wiktionary Dual may refer to Dual mathematics , a notion of paired concepts that mirror one another Dual category theory , a formalization of mathematical duality . . . see more cases in Category Duality theories Dual grammatical number , a grammatical category used in some languages Duality electrical circuits Dual diagnosis , a psychiatric diagnosis of co occurrence of substance abuse and a mental problem Dual fertilization, simultaneous application of a P type and N type fertilizer DUAL cognitive architecture , an artificial intelligence design model DUAL algorithm , or Diffusing update algorithm, used to update Internet protocol routing tables DUAL table , a special one row and one column database table Dual SIM cellphone Dual brand , a manufacturer of Hifi equipment Dual county , referring to a Gaelic Athletic Association county which traditionally competes at a similar level in both Gaelic football and hurling Media Dual album , an album of traditional Scottish and Irish music recorded by amonn Doorley, Muireann Nic Amhlaoibh, Julie Fowlis and Ross Martin, released 2008 Dual film Dual Heroes Dual Heroes , an episode of Heroes Dual Parallel Trouble Adventure , an anime series See also Special PrefixIndex Dual All page titles starting from Dual Duality disambiguation Duel disambiguation , a homonym Double disambiguation disambiguation de Dual es Dual fr Dual ja pl Dual sv Dual zh ... more details
News Tech Buzz DualLicensing Having Your Cake and Eating It Too Bot generated title ref ref http linux.sys con.com read 49061.htm DualLicensing Open Source Business Models Linux Bot generated title ref Since in most cases, only the copyright holder can change the licensing terms of a software, multi licensing is mostly used by companies that wholly own the software which they are licensing. Confusion ... Ruby , whose ruby License license contains explicit GPL duallicensing. Market segregation in proprietary ... watch.ac.uk resources duallicence2.xml DualLicensing information from OSS Watch Article http linuxjournal.com article 5923 The DualLicensing Model May 01 2002 by Don Marti Article http linuxinsider.com story 38172.html DualLicensing Having Your Cake and Eating It Too Nov 16 2004 by Philip H. Albert Article http linuxjournal.com node 1000069 Does duallicensing threaten free software? Jul 27 2006 by Glyn Moody Article http linux.sys con.com read 49061.htm DualLicensing Open Source Business Models by Heather Meeker Paper http opensource.mit.edu papers valimaki.pdf DualLicensing in Open ...Multi licensing is the practice of distributing software under two or more different sets of terms and conditions ... the number of licenses used, e.g. dual licensed for software licensed under two different ... usual motivations for multi licensing are license compatibility and market segregation based business models. Business models Multi licensing is commonly done to support free software business models ... 2009 02 10 author Digium Incorporated ref Multi licensing is used by the copyright holders of some ... use multi licensing to discriminate the rights and freedoms different recipients receive. Such licensing ... A second use of multi licensing with free software is for license compatibility, allowing ... MPL title Mozilla Code Licensing accessdate 2007 09 17 author Mozilla Foundation ref Perl , which is dual licensed under the GPL or Artistic License ref cite web url http dev.perl.org licenses title ... more details
Licensing Act may refer to several Act of Parliament Acts of Parliament Licensing Order of 1643 , an Act imposing pre publication censorship and prompting Milton to write Areopagitica Licensing of the Press Act 1662 , an Act regulating the printing industry Licensing Act 1737 , an Act for the licensing of theatrical premises Licensing Act 1872 , Licensing Act 1964 , Licensing Act 1988 , and Licensing Act 2003 , all Acts concerning the licensing of premises to sell alcohol The Licensing Scotland Act 1853 16 & 17 Vict. c.63 See also List of short titles disambig ... more details
Licensing Trusts were born out of the prohibition of alcohol era, partly as a reaction to the excesses of New Zealand s pioneering times, but also as a major social experiment. Invercargill Licensing Trust was the first Trust established in 1944. The uniqueness of Licensing Trusts revolves around A primary ... responsibility to efficiently operate commercial businesses profitably. Licensing Trusts belong ... to maximise profits. History The establishment of Licensing Trusts must be seen against the background ... of liquor licensing. Even though there was a desire to have alcohol available, there was wide spread concern that the abuses of the past were not resurrected. The birth of Licensing Trusts arose out of this conservative ... for trying something new. The Architect Of Licensing Trusts Henry Greathead Rex Mason KC CMG All great .... Who then was the originator of the licensing