In mathematics , especially in linear algebra and matrix theory , the duplication matrix and the elimination matrix are linear transformation s used for transforming vectorization mathematics Half vectorization half vectorization s of matrix mathematics matrices into vectorization mathematics vectorizations or respectively vice versa. Duplication matrix The duplication matrix D sub n sup is the unique n sup 2 sup n n 1 2 matrix which, for any n n symmetric matrix A , transforms vech A into vec A D sub n sub vech A vec A . For the 2 2 symmetric matrix A math left begin smallmatrix a & b b & d end smallmatrix right math , this transformation reads math begin bmatrix 1&0&0 0&1&0 0&1&0 0&0&1 end bmatrix begin bmatrix a b d end bmatrix begin bmatrix a b b d end bmatrix math Elimination matrix The elimination matrix L sub n sup is the unique n n 1 2 n sup 2 sup matrix which, for any n n matrix A , transforms vec A into vech A L sub n sub vec A vech A . ref harvtxt Magnus Neudecker 1980 , Definition 3.1 ref For the 2 2 matrix A math left begin smallmatrix a & b c & d end smallmatrix right math , this transformation reads math begin bmatrix 1&0&0&0 0&1&0&0 0&0&0&1 end bmatrix begin bmatrix a c b d end bmatrix begin bmatrix a c d end bmatrix math . Notes references References Citation last1 Magnus first1 Jan R. last2 Neudecker first2 Heinz title The elimination matrix some lemmas and applications doi 10.1137 0601049 year 1980 journal Society for Industrial and Applied Mathematics. Journal on Algebraic and Discrete Methods issn 0196 5212 volume 1 issue 4 pages 422 449 . Jan R. Magnus and Heinz Neudecker 1988 , Matrix Differential Calculus with Applications in Statistics and Econometrics , Wiley. ISBN 0 471 98633 X. Jan R. Magnus 1988 , Linear Structures , Oxford University Press. ISBN 019520655X Category Matrices de Eliminationsmatrix ... more details
Wiktionarypar duplication duplicate duplicator Duplication , duplicate , and duplicator may refer to Art and fiction Duplicate 1998 film Duplicate 1998 film , a Bollywood film directed by Mahesh Bhatt Duplicate 2009 film Duplicate 2009 film , a 2009 Malayalam film Duplicates film Duplicates film , a 1992 television film starring Gregory Harrison and Kim Greist The Duplicate , a children s book by William Sleater Duplicate Boy , a DC comics superhero Batman Duplicate , a villain in Batman The Animated Series The Duplicate Man , an episode of The Outer Limits The Calvin and Hobbes Cardboard boxes duplicator machine in Calvin and Hobbes Biology and genetics Gene duplication , a process which can result in free mutation Chromosomal duplication , which can cause Bloom and Rett syndrome Polyploidy , a phenomenon also known as ancient genome duplication Enteric duplication cysts , certain portions of the gastrointenstinal tract Diprosopus , a form of cojoined twins also known as craniofacial duplication Diphallia , a medical condition also known as penile duplication Computing Duplicate code , a source code sequence that occurs more than once in a program Duplicate characters in Unicode Mathematics Duplication matrix , a linear transformation dealing with half vectorization Doubling the cube , a problem in geometry also known as duplication of the cube A type of multiplication theorem called the Legendre duplication formula or simply duplication formula Technology Duplicating machines , machines and processes designed to reproduce printed material, photocopying being among the best known today see also List of duplicating processes Loop bin duplicator , a device designed to copy pre recorded audio tapes Double track , a method of railway design also known as track duplication In Road Duplication road construction , conversion of a single carriageway into Dual carriageway Other ... Duplicita de Duplikation fr Duplication pt Duplica o ... more details
Wiktionary Elimination may refer to tocright Science and medicine Elimination reaction , an organic reaction in which two functional groups split to form an organic product Elimination, clearance medicine clearance of a drug or other foreign agent from the body Elimination, the destruction of an infectious disease in one region of the world as opposed to its eradication from the entire world Logic and mathematics Elimination theory , the theory of the methods to eliminate variables between polynomial equations. Elimination, the rule of inference known as the disjunctive syllogism Elimination, with steps of elimination over linear equalities, using the Gaussian elimination algorithm Elimination, for systems of linear inequalities, using the Fourier Motzkin elimination algorithm Games and competitions Elimination tournament disambiguation , a knock out style of tournament competition Elimination arcade game Elimination arcade game , 1974 arcade game by Atari Inc. subsidiary Key Games Elimination, a variant of the lifestyle invading game Assassin game Assassin , played with clothes pins Elimination from possibility of reaching postseason in a sports league Music Elimination Deceptikonz album Elimination Deceptikonz album , 2002 Elimination Jughead s Revenge album Elimination Jughead s Revenge album , 1994 Elimination , a 1989 single from Overkill s album The Years of Decay Elimination, a British Heavy Metal band, based in Ipswich Colchester. Accounting Elimination Accounting , the act of recording amounts in a consolidation statement to remove the effects of inter company transactions See also Eliminator disambiguation disambiguation cs Eliminace de Elimination es Eliminaci n fr limination he nl Eliminatie nn Eliminasjon pl Eliminacja ru sk Elimin cia zh ... more details
