost of risk means that recessions are extremely destructive'.[9] Evidence from effects on subjective wellbeing Justin Wolfers has shown that macroeconomic volatility reduces subjective wellbeing; the effects are somewhat larger than expected under the Lucas approach. According to Wolfers, 'eliminating unemployment volatility would raise well-being by an amount roughly equal to that from lowering the average level of unemployment by a quarter of a percentage point                   G.XO.   e- Cash and e- Money on  Send and receive money instantly    All of our payment acceptance methods are quick, we aim to get our customers their hard earned money as quickly as possible. The quickest is our Digital Wallet which allows you to instantly pay and get paid using Due Cash. 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With our digital wallet, you'll be able to send and receive payments in real time using Due Cash. Feel free to send money anywhere in the world as our wallet works great in a global environment! Coming Soon!                                     H. XO    working capital impact cash flow    Working capital represents the difference between a firm’s current assets and current liabilities. Working capital, also called net working capital, is the amount of money a company has available to pay its short-term expenses. Positive working capital is when a company has more current assets than current liabilities, meaning the company can fully cover its short-term liabilities as they come due in the next 12 months. Positive working capital is a sign of financial strength. However, having an excessive amount of working capital for a long time might indicate the company is not managing their assets effectively. Negative working capital is when the current liabilities exceed the current assets, and the working capital is negative. Working capital could be temporarily negative if the company had a large cash outlay as a result of a large purchase of products and services from its vendors. However, if the working capital is negative for an extended period of time, it may be a cause of concern for certain types of companies, indicating that they are struggling to make ends meet and have to rely on borrowing or stock issuances to finance their working capital. Understanding Cash Flow Cash Flow is the net amount of cash and cash-equivalents being transferred in and out of a company.  Positive cash flow indicates that a company's liquid assets are increasing, enabling it to settle debts, reinvest in its business, return money to shareholders, pay expenses and provide a buffer against future financial challenges. Negative cash flow can occur if operating activities don't generate enough cash to stay liquid. This can happen if profits are tied up in accounts receivable and inventory, or if a company spends too much on capital expenditures. Understanding the cash flow statement – which reports operating cash flow, investing cash flow, and financing cash flow – is essential for assessing a company’s liquidity, flexibility, and overall financial performance. How Working Capital Impacts Cash Changes in working capital are reflected in a firm’s cash flow statement. Here are some examples of how cash and working capital can be impacted. If a transaction increases current assets and current liabilities by the same amount, there would be no change in working capital. For example, if a company received cash from short-term debt to be paid in 60 days, there would be an increase in the cash flow statement. However, there would be no increase in working capital, because the proceeds from the loan would be a current asset or cash, and the note payable would be a current liability since it's a short-term loan.  If a company purchased a fixed asset such as a building, the company's cash flow would decrease. The company's working capital would also decrease since the cash portion of current assets would be reduced, but current liabilities would remain unchanged because it would be long-term debt.  Conversely, selling a fixed asset would boost cash flow and working capital. If a company purchased inventory with cash, there would be no change in working capital because inventory and cash are both current assets. However, cash flow would be reduced by the inventory purchases.  The Bottom Line A company’s working capital is a core part of funding its daily operations. However, it's important to analyze both working capital and cash flow of a company to determine whether the financial activity is a short-term or long-term event. A boost in cash flow and working capital might not be good if the company is taking on long-term debt that it doesn't generate enough cash flow to pay off. Conversely, a large decrease in cash flow and working capital might not be so bad if the company is using the proceeds to invest in long-term fixed assets that will generate earnings in the years to come.                 I . XO   The Difference Between "Hard Money" and "Soft Money" Hard money and soft money are terms that can be understood in various contexts. In economics, it is often used to describe (hard) coin money and (soft) paper money, respectively. These terms can also be used to refer to political contributions in the United States, which can be made directly to a specific candidate (hard money) or indirectly to political parties and political action committees (soft money). The rules governing the two types of contributions differ, and it may be prudent to check these rules in detail before making a contribution.  Hard and soft money can also refer to how clients pay the brokers or financial services providers, where hard money refers to direct payments for services rendered (e.g. brokerage commissions) and soft money to payments for indirect items (e.g. in settling a costly error by providing free research). Soft money arrangements in the financial industry are common, but are must usually disclosed to stakeholders and regulators.  