trust concept? It is folklore amongst licensing trusts ... the introduction of the first licensing trust legislation certainly suggests so. But the licensing .... The Carlisle Scheme was also significantly different in key areas from the licensing trust legislation ... for the licensing legislation and thus shepherded the licensing trusts acts through Parliament ... evidence too that Mason was strongly committed to the concept of licensing trusts the Hansard ... in 1947 and his ordering of the ballot paper, and his personal papers. While not all Licensing Trusts ... of model hotels in the Invercargill licensing district in the interests of the public well being, and of providing ... of the profits for public purposes. The Invercargill Licensing Trust Act 1944 came into force on 17 April 1944. The Masterton Licensing Trust Act followed in December 1947, and the Licensing Act in 1949. Trusts Established, and Demised 28 Licensing Trusts were established, 19 remain active today .... Licensing Trusts were moderating the use of alcohol in their communities long before harm minimisation ... Community ownership, as exampled in Licensing Trusts, has endured and endeared itself as a concept ... more details
Licensing of patents Stick licensing is the practice of licensing a patent or other form of intellectual property where the patent holder threatens to sue the licensee for patent infringement if the licensee does not take a license. ref http iplcllc.com docs Article OutsideHelp.pdf Charles R. Neuenschwander, Licensing Patents in Unfriendly Waters The Use of Outside Help in Assertive Programs , The Licensing Journal, February 2004 ref In contrast to the stick licensing, the carrot licensing is a friendly approach in luring the target to adopting one s invention and taking a license . ref Matthew Y Ma, Fundamentals of patenting and licensing for scientists and engineers , World Scientific, 2009, ISBN 9812834206, 9789812834201, p 188. ref References reflist See also Carrot and stick Patent troll law stub Category Business law Category Intellectual property law Category Licenses ... more details
Image HDMI Logo.svg right 256px HDMI Licensing , limited liability company LLC was founded by Hitachi, Ltd. Hitachi , Panasonic , Philips , Silicon Image Inc. Silicon Image , Sony , Thomson SA Thomson RCA and Toshiba and is their licensing vehicle for the HDMI standard. External links http www.hdmi.org HDMI Licensing, LLC http www.hdmi.org pdf HDMI Final brochure.pdf HDMI Final brochure and the http www.hdmi.org pdf HDMI Insert FINAL 8 30 06.pdf HDMI 1.3 Update Hitachi Philips Toshiba Category Licensing Category Film and video technology Category Companies established in 2002 ... more details
Unreferenced date January 2011 Floating licensing is a software license software licensing approach in which a limited number of licenses for a software application are shared among a larger number of users over time. When an authorized user wishes to run the application they request a license from a central license server. If a license is available the license server allows the application to run. When they finish using the application, or when the allowed license period expires, the license is reclaimed by the license server and made available to other authorized users. The license server can manage licenses over a local area network , an intranet or virtual private network , or the Internet . Floating licensing, also sometimes known as concurrent licensing or network licensing, is often used for high value applications in corporate environments, such as electronic design automation or engineering tools. See also Software metering License manager License borrowing License queuing Category Software licenses Category System administration de Floating License Server fr Licence flottante ... more details
A cross licensing agreement is a contract between two or more parties where each party grants rights to their intellectual property to the other parties. Patent law Licensing of patents In patent Patent legal concepts law , a cross licensing agreement is an agreement according to which two or more parties grant a license to each other for the exploitation of the subject matter claim patent claim ed in one or more of the patents each owns. ref http books.google.com books?hl en&lr &id Nc33ZS5nRa0C&oi fnd&pg PA119&dq 22cross license 22&ots N1uqVPQXMa&sig A0DT6eajD67L S174aIETN66YXM PPA119,M1 Shapiro, Carl, Navigating the Patent Thicket Cross Licenses, Patent Pools, and Standard Setting Innovation Policy and the Economy , MIT Press2001, p119 et seq. ref Very often, the patents that each party owns covers different essential aspects of a given commercial product. Thus by cross licensing, each party maintains their freedom to bring the commercial product to market. The term cross licensing implies that neither party pays monetary royalties to the other party, however, this may be the case. For