mathematics matrices used in mathematics , science and engineering . A matrix plural matrices ... , as shown at the right. Matrices have a long history of both study and application, leading to diverse ways of classifying matrices. A first group is matrices satisfying concrete conditions of the entries, including constant matrices. An important example is the identity matrix given by math I n begin ... bmatrix . math Further ways of classifying matrices are according to their eigenvalue s or by imposing conditions on the matrix product product of the matrix with other matrices. Finally, many domains, both in mathematics and other sciences including physics and chemistry have particular matrices that are applied ... page button. Matrices with explicitly constrained entries The following lists matrices whose entries are subject to certain conditions. Many of them apply to square matrices only, that is matrices with the same ... matrix A matrix partitioned in sub matrices called blocks. Block tridiagonal matrix A block matrix ... A matrix partitioned into sub matrices, or equivalently, a matrix whose entries are themselves matrices ... elements. Sparse matrix algorithms can tackle huge sparse matrices that are utterly impractical for dense ... mathematics Z matrix A matrix with all off diagonal entries less than zero. Constant matrices The list below comprises matrices whose elements are constant for any given dimension size of matrix. The matrix ... ij sub 1. Pascal matrix A matrix containing the entries of Pascal s triangle . Pauli matrices A set of three 2 2 complex Hermitian and unitary matrices. When combined with the I sub 2 sub identity matrix, they form an orthogonal basis for the 2 2 complex Hermitian matrices. Redheffer ... by one position. Zero matrix A matrix with all entries equal to zero. a sub ij sub 0. Matrices ... matrix with nonpositive off diagonal entries. Special case of an M matrix . Matrices satisfying conditions ... Notes Matrix congruence Congruent matrix Two matrices A and B are congruent if there exists an invertible ... more details
Image gene duplication.png thumb 200px Schematic of a region of a chromosome before and after a duplication event Gene duplication or chromosomal duplication or gene amplification is any duplication of a region ... retrotransposition event, or duplication of an entire chromosome. ref name Zhang 2003 cite journal author Zhang J title Evolution by gene duplication an update journal Trends in Ecology & Evolution ... of organisms. A duplication is the opposite of a Deletion genetics deletion . Duplications arise ... elements between two chromosomes. The product of this recombination are a duplication at the site of the exchange ... ref Gene duplication as an evolutionary event File EvolutionOfDuplicateGenes.png thumb right 500px Evolutionary fate of duplicate genes Gene duplication is believed to play a major role in evolution ... Raes 2004 cite journal author Taylor JS, Raes J title Duplication and divergence the evolution of new ... in his classic book Evolution by gene duplication 1970 . ref name Ohno 1970 cite book author Ohno, S. year 1970 title Evolution by gene duplication publisher Springer Science Business Media Springer Verlag isbn 0 04 575015 7 authorlink Susumu Ohno ref Ohno argued that gene duplication is the most ... Polyploidy genome duplication events are not uncommon. It is believed that the entire yeast genome underwent duplication about 100 million years ago. ref name Kellis 2004 cite journal author Kellis M, Birren BW, Lander ES title Proof and evolutionary analysis of ancient genome duplication in the yeast ..., wheat is hexaploid a kind of polyploid , meaning that it has six copies of its genome. The duplication ... duplication degeneration complementation model, ref name Force 1999 cite journal author Force A., Lynch ... gene is distributed among the two copies. The two genes that exist after a gene duplication event .... If they are paralogs and resulted from a gene duplication event, their functions are likely to be too ... pages 103 21 year 2006 month October pmid 17015230 doi 10.1016 j.neuron.2006.09.027 ref Gene duplication ... more details