Hard Money When cash is contributed directly to a political candidate, it is known as a "hard money" contribution. These contributions may only come from an individual or a political action committee, and must follow the strict limits set forth by the Federal Election Commission (FEC). For example, during the 2017-2018 election cycle, donors were subject to the following limits: $5,000 per candidate, per election, from a non-connected committee that qualifies as a multi-candidate committee. Donating to a candidate or candidates in excess of those federal limits can result in criminal charges including fines and jail time for violating campaign finance laws. To each candidate or candidate committee per election To national party committee per calendar year To state, district & local party committee per calendar year To any other political committee per calendar year $2,500 $30,800 $10,000 (combined limit) $5,000 Soft Money When cash is contributed to a political party or political action committee (PAC) with no limits attached to the amount that can be received, this is known as a "soft money" contribution. The funds can come from individuals and political action committees as with "hard money," but they can also come from any other source, such as corporations. The law says this money can only be used for "party-building activities" such as advocating the passage of a law and voter registration, and not for advocating a particular candidate in an election. The supreme court case Citizens United says that soft money contributions can be unlimited in that they constitute a form of free speech that is protected by the First Amendment, although this ruling has remained controversial. PACs that receive unlimited funds as soft money cannot be directly linked to or directed by the political candidate or candidates that they support. This is an important caveat, since if it is found out that a candidate is dictating what message or television ad the PAC or Super PAC will air, they are considered to be directly influencing how the money is used, making it a hard money contribution—and violating campaign finance laws.     Hard Money vs. Soft Money: Difference Hard Money: In the United States, political contributions are usually divided into hard money and soft money. Hard money is the money given by a contributor directly to the presidential candidate, and is limited in amount, since it is governed by the regulations of the Federal Election Commission (FEC). The FEC stipulates the guidelines as to how one can contribute, in this case. It is given directly to a particular person for his/her election activities. Soft Money: Soft money is a political contribution that is unregulated. Labor unions and corporations are allowed to give soft money, only to parties, and cannot give them to individual candidates for federal office. This can be used for party-building activities, and cannot be used for a particular candidate. These funds are mostly used for advertisements and other activities. However, with the rising problems of unfair practices and corruption seeping in due to politics, the FEC sought to regulate soft money too. There are regulations on both hard money and soft money, as of today.                      Z . XO   Electronic Money to e- Cash Transformation What is Electronic Money Electronic money is money which exists in banking computer systems and is available for transactions through electronic systems. Its value is backed by fiat currency and it can be exchanged into physical form however its uses are often more convenient electronically. BREAKING DOWN Electronic Money Electronic money is used for purchases and transactions globally. While it can be exchanged for fiat currency, it is much more conveniently monitored and utilized through electronic banking systems and electronic processing. The value of electronic money is established by its fiat currency which makes it different from emerging cryptocurrencies. Electronic money is backed by the central bank system. However, In the United States, only a small fraction of the currency is utilized in physical form. The remaining percentage of it is held in bank vaults and also against collateral. Currency in Circulation Electronic money can be held in various accounts. Most individuals and businesses store their money with banks which provide electronic records of the cash on deposit. Other forms of stored value electronic money include digital wallets such as PayPal and Square or prepaid cards which allow users to deposit fiat currency for electronic money. With all types of stored electronic money sources the need for fiat currency varies and as such the banking system provides for this through varying means. While banks transact fiat currency to electronic money for their customers they also hold that money in vaults at their physical locations. Since the use of electronic money is more common than physical currency, banks also deposit their cash with one of the 12 Federal Reserve banks across the nation. A primary function of the U.S. Federal Reserve and its 12 supporting banks is to manage the fiat currency in physical form. Thus, the Fed also has control over the money supply through its monetary policies and open market operations. The Fed also controls the reissuance of money and the printing of new money when fiat currency is no longer available for distribution. Electronic Payment Processing In the U.S. many people receive their paychecks through direct deposit, move money with electronic fund transfers, and spend money with credit and debit cards. While physical currency still has advantages in certain situations, its role has gradually diminished. Many consumers and businesses feel that electronic money is more secure because it is not easily lost or damaged and can be available for use at nearly all merchants across the U.S. Therefore, the U.S. financial market has a secure and well established infrastructure for transacting electronic money. The primary means for electronic money transactions is through payment processing networks. In the U.S. Visa and Mastercard are the two primary payment processing networks facilitating the transactions of electronic money across the nation. Banks and financial institutions partner with electronic money networking processors to issue their customers branded network cards which facilitate the transactions of electronic money from bank accounts to merchants. Digital wallets are also available following similar transaction protocals. Electronic money is also easily transacted through e-commerce allowing consumers to shop and purchase all types of goods and services online. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++                                 e-  MONEY = Mine On Natural Energy You                                 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++