example, Microsoft and JVC entered into a cross license agreement in January 2008. ref http www.betanews.com ... infringement lawsuit. Parties that enter into cross licensing agreements must be careful not to violate ... TFEU , previously Art. 81 and 82 of the EC Treaty , abuse of dominant position, etc. as well as licensing ... Mark Nowotarski, Introducing Patents into a Major Service Industry Licensing Executives Society ... of cross licensing is that it is ineffective against patent holding companies . The primary ... software may involve a combination of patent, copyright, and trademark licensing. See also Defensive termination Licensing strategic alliance Licensing Executives Society International Patent ... Example of patent cross licensing agreement http blogs.zdnet.com microsoft ?p 5346&tag nl.e539 Microsoft having issues with Amazon over cross licensing Category Strategic alliances Category ... more details
A Licensing Factor is a protein or complex of proteins that allows an origin of replication to begin DNA replication at that site. They are thought to primarily occur in Eukaryotes Eukaryotic cells , since Prokaryotes use simpler systems to initiate replication. Function of licensing factors Origins of replication represent start sites for DNA replication and so their firing must be regulated to maintain the correct Karyotype of the cell in question. The origins are required to fire only once per cell cycle , an observation that lead to the postulated existence of licensing factors by biologists in the first place. If the origins were not carefully regulated then DNA replication could be restarted at that origin giving rise to multiple copies of a section of DNA. This could be very damaging to cells and could have detrimental effects on the organism as a whole and so is to be avoided. The control that licensing factors exert over the cycle represents a flexible system, necessary so that different cell types in an organism can control the timing of DNA replication to their own cell cycle. Location of licensing factors The factors themselves are found in different places in different organisms. For example in metazoan organisms, they are commonly synthesised in the cytoplasm of the cell to be imported into the nucleus when required. The situation is different in yeast where the factors present are degraded and resynthesised throughout the cell cycle but are found in the nucleus for most of their existence. Example of licensing factor action in Saccharomyces cerevisiae , brewers ... and Cdt1 fulfil the role of licensing factors. They are only produced in G1 phase in addition to which .... Taking this into account it becomes clear that they can indeed act as licensing factors but only together. It has been suggested that the whole Pre Replication Complex be called the licensing factor ... links http www.jbc.org cgi content abstract 276 48 44905 Recent paper on licensing in human cells DNA ... more details
Refimprove date September 2010 Licensing means renting or leasing of an intangible asset. Examples of intangible ... Jordan or a brand The Ritz Carlton . An arrangement to license a brand requires a licensing agreement. A licensing agreement authorizes a company which markets a product or service a licensee to lease or rent a brand from a brand owner who operates a licensing program a licensor . ref name Brand Licensing Expert http www.brandlicensingexpert.com BrandLicensingExpert.com Peter Canalichio, Licensing ... brand managers enter or extend into new product categories via licensing they create an opportunity ... to enter a new market. To achieve this, licensees expect that the brand they are licensing ... objectives. The licensing contract forces the licensee to achieve certain sales targets ... business radio interviews swine flu expert dr elaina george brand licensing expert pete canalichio and batteries ... marketing Brand licensing is the process of creating and managing contracts between the owner of a brand ... period of time, within an agreed territory. Licensing is used by brand owners to extend a trademark ... ref Brand licensing is a well established business, both in the area of patent s and trademarks. Trademark licensing has a rich history in American business, largely beginning with the rise of mass ... as movies and later television became a staple of American business. The rise of brand licensing ... the brand licensing marketplace much more lucrative, as companies realized they could make real dollars ... under license by companies unrelated to the companies who own the brand. Brand licensing in India ... the No Rules brand in India. Character Licensing is another big licensing segment of brand licensing in India. The big players in the character licensing industry in India are Walt Disney , Viacom ... licensing in Italy Brand Licensing in Italy started in the seventies with very few Licensing Agencies ... International Characters , founded in 1973 by Mr. Gianfranco Mari contributed to create the licensing ... more details