Segmental duplications are segments of DNA with near identical sequence. ref http genomebiology.com 2003 4 4 R25 Genome wide detection of segmental duplications ref Segmental duplications SDs give rise to low copy repeats LCRs and are believed to have played a role in creating new primate genes as reflected in human genetic variation. In humans, chromosomes Y and 22 have the greatest proportion of SDs 50.4 and 11.9 respectively. ref Cite journal doi 10.1038 nrg1895 title Primate segmental duplications crucibles of evolution, diversity and disease year 2006 author Bailey, Jeffrey A. journal Nature Reviews Genetics volume 7 pages 552 64 pmid 16770338 last2 Eichler first2 EE issue 7 ref Detection Method The two widely accepted methods for SD detection are whole genome assembly comparison WGAC and whole genome shotgun sequence detection WSSD . See also Copy number variation Pseudogenes Molecular evolution Human genome Comparative genomics Inparanoid Tandem exon duplication References reflist Category Molecular genetics Category Mutation genetics stub ... more details
In linear algebra , a set of matrix mathematics matrices math A 1, ldots,A k math is said to Commute mathematics commute if they commute pairwise, meaning math A iA j A jA i math for every pair i , j equivalently, the commutator vanishes math A i,A j math more abstractly, if the algebra they generate is an abelian Lie algebra . Properties Commuting matrices over an algebraically closed field are Triangular matrix Simultaneous triangularisability simultaneously triangularizable indeed, over the complex numbers they are unitarily simultaneously triangularizable. Further, if the matrices math A i math have eigenvalues math alpha i,m , math then a simultaneous eigenbasis can be chosen so that the eigenvalues of a polynomial in the commuting matrices is the polynomial in the eigenvalues. For example, for two commuting matrices math A,B math with eigenvalues math alpha i, beta j, math one can order the eigenvalues and choose the eigenbasis such that the eigenvalues of math A B math are math alpha i beta i math and the eigenvalues for math AB math are math alpha i beta i. math This was proven by Frobenius , with the two matrix case proven in 1878, later generalized by him to any finite set of commuting matrices. This is generalized by Lie s theorem , which shows that any representation of a solvable Lie algebra is simultaneously upper triangularizable, the case of commuting matrices being the abelian Lie algebra case, abelian being a fortiori solvable. History References given in Harv Drazin 1951 . The notion of commuting matrices was introduced by Arthur Cayley Cayley in his Memoir on the theory of matrices, which also provided the first axiomatization of matrices. The first significant results proved on them was the above result of Frobenius in 1878. References reflist refbegin Citation first M. last Drazin journal Proceedings of the London Mathematical Society year 1951 series 3 volume 1 pages 222 231 doi 10.1112 plms s3 1.1.222 issue 1 title Some Generalizations ... more details
In mathematics , Krawtchouk matrices are matrix mathematics matrices whose entries are values of Krawtchouk polynomials at nonnegative integer points. ref N. Bose, Digital Filters Theory and Applications North Holland Elsevier, N.Y., 1985 ref ref http aps.arxiv.org abs quant ph 0702073 P. Feinsilver, J. Kocik Krawtchouk polynomials and Krawtchouk matrices, Recent advances in applied probability , Springer Verlag, October, 2004 ref The Krawtchouk matrix K sup n sup is an n 1 n 1 matrix. Here are the first few examples p center math K 0 begin bmatrix 1 end bmatrix qquad K 1 left begin array rr 1&1 1& 1 end array right qquad K 2 left begin array rrr 1&1&1 2&0& 2 1& 1&1 end array right qquad K 3 left begin array rrrr 1&1&1&1 3&1& 1& 3 3& 1& 1&3 1& 1&1& 1 end array right math p br p math K 4 left begin array rrrrr 1&1&1&1&1 4&2&0& 2& 4 6&0& 2&0&6 4& 2&0&2& 4 1& 1&1& 1&1 end array right qquad K 5 left begin array rrrrrr 1& 1& 1& 1& 1& 1 5& 3& 1& 1& 3& 5 10& 2& 2& 2& 2& 10 10& 2& 2& 2& 2& 10 5& 3& 1& 1& 3&5 1& 1& 1& 1& 1& 1 end array right . math center See also Matrix mathematics Square matrices Square matrix References reflist External links http chanoir.math.siu.edu kravchuk Krawtchouk encyclopedia Category Matrices Linear algebra stub ru sl Krav ukove matrike uk ... more details
The Pauli matrices are a set of three 2 × 2 complex number complex matrix mathematics matrices which ... sigma 3 sigma z begin pmatrix 1&0 0& 1 end pmatrix math These matrices were used by, then named after ... considered the zeroth Pauli matrix math sigma 0 math , the Pauli matrices span the full vector space of 2x2 Hermitian matrices. In the language of Quantum Mechanics quantum mechanics , hermitian matrices are observables, so the Pauli matrices span the space of observable s of the 2 dimensional complex ... matrices after multiplication by i to make them anti hermitian , also generate transformations in the sense of Lie algebra s the matrices math i sigma 1,i sigma 2,i sigma 3 math form a basis for math ... of 3 dimensional space. Moreover, the Algebra over a field algebra generated by the three matrices ... 