Occupational licensing is the requirement to hold a license issued by a regulatory body or professional organisation, before practising a trade, profession or other occupation. Such requirements are commonly defended as a form of consumer protection against the risk of loss from unqualified or incompetent service providers. Economists including Milton Friedman have criticised occupational licensing as a restriction on competition . Some left wing critics agree, arguing that it serves as a way for members of certain trades to use state power to maintain their class power by restricting entry to the trade and making it difficult, though not impossible, for the poor to enter the professions. ref Magali Larson, The Rise of Professionalism A Sociological Analysis Univ of California Press, 1979 . ref Occupational research receives relatively sparse treatment in Labor Economics textbooks compared to other market regulations such as the minimum wage or labor unions. One possible explanation, advocated by libertarian Chicago School economists, is that labor economists favor government regulation. Given the amount of evidence pointing to the inefficiency of occupational licensing, labor economists may choose to avoid its treatment from sympathy for government regulation. ref Stephenson, E. Frank, and Erin E. Wendt. 2009. Occupational Licensing Scant Treatment in Labor Texts. Econ Journal Watch 6 2 181 194. http econjwatch.org articles occupational licensing scant treatment in labor texts ref References references Aspects of occupations Translations take off from the no wiki tag, when the article in the other language has been created es licencia ocupacional economics stub Category Labor economics Category Licensing ... more details
Wikify date August 2009 An authority that grants licenses, for example the Coast Guard or Department of Transportation the authority who has jurisdiction over either a geographical region, such as the coast of a country, or vessels plying their trade within its boundaries, or authority over its citizens, and meets their licensing requirements by providing testing, standards, renewal, etc. This authority extends to being able to revoke licenses in cases of negligence. For example, most US citizens would obtain their license s from the US Coast Guard and from the UK from the DOT there, however a US skipper might need a EU or UK ticket to operate a British flagged vessel, and would not normally be barred from obtaining one by virtue of lack of citizenship alone. In the US a Master Mariner takes an oath of allegiance and may be called into service in an auxiliary capacity, such as coast guard reserve. DEFAULTSORT Licensing Authority Category Licenses ... more details
Music licensing is the license d use of copyright ed music . Music licensing is intended to ensure that the owners .... Definitions The following words and phrases appear in discussion of music licensing license the right ... a recorded copy of a copyrighted work. Types of licensing contracts can include 1 A flat fee for a defined ... or the total revenues acquired as a result of its distribution. Most music licensing agreements include ... music 20licensing&f false title Kohn on music licensing Al Kohn, Bob Kohn Google Books publisher Books.google.com ... been pre negotiated for price, distribution and legal use, generally through licensing for film ... infringed on this original work. synchronization rights synchronization licensing the licensing ... program, video, DVD, etc. master use licensing the licensing of the recording of a musical work ... . Broadcasting Broadcasting, in the context of music licensing, means the playback of pre recorded ... for this service is used to cover licensing costs. Radio stations pay fees for the rights to broadcast music. Fees are paid to licensing bodies such as Broadcast Music Incorporated BMI and the American ... of music usage. BMI and ASCAP determine how to divide up the licensing profits among copyright ... title HowStuffWorks How Music Licensing Works publisher Entertainment.howstuffworks.com ... auditing the music being played. The audit results are submitted to the licensing relevant ... each artist has received. Home video Licensing issues are often encountered when television shows or films ... without incurring additional licensing fees. If the process of clearing the rights to the song ... make extensive use of copyrighted music such that the cost of after market licensing is high are withheld ..., who receives licensing revenues through the ASCAP. The music itself was written in 1893, and due to multiple ... http www.magnatune.com artists license license template.html Real world example of a licensing contract ... on music licensing in film and TV Category Music industry ... more details