3 begin pmatrix 1&0 0&1 end pmatrix I math where I is the identity matrix , i.e. the matrices are involutory. The determinant s and trace of a matrix trace s of the Pauli matrices are math det sigma ... , the Pauli matrices form an orthogonal basis, in the sense of Hilbert Schmidt operator Hilbert Schmidt , for the real Hilbert space of 2 × 2 complex Hermitian matrices, or the complex Hilbert space of all 2 × 2 matrices. Eigenvectors and eigenvalues Each of the hermitian Pauli matrices has ... vector operation the Pauli matrices are treated in a scalar like fashion, commuting with the vector basis elements. Commutation relations The Pauli matrices obey the following commutator commutation ... commute with the pauli matrices as well as math e i vec a cdot vec sigma I cos a i hat n cdot vec sigma ... matrices is to write the vector index math i math in the superscript, and the matrix indices ... relation for the Pauli matrices can be written math vec sigma cdot vec sigma sum i 1 3 sigma i alpha ... matrices, along with the identity matrix math I math , form an orthogonal basis for the complex Hilbert space of all 2 × 2 matrices mean that we can express any matrix math M math as math ... more details
Image Mat.svg right thumb The structure of a matrice of concepts The matrices of concepts are a conceptual tool put forth by philosopher Paul Franceschi, that aim at providing an alternative to the semiotic square described by Algirdas Greimas . To the difference of the semiotic square, a matrix of concepts is made up of 6 concepts, from which two are neutral, two are positive and two are negative. The relationships between the 6 concepts of the same matrix can be stated as follows A0 and 0 are dual or inverse A and are contraries A and are contraries A and are complementary, in the same way as and A and A are corollary, in the same way as and A0 and A are related, in the same way as A0 and A , 0 and , 0 and The applications of the matrices of concepts relate to paradigmatic analysis , but also to the dialectical plan , and more generally to the study of concepts . References Paul Franceschi, http www.paulfranceschi.com fr images documents plan dial en.pdf English translation of a paper initially published in French under the title Le plan dialectique pour une alternative au paradigme , Semiotica, vol. 146 1 4 , 2003, pp. 353 367 Andris Teikmanis, http www.ut.ee SOSE conference summer school 2011 papers Teikmanis TSSS2011.pdf The use of semiotic modelling as a research tool of art history , Tartu Summer School of Semiotics , August 2011 See also the semiotic square Category Semiotics fr Matrice de concepts ... more details
In mathematical physics , the gamma Matrix mathematics matrices , math gamma 0, gamma 1, gamma 2, gamma 3 math , also known as the Paul Dirac Dirac matrices , are a set of conventional matrices with specific ... dimensional gamma matrices . When interpreted as the matrices of the action of a set of Orthogonality ... and physics vectors in Minkowski space , the column vectors on which the matrices act become a space ... of vectors contravariant gamma matrices are math gamma 0 begin pmatrix 1 & 0 & 0 & 0 0 ... & 1 1 & 0 & 0 & 0 0 & 1 & 0 & 0 end pmatrix . math Analogue sets of gamma matrices can be defined in any dimension and signature of the metric. For example the Pauli matrices are a set of gamma matrices ... for the gamma matrices to generate a Clifford algebra is the anticommutation relation math displaystyle ... fundamental than the numerical values used in the gamma matrices. Covariant gamma matrices are defined ... nu I 4 math or a multiplication of all gamma matrices by math i math , which of course changes their hermiticity ... gamma matrices are then defined by math displaystyle gamma mu eta mu nu gamma nu left gamma ... of the gamma matrices is essential for them to serve as coefficients in the Dirac equation ... gamma matrices as follows math gamma 5 i gamma 0 gamma 1 gamma 2 gamma 3 begin pmatrix 0 & 0 & 1 & 0 ... 5 math uses the letter gamma, it is not one of the gamma matrices. The number 5 is a relic of old ... be seen by exploiting the fact that all the four gamma matrices anticommute, so math gamma 0 ... gamma 5 2 I 4. , math It anticommutes with the four gamma matrices math left gamma 5, gamma mu right ... NavContent style text align left From the definition of the gamma matrices, math gamma mu gamma nu gamma ... the trace of three gamma matrices. Step one is to put in one pair of math gamma 5 , math s in front ... of 2 div div class NavContent style text align left If an odd number of gamma matrices appear in a trace ... anticommute it with all of the other gamma matrices. This means that we anticommute it an odd number ... more details