confusing date February 2012 globalize date February 2012 Petroleum licensing or exploration license is the act of attributing licenses geographical areas at land and or sea to a company or a Join Venture , for the act of petroleum exploration. Each sovereign country distributes licenses in what is typically called a licensing round. The procedure for such, can greatly vary from country to country. The largest change is usually if it is a bid system or a grant system. In the bid system, each company or joint venture will offer a bid to gain the rights for the petroleum exploration at the license for a limited period of time. The highest bid, will obtain the rights. In the grant system, the license will be granted to the company or join venture that shows the highest interest and ability for the exploration of the license. This can be shown by the company experience, projected plan for the exploration by high investment and or longest presence on the country as a petroleum exploration company. Countries Licensing Rounds United Kingdom The Department of Energy and Climate Change DECC formerly the Department of Trade and Industry United Kingdom Department of Trade and Industry ref http og.decc.gov.uk en olgs cms licences lic rounds Departament of Energy and Climate Change License information data ref grants licences. The UKCS United Kingdom Continental Shelf is divided into quadrants of 1 degree latitude and one degree longitude. Each quadrant is divided into 30 blocks measuring 10 minutes of latitude and 12 minutes of longitude. Some blocks are divided further into part blocks ... via periodic now annual licensing rounds. Blocks are awarded on the basis of the work programme ... licensing rounds with less demanding terms and the fallow acreage initiative, where non active licences ... formed by re licensing relinquished areas. One of the attractiveness of the license blocks in Norway ... attributed in next licensing rounds, or even kept as relinquished if the government believes there is little ... more details
Expert subject Law date February 2009 Cleanup rewrite date February 2009 Nuclear Licensing blockquote In the following, the names of U.S. federal regulations will be abbreviated in the standard way. For example, Code of Federal Regulations, Title 10, Part 50, Section 59 will be given as 10CFR50.59 . A list of all U.S. federal regulations is provided at the Government Printing Office Site, or 10 CFR can be found at the Nuclear Regulatory Commission NRC website in their public document section http www.nrc.gov reading rm doc collections cfr . blockquote Nuclear power Nuclear materials and use of those materials see also Radioactive Materials typically requires a license of some sort from the government s in which the activities will be conducted. In the United States, licenses are issued either by the U.S. Nuclear Regulatory Commission , or in some cases by the individual states who have been delegated authority for some licensing activities, e.g. Arizona Arizona Radiation Regulatory Agency . Countries other than the U.S.A. use different licensing schemes, typically at the national level, with formal or informal participation at the local government level. For example, in Great Britain, the Health and Safety Executive http www.hse.gov.uk aboutus hsc iacs nusac index.htm oversees licenses and nuclear safety. United States In the United States, recent licensing activities have been focused on the next generation of nuclear reactors being planned. Efforts are underway to prepare the documents required by the U.S. Nuclear Regulatory Commission, including Environmental Reports also known as an Environmental Impact Report and Final Safety Analysis Reports, consistent with 10CFR50, 10CFR51 and 10CFR52. The regulations were revised to permit one step licensing in an effort to remove regulatory risk and better define the rules and processes needed to obtain a license for a nuclear power plant in the United States. The NRC now lists http www.nrc.gov reactors new reactor licensing.html ... more details
Mergeto Playboy Enterprises discuss Talk Playboy Enterprises Merge discussion date September 2009 The Playboy Licensing Group is a division of Playboy Enterprises . The Licensing segment licenses the Playboy name, the Rabbit Head design and other images, trademarks, and artwork, as well as the Spice name and trademarks for various men s and women s apparel, men s underwear and women s lingerie, accessories, collectibles, cigars, watches, jewelry, fragrances, small leather goods, stationery, music, eyewear, barware, and home fashions. In 2008, Playboy went into its first wine venture with Gargiulo Vineyards, producing a 12 bottle set featuring the images of playmate s from the 1960s and 70s. ref cite web url http www.novusvinum.com news latest news.html playboy title Buy It For The Wine accessdate 2008 11 05 work News Article publisher Novus Vinum date 2008 10 13 ref The Company s trademarks and copyrights are critical to the