matrix positive definite matrices. For general matrices, Gaussian elimination is usually considered ... tensors Gaussian elimination does not generalize in any simple way to higher order tensors matrices ...In linear algebra , Gaussian elimination is an algorithm for solving system of linear equations systems ... form in numerical analysis or row echelon form in abstract algebra . Gauss Jordan elimination , an extension ... row echelon form . Gaussian elimination alone is sufficient for many applications, and requires fewer calculations than the Gauss Jordan version. History The method of Gaussian elimination appears ... is now called Gaussian elimination a standard lesson in algebra textbooks by the end of the 18th century. Carl Friedrich Gauss in 1810 devised a notation for symmetric elimination that was adopted in the 19th ... over the history of the subject. Algorithm overview The process of Gaussian elimination has two parts. The first part Forward Elimination reduces a given system to either triangular form triangular ... substitution back substitution to find the solution of the system above. Stated equivalently for matrices ... turns out to be very useful to analyze the algorithm, is that Gaussian elimination computes a matrix decomposition . The three elementary row operations used in the Gaussian elimination multiplying ... matrix with invertible matrices from the left. The first part of the algorithm computes an LU decomposition ... & qquad L 2 2x && && y && && 2z && && 3 & qquad L 3 end alignat math Therefore, the Gaussian Elimination ... & 8 3 & 1 & 2 & 11 2 & 1 & 2 & 3 end array right math which, at the end of the first part Gaussian elimination ... math That is, it is in row echelon form . At the end of the algorithm, if the Gauss&ndash Jordan elimination ... of elementary row operations and the Gaussian elimination algorithm, the left block of B can be reduced ... Jordan elimination for finding inverses. If the algorithm is unable to reduce A to triangular form, then A is not invertible. General algorithm to compute ranks and bases The Gaussian elimination ... more details
Elimination tournament may refer to any of several types of tournament in which each player has a set number of losses before elimination from the competition. Single elimination tournament , in which a player is eliminated after losing to a single opponent Double elimination tournament , in which a player is eliminated after two losses Triple elimination tournament , a rare format in which a player is eliminated only after three losses See also Swiss system tournament Round robin tournament Disambig zh ... more details
Infobox Single Name Progress of Elimination Cover Progress of Elimination.jpg Artist Boss rapper Boss from Album Born Gangstaz B side Livin Loc d Released October 12, 1993 Format Gramophone record Vinyl , Cassette single Cassette , CD single CD Recorded 1993 Genre Hip hop music Hip hop Length 3 12 Label Def Jam Recordings Def Jam Writer Lichelle Laws Producer Def Jef Type singles Chronology Boss rapper Boss Last single Recipe of a Hoe br 1993 This single Progress of Elimination br 1993 Next single Progress of Elimination was the third and final single released from Boss rapper Boss debut album, Born Gangstaz . Unlike the first two singles from the album, Progress of Elimination failed to make it to any Billboard charts. Single track listing A Side Progress of Elimination LP Mix 3 12 Progress of Elimination Still Talkin Remix 3 29 Progress of Elimination Instrumental 3 29 Progress of Elimination Acapella 2 35 Progress of Elimination No Godamn Trak Remix 2 43 B Side Progress of Elimination Niggaz Iz Dyin Remix 3 39 Progress of Elimination Beatin Da Street Remix 3 39 Progress of Elimination Niggaz Iz Dyin Instrumental 3 39 Livin Loc d LP Mix 3 36 Livin Loc d Instrumental 4 09 Category 1993 singles Category Boss songs ... more details
Image Grieco elimination.png right 400px The Grieco elimination The Grieco elimination is an organic reaction describing the elimination reaction of an aliphatic primary alcohol through a selenide to a terminal alkene Ref Grieco Ref Sharpless . The alcohol first reacts with o nitrophenylselenocyanate and tributylphosphine to a selenide in a nucleophilic substitution on electron deficient selenium . In the second step the selenide is oxidized with hydrogen peroxide to a selenoxide in which elimination takes place with expulsion of a selenol in a fashion similar to that of the Cope elimination . This reaction takes part in the synthesis of ring C of the Danishefsky Taxol total synthesis Synthesis C ring Danishefsky Taxol synthesis . References Note Grieco Organoselenium chemistry. A facile one step synthesis of alkyl aryl selenides from alcohols Paul A. Grieco, Sydney Gilman, Mugio Nishizawa J. Org. Chem. 1976 41 8 1485 1486. DOI 10.1021 jo00870a052 Note Sharpless Olefin synthesis. Rate enhancement of the elimination of alkyl aryl selenoxides by electron withdrawing substituents K. Barry Sharpless and Michael W. Young J. Org. Chem. 1975 947 949. DOI 10.1021 jo00895a030 Category Elimination reactions Category Name reactions DEFAULTSORT Grieco Elimination nl Grieco eliminatie zh Grieco ... more details
Model Elimination is the name attached to a pair of proof procedure s invented by Donald W. Loveland, the first of which was published in 1968 in the Journal of the ACM. Their primary purpose is to carry out automated theorem proving , though they can readily be extended to logic programming , including the more general disjunctive logic programming . Model Elimination is closely related to Resolution logic resolution while also bearing characteristics of a Method of analytic tableaux Tableaux method. It is a progenitor of the SLD resolution procedure used in the Prolog logic programming language. While somewhat eclipsed by attention to and progress in Resolution theorem provers, Model Elimination has continued to attract the attention of researchers and software developers. Today there are several theorem provers under active development that are based on the Model Elimination procedure. References Loveland, D. W. 1968 Mechanical theorem proving by model elimination. Journal of the ACM, 15, 236 251. Category Automated theorem proving Category Logical calculi Category Logic in computer science ... more details
been accomplished, elimination operations may be transferred, if directed, to other U. S. Government ... elimination operations consist of four principal operational level tasks isolation exploitation destruction and monitoring and redirection. WMD elimination operations may be conducted during any phase of a combatant command s campaign or as an independent operation. That is, the four steps of WMD elimination ... operations. Most non DOD agencies require a secure environment to support WMD elimination ... for WMD elimination should be considered when planning or conducting operations in all WMD MMAs. See also Joint Elimination Coordination Element JECE Joint Task Force for Elimination of WMD JTF E DEFAULTSORT Elimination Category United States Department of Defense doctrine ... more details
Image EliminationReactionCyclohexene.svg frame right Elimination reaction of cyclohexanol to cyclohexene ... ref An elimination reaction is a type of organic reaction in which two substituent s are removed ... and unimolecular respectively. In most organic elimination reactions, hydrogens are lost to form ... that a molecule undergoes reductive elimination , by which the valence of an atom in the molecule decreases by two. An important class of elimination reactions are those involving alkyl halide s, with good leaving group s, reacting with a Lewis base to form an alkene . Elimination may be considered ... the E2 mechanism. E2 stands for bimolecular elimination. The fundamental elements of the reaction ... bond. C C molecular geometry Pi bond . Specificities E2 is a one step process of elimination ... E2 Elimination Reaction.png center 500px Scheme 1. E2 reaction mechanism An example of this type ... is linked from E1 E1 is a model to explain a particular type of chemical elimination reaction. E1 stands for unimolecular elimination and has the following specificities. It is a two step process of elimination ionization and deprotonation . Ionization the carbon halogen bond breaks to give a carbocation ... Image E1 eliminationNash2008.svg center 500px E1 elimination Nash 2008, antiperiplanar relationship in blue Only reaction product A results from antiperiplanar elimination, the presence of product ... s Image E1 Elimination Reaction.png center 600px Scheme 2. E1 reaction mechanism An example in scheme ..., the E1 pathway can be favored by increasing the heat. E2 and E1 elimination final notes The reaction ... leaving group. There is a certain level of competition between elimination reaction and nucleophilic ... sub 2 and also between E1 and SN1 reaction S sub N sub 1 . Substitution generally predominates and elimination occurs only during precise circumstances. Generally, elimination is favored over substitution ... ion. In accordance with a E2 elimination the reaction with t butyl chloride results in a KIE ... more details
The Chugaev elimination is a chemical reaction that involves the elimination of water from alcohol s to produce alkene s. The intermediate is a xanthate . It is named for its discoverer, the Russian chemist Lev Aleksandrovich Chugaev . Image Cugaevalg.png 700px In the first step, a potassium xanthate is formed out of the alkoxide and carbon disulfide CS sub 2 sub . With iodomethane , it is transformed into a xanthate . Image Chugaev2.gif At about 200 C, the alkene is formed by a elimination reaction syn elimination . In a 6 membered cyclic transition state the hydrogen atom is moved from the C atom to the sulfur. The side product decomposes to carbonyl sulfide OCS and methanethiol . Image Chugaev3.gif References cite book last Latscha first Hans P. title Chemie Basiswissen location Berlin year 2002 publisher Springer cite journal title Ueber das Thujene Thujen , ein neues bicyclisches Terpen author Lev Aleksandrovich Chugaev L. Tschugaeff journal Berichte der deutschen chemischen Gesellschaft volume 33 issue 3 pages 3118 3126 year 1900 url doi 10.1002 cber.19000330363 Category Elimination reactions Category Name reactions de Tschugajew Reaktion es Reacci n de Chugaev id Eliminasi Chugaev nl Chugaev reactie ja ru zh ... more details