success and potential growth of all of its businesses. Its trademarks, which are renewable periodically and which can be renewed indefinitely, include Playboy, the Rabbit Head Design, Playmate and Spice. The Company also owns numerous domain names related to its online business. In 2005, Playboy moved into the top 50 World s largest licensors. ref cite web url http library.corporate ir.net library 10 100 100055 items 192613 PBY AR 2005.pdf title 2005 Annual Report accessdate April 7, 2007 date 2006 03 06 publisher Playboy Enterprises, Inc. , pg 4. ref Currently the Licensing division accounts for about 10 of the revenue of the Playboy Enterprises. ref cite web url http biz.yahoo.com e 070316 pla10 k.html accessdate April 7, 2007 publisher Yahoo.com title Form 10 K for PLAYBOY ENTERPRISES INC date 2007 03 16 Dead link date October 2010 bot H3llBot ref References Reflist playboy Category Companies based in Chicago, Illinois Category Playboy ... more details
Opium licensing is a policy instrument used to counter illegal drug cultivation and production. It has been used in countries such as Turkey and India to curb illegal opium production. The main mechanism used under opium licensing is a shift from cultivation and or production for the illegal market towards legal uses such as the production of essential medicines such as morphine and codeine . Proposal for Afghanistan COI date March 2010 Currently, an international think tank called The International Council on Security and Development ICOS , formerly known as The Senlis Council, is investigating whether this policy option could be used to solve the massive drug problem in Afghanistan . ref http www.senliscouncil.net Security and Development Policy Group The Senlis Council Bot generated title ref The organization is calling for a new village based poppy for medicines system that would be able to boost rural development, create stability and increase the grip the Hamid Karzai Karzai Administration has on isolated poppy growing areas in the country. Equally, cheap Afghan made could respond to the acute shortage of poppy based medicines internationally. In June 2007, the Council released a technical blueprint for a poppy for medicine project in Afghanistan and called for a pilot project to create Afghan Morphine to be put in place at the next planting season see The Senlis Council Poppy for Medicine http www.senliscouncil.net modules publications documents poppy medicine technical dossier Counterarguments The Bush Administration objected to ICOS s recommendations. In February 2007, the U.S. Department of State, through the Bureau of International Narcotics and Law Enforcement Affairs, issued a response to the ICOS s proposal. They argued that the price difference between licit ... licensing program. ref http www.state.gov p inl rls rpt 80734.htm U.S. Opposes Efforts to Legalize ... Reflist DEFAULTSORT Opium Licensing Category Economy of Afghanistan Category Illegal drug trade in Afghanistan ... more details
In mathematics , the dual group may be The Pontryagin duality Pontryagin dual of a locally compact abelian group The Langlands dual of a reductive algebraic group The Deligne Lusztig group Deligne Lusztig dual of a reductive group over a finite field. disambig ... more details
Unreferenced date December 2009 In functional analysis and related areas of mathematics a dual topology is a locally convex topology on a dual pair , two vector space s with a bilinear form defined on them, so that one vector space becomes the continuous dual of the other space. The different dual topologies for a given dual pair are characterized by the Mackey Arens theorem. All locally convex topologies with their continuous dual are trivially a dual pair and the locally convex topology is a dual topology. Several topological properties depend only on the dual pair and not on the chosen dual topology and thus it is often possible to substitute a complicated dual topology by a simpler one. Definition Given a dual pair math X, Y, langle , rangle math , a dual topology on math X math is a locally convex topology math tau math so that math X, tau simeq Y. math That is the continuous dual of math X, tau math is equal to math Y math up to linear isomorphism . Properties Theorem by George Mackey Mackey Given a dual pair, the bounded set topological vector space bounded set s under any dual topology are identical. Under any dual topology the same sets are barrelled set barrelled . Characterization of dual topologies The Mackey Arens theorem , named after George Mackey and Richard Friedrich Arens Richard Arens , characterizes all possible dual topologies on a locally convex space s. The theorem shows that the coarser topology coarsest dual topology is the weak topology , the topology of uniform convergence on all finite subsets of math X math , and the finer topology finest topology is the Mackey topology , the topology of uniform convergence on all weakly compact subsets of math X math . Mackey Arens theorem Given a dual pair math X, X math with math X math a locally convex space and math X math its continuous dual then math tau math is a dual topology on math X math if and only ... compact subsets of math X math DEFAULTSORT Dual Topology Category Topology of function spaces ... more details