Mortgage elimination is the term commonly used to describe a type of mortgage fraud in the United States . In this scam, the promoter first convinces a mortgage law mortgage holder lender that the debt that has been contracted is invalid or legally unenforceable, usually due to a combination of technicalities in the Security finance note , Trust deed real estate deed of trust , or other loan documentation signed the promoters often link their rationale for debt elimination to illegality of certain lending practices, the Federal Reserve , and the monetary system of the United States in general. Through a series of illegal maneuvers involving the creation of a trust, a demand letter, and a false re conveyance of title, the promoter and the original mortgage holder concert to create the appearance of a title free of liens and encumbrances so that another loan may be taken out on the property. ref http www.southcoasttoday.com apps pbcs.dll article?AID 20070325 NEWS 703250408 ref The United States FBI has put out specific warnings regarding this type of scam. ref http www.fbi.gov page2 dec05 tipstopreventfraud121405.htm ref The Dorean Group is a high profile promoter of this type of scam. ref http www.eastbayexpress.com eastbay dirty deeds Content?oid 1080755 ref ref http www.mortgagefraudblog.com index.php weblog permalink dorean group principals found guilty ref References reflist External links http www.the7thfire.com debt elimination mortgage elimination services.htm The 7th Fire a popular site advocating mortgage elimination Fraud Scams and confidence tricks Category Mortgage Category Finance fraud finance stub ... more details
Quantifier elimination is a concept of simplification used in mathematical logic , model theory , and theoretical computer science . One way of classifying Well formed formula formulas is by the amount of quantifiers quantification . Formulae with less Quantifiers Nesting depth of quantifier alternation are thought of as being simpler, with the quantifier free formulae as the simplest. A logical theory theory has quantifier elimination if for every formula math alpha math , there exists another formula math alpha QF math without quantifiers which is Logical equivalence equivalent to it modulo the theory . Examples Examples of theories that have been shown decidable using quantifier elimination ... elimination can also be used to show that combining Decidability logic decidable theories leads to new ... and decidability If a theory has quantifier elimination, then a specific question can be addressed ... we call it a quantifier elimination algorithm . If there is such an algorithm, then Decidability ... elimination algorithms to decide validity of sentences. Related concepts Various model theoretic ideas are related to quantifier elimination, and there are various equivalent conditions. Every theory with quantifier elimination is model complete . A first order theory T has quantifier elimination if and only ... in B and C . Basic ideas To show constructively that a theory has quantifier elimination, it suffices ... x. lnot F. math History In early model theory, quantifier elimination was used to demonstrate that various ... technique was to show first that a theory admits elimination of quantifiers and thereafter prove .... Theories could be decidable yet not admit quantifier elimination. Strictly speaking, the theory of the additive natural numbers did not admit quantifier elimination, but it was an expansion of the additive ... to ensure that it admits quantifier elimination for example, one can introduce a relation symbol ... field DCF . See also elimination theory conjunction elimination mathematical elimination References ... more details
Unreferenced auto yes date December 2009 Elimination races in bicycle racing are a form of race wherein during the course of the race, certain participants are eliminated through various criteria. The most common types of elimination races are the Miss and Out and the Win and Out. Miss and Out The Miss and Out or Devil Take the Hindmost is a race run for individual competitors or, more rarely, for teams of two relaying each other as in the Madison cycling Madison . At the end of every lap or every set number of laps the last rider to cross the line is eliminated from the race. When just a handful of riders remain, they sprint for the finish. Tactically, the real racing in a devil happens at the back of the field. With riders at the front riding steadily and those behind moving up on the elimination laps to find a safe spot, the race favours riders with nerve and track craft. The telescoping of the field means crashes are more common than in other races, especially among inexperienced riders. Win and Out The Win and Out is similar to the Miss and Out, however, rather than the last rider being eliminated the first rider to cross the line is removed from the race. The first rider removed wins first place, the second rider removed wins second place, and so on. Portal Cycling Track cycling DEFAULTSORT Elimination Races Category Track cycling Cycling stub de Ausscheidungsfahren es Carrera de eliminaci n fr Course l limination ... more details
Elimination Blackjack is a tournament format of blackjack invented by Russ Hamilton , and is played on the Ultimate Blackjack Tour and in various Casino casinos . It combines the game of blackjack with elements of No Limit Texas Hold Em . Unlike Texas Hold Em tournaments, players are still competing against the same dealer that is why the results of most players at the table are likely to be the same ref cite web url http www.blackjackinfo.com bjtourn basics.php title Blackjack Tournament Strategy Basics publisher BlackjackInfo.com accessdate 2010 06 17 ref . UltimateBet.com, a sponsor of the Ultimate Blackjack Tour , offers online elimination blackjack tournaments. ref http www.blackjacktactics.com blackjack elimination Blackjack Tactics ref Rules A round of elimination blackjack in most cases is thirty hands in length. Depending upon the organization hosting the event, a player will start with between 10,000 and 100,000 in chips. While certain organizations have their own house rules, elimination blackjack usually follows the following rules The house must hit on soft 17 and anything below, and must stay on hard 17 and anything above. A player may split pairs up to four times with the exception of aces. Some rule sets also allow splitting different cards valued at 10, such as a queen and a jack. A shoe of six decks is used. A player s bet must stay within the minimum and maximum bet allowed at the table this rule is excluded in the World Series of Blackjack . The maximum bet is usually at least several times bigger than the starting chip stack. A player may surrender their hand and thus recover one half of their original bet. A player may buy insurance if the up card for the house ... per table. A player has twenty five seconds in a normal hand to make a decision. In an elimination ... cutoff points are hands 8, 16, and 25 so called elimination hands . A player is always eliminated from the game in an elimination hand, even if a player has been eliminated in the previous hand. Winning ... more details
Infobox Album See Wikipedia WikiProject Albums Name The Process of Elimination Type studio Artist Leng Tch e Cover Cover tpoe large.jpg Released June 28, 2005 Recorded CCR studios in Belgium Genre Deathgrind Length 33 28 Label Relapse Records Producer Reviews Last album ManMadePredator br 2003 This album The Process of Elimination br 2005 Next album Amusical Propaganda for Sociological Warfare br 2006 The Process of Elimination is Leng Tch e s third full length album and their first on Relapse Records . A video was made for Derisive Conscience. Track listing The Fist Of The Leng Tch e 01 50 Don t Touch My Spandex 01 22 Overkill Bill 0 51 Another Hit Single 02 07 Bobby Joe s Slumber Party 0 37 Remote Controlled 01 22 http www.razorgrind.com 1 mp3 glamour.mp3 Glamourgirl Concubine 01 31 Ingest Dissent 01 11 Schematic 0 45 Man s Inhumanity To Man 0 39 Motorgrinding 01 27 Fat Camp 01 11 Icon Resizer 01 34 http shop.relapse.com dbmedia video Leng Tche Derisive Conscience.wmv Derisive Conscience 01 22 Patriotic Pleasure 01 11 The Plastic Motive 01 14 Testosterone Collar 01 05 Scene Scenery 02 04 http www.razorgrind.com 1 mp3 clarity.mp3 Clarity Denied 01 37 Mediocrity Contest 01 11 P.I.M.P. 02 04 Reality? TV 01 16 Alliance of Blockheads 0 59 Terminal Excess Patient 02 48 Lineup Boris vocals Sven drums Geert guitar Jan guitar Nicolas bass DEFAULTSORT Process of Elimination Category 2005 albums Category Leng Tch e albums Category Relapse Records albums 2000s death metal album stub it The Process of Elimination ... more details
The terms mathematical elimination and mathematically eliminated mean to be excluded in a decision, based on numerical counts, due to insufficient total numbers, even if all remaining events were 100 in favor. The excluded outcome is considered to be eliminated due to the mathematical probability being zero 0 . The term is used in elections when a candidate lacks sufficient votes to win, even if that candidate could garner all remaining votes. In sports, the term mathematically eliminated ref name BBG Blunder Book Gigantic , Goldberg Hirsch, M. H. Goldberg, p. 179, 1988, webpage http books.google.com books?id Zd4oeHzIBRgC &pg RA3 PA179&lpg RA3 PA179 Books Google RgC 179 . ref refers to situations where there are not enough future games or competitive events remaining to be played to avoid defeat, even if all future events were won. History The term mathematically eliminated has been in use for more than 100 years, ref name AJP General Intelligence , Chapter 3, American Journal of Psychology , Volume XV, No. 1, January 1904, p. 226, webpage http books.google.com books?id 1Me3AAAAIAAJ&pg PA226 &lpg PA226 Book Google AAJ . ref although the meaning has varied. In a 1904 article, in the American Journal of Psychology , Volume XV, errors of measurement were described as quantifiable to be mathematically eliminated from the analysis of the remaining data. ref name AJP See also elimination theory conjunction elimination dead code elimination References reflist DEFAULTSORT Mathematical Elimination Category Voting Math stub ... more details
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