In computer architecture , dual processor can refer to two different types of multiprocessing A computer with two central processing unit s A dual core central processing unit two processors combined into a single integrated circuit or package. disambig ca Processament dual ... more details
Dual Alliance may refer to The Dual Alliance 1879 between Germany and Austria Hungary The Franco Russian Alliance or Dual Alliance of 1894, between France and Tsarist Russia See also Triple Alliance disambiguation Disambig It was an alliance between France and Russia ... more details
Dual identity can refer to A secret identity , such as Clark Kent and Superman In mathematics, the coidentity of a dual group object or the counit of a coalgebra dab ... more details
congruent angles in the dual a tangential polygon , and conversely. For example, the dual of an acute ... of a dual polyhedron is the dual polygon of the corresponding vertex figure . Kinds of duality Rectification The simplest qualitative construction of a dual polygon is a Rectification geometry rectification ... 2008 As with dual polyhedra, one can take a circle be it the inscribed circle , midcircle , or circumscribed circle and perform polar reciprocation in it. Projective duality see also Dual curve Under projective duality , the dual of a point is a line, and of a line is a point thus the dual of a polygon is a polygon, with edges of the original corresponding to vertices of the dual and conversely. From the point of view of the dual curve , where to each point on a curve one associates the point dual to its tangent line at that point, the projective dual can be interpreted thus every point ... to the same vertex in the dual polygon at a vertex, the tangent lines to that vertex are all lines through that point with angle between the two edges the dual points to these lines are then the edge in the dual polygon. Combinatorially Combinatorially, one can define a polygon as a set of vertices ... an edge, and dually, two adjacent edges determine a vertex. Then the dual polygon is obtained ...,BC,CA , the dual triangle has vertices AB,BC,CA , and edges B,C,A , where B connects AB & BC, and so ... dual polyhedra . See also Dual curve Dual polyhedron Self dual polygon polygons DEFAULTSORT Dual Polygon ... more details
Dual purpose is a noun and adjective referring to things serving two purpose s. It can specifically refer to Dual use technology Dual purpose gun , naval artillery mounting designed to engage both surface and air targets Dual Purpose Improved Conventional Munition Dual sport motorcycle Dual purpose motorcycle , designed for both on and off road use London Fire Brigade equipment Dual Purpose Pump Ladder Dual purpose pump ladder , standard type of firefighting vehicle used by the London Fire Brigade Fighting knife Viaduct , road bridge aqueduct Dual purpose breed , could warrant its own article an animal or plant breed such as List of chicken breeds Dual purpose chickens , beef breeds beef dairy cattle , sheep Breeds sheep , List of goat breeds goats , duck s, geese , pig s, List of hop varieties hops , etc. that provide at least 2 kinds of resources food such as meat, eggs, and milk wool, hide or skills such as with some hunting dog s and pigeon s See also Dual disambiguation Purpose Hybrid disambiguation Multi purpose disambiguation Single purpose disambiguation disambiguation ... more details
Unreferenced date November 2006 In mathematics , the dual bundle of a vector bundle E X is a vector bundle E X whose fibers are the dual space s to the fibers of E . The dual bundle can be constructed using the associated bundle construction by taking the dual representation of the structure group . Specifically, given a local trivialization of E with Topology transition functions t sub ij sub , a local trivialization of E is given by the same open cover of X with transition functions t sub ij sub t sub ij sub sup T sup sup &minus 1 sup the inverse matrix inverse of the transpose . The dual bundle E is then constructed using the fiber bundle construction theorem . For example, the dual to the tangent bundle of a differentiable manifold is the cotangent bundle . If the base space X is paracompact and Hausdorff space Hausdorff then a finite rank vector bundle E and its dual E are isomorphic as vector bundles. However, just as for vector space s, there is no natural isomorphism canonical choice of isomorphism unless E is equipped with an inner product . DEFAULTSORT Dual Bundle Category Vector bundles ... more details
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