In linear algebra , a QRdecomposition also called a QR factorization of a matrix mathematics matrix is a matrix decompositiondecomposition of a matrix A into a product A QR of an orthogonal matrix Q and an upper triangular matrix R . QRdecomposition is often used to solve the linear least squares ... a lower triangular matrix. Computing the QRdecomposition There are several methods for actually computing the QRdecomposition, such as by means of the Gram Schmidt process , Householder transformation ... and an orthogonal matrix Q . The only difference from QRdecomposition is the order of these matrices. QRdecomposition is Gram Schmidt orthogonalization of columns of A, started from the first column ... Householder reflections File Householder.svg thumb Householder reflection for QRdecomposition ... math A QR math is a QRdecomposition of math A math . This method has greater numerical stability ... the number of operations in the k th step of the QRdecomposition by the Householder transformation ... is the required QRdecomposition. Using Givens rotations QR decompositions can also be computed ... Q T G 3G 2G 1 math . Thus, we have math G 3G 2G 1A Q TA R math , and the QRdecomposition is math A QR math . Connection to a determinant or a product of eigenvalues We can use QRdecomposition to find ... the definition of QRdecomposition for non square complex matrix and replacing eigenvalues with singular values. Suppose a QRdecomposition for a non square matrix A math A Q begin pmatrix R O end pmatrix ... i lambda i Big . math In conclusion, QRdecomposition can be used efficiently to calculate a product ... inverse, inverse solutions using QRdecomposition are more numerically stable as evidenced by their reduced ... University Press publication place New York isbn 978 0 521 88068 8 chapter Section 2.10. QRDecomposition ... Performs QRdecomposition of matrices. http netlib.org lapack lug node39.html LAPACK users manual gives details of subroutines to calculate the QRdecomposition http documents.wolfram.com mathematica ... more details
QR may stand for Qatar Airways IATA code Queensland Rail , a company responsible for the railway system in Queensland, Australia Queen s Regulations , a guidance on conduct in the UK s armed forces Queensr che , a progressive metal band Karakalpakstan Qoraqalpog iston Respublikasi , Uzbekistan, under ISO 3166 2 subcode UZ QR Nippon Cultural Broadcasting , a Tokyo radio station, from call sign JOQR Quintana Roo , a state of Mexico Quintana Roo company , a triathlon specific wetsuit and bicycle company Quick release skewer , a device used to secure the wheels on a bicycle Quiet Riot , a heavy metal band Quarterly Review , a defunct literary and political periodical Queen s Radio , a student radio station at Queen s University Belfast Queen s Rangers , a military unit who fought in the American War of Independence QR code Quick Response code , a two dimensional code Nissan QR engine ATCvet code QR Respiratory system , a section of the Anatomical Therapeutic Chemical Classification System for veterinary medicinal products In mathematics QRdecomposition , a decomposition of a matrix QR algorithm , an eigenvalue algorithm using QRdecomposition Quadratic reciprocity , a theorem from modular arithmetic Quasireversibility , a property of some queues disambig Category Initialisms de QR fa QR fr QR ko QR it QR sw QR nl Qr ja QR ru QR sv QR zh QR ... more details
A mummified rat. Signs of death Decomposition or rotting is the process by which organic substances ... stages of decomposition. The science which studies decomposition is generally referred to as taphonomy ... biotic decomposition biodegradation . The former means degradation of a substance by chemical or physical ... Words Dictionary WWD ref typically by microorganisms. Human decomposition Stages Five general stages are used to describe the process of decomposition Fresh, Bloat, Active and Advanced Decay, and Dry ... ref The general stages of decomposition are coupled with two stages of chemical decomposition autolysis ... Decomposition Chemistry in a Burial Environment isbn 1 4200 6991 8 ref These two stages contribute to the chemical process of decomposition , which breaks down the main components of the body Fresh The fresh ... author Carter D.O., Yellowlees, D., Tibbett M. title Cadaver decomposition in terrestrial ecosystems ... pages 13 334 chapter Decomposition of Human Remains isbn 1 58829 640 7 ref Once the heart stops ... changes caused by decomposition are limited during the fresh stage, although autolysis may cause ... stage of decomposition, known as bloat. ref name Carterjournal Blowflies and flesh flies are the first ... 2008 pages 29 51 chapter Cadaver Decomposition and Soil Processes isbn 1 4200 6991 8 ref The gases produced ... of decomposition fluids into the surrounding environment. ref name Carterbook The purged fluids accumulate around the body and create a cadaver decomposition island CDI . ref name Carterjournal ... to pupate. ref name Carterjournal Advanced Decay Decomposition is largely inhibited during advanced ... cite journal author Dent B.B., Forbes S.L., Stuart B.H. title Review of human decomposition processes ... Image decomposition stages.jpg frame center Pig carcass in the different stages of decomposition Fresh Bloat Active decay Advanced decay Dry remains Plant decomposition See also Composting Anaerobic ... frame is approximately 12 hours apart, as the fruit shrivels and becomes covered with mold . Decomposition ... more details
Fiziki , vol.1, no. 4, pages 555 570 1961 . ref The basic idea is to perform a QRdecomposition , writing ... 0 , we compute the QRdecomposition A sub k sub Q sub k sub R sub k sub where Q sub k sub is an orthogonal ... sequence of orthogonal similarity transforms, somewhat like a two sided QRdecomposition. ref ... For QRdecomposition, the Householder reflectors are multiplied only on the left, but for the Hessenberg case they are multiplied on both left and right. Determining the QRdecomposition of an upper ... reduction. ref name Demmel ref name Trefethen Determining the QRdecomposition of a symmetric ... no QRdecomposition s are explicitly performed, some authors, for instance Watkins, ref Watkins, David ... algorithm works with a complete basis of vectors, using QRdecomposition to renormalize and orthogonalize ... algorithm was preceded by the LR algorithm , which uses the LU decomposition instead of the QRdecomposition ... step using Householder reflections and, if appropriate, QRdecomposition , this forms the http www.netlib.org ...In numerical linear algebra , the QR algorithm is an eigenvalue algorithm that is, a procedure to calculate the eigenvalues and eigenvectors of a Matrix mathematics matrix . The QR transformation was developed ... independently. ref J.G.F. Francis, The QR Transformation, I , The Computer Journal , vol. 4, no. 3, pages ... at oxfordjournals.org br J.G.F. Francis, The QR Transformation, II The Computer Journal , vol. 4 ... in the other order, and iterate. The practical QR algorithm Formally, let A be a real matrix ... point reduces the number of steps required for convergence of the QR algorithm. If the original ... sup T sup and QR methods for symmetric tridiagonal matrices, The Computer Journal 6 1 , 99 101 .... A typical symmetric QR algorithm isolates each eigenvalue then reduces the size of the matrix with only one or two iterations, making it efficient as well as robust. The implicit QR algorithm In modern computational practice, ref Golub and Van Loan, chapter 7 ref the QR algorithm is performed in an implicit ... more details
File Wikipedia mobile en.svg thumb QR code for the URL of the English Wikipedia Mobile main page, nowiki http en.m.wikipedia.org nowiki Distinguish Quadratic residue code QR Code abbreviated from Quick ... QRCodefeatures cite web url http www.denso wave.com qrcode qrfeature e.html title QR Code features ... Wave in 1994 to track vehicles during the manufacturing process, the QR Code is one of the most popular ... title QR Code About 2D Code publisher Denso Wave accessdate 3 October 2011 ref Unlike the old bar code that was designed to be mechanically scanned by a narrow beam of light, the QR code is detected ... to binary numbers and validity checked with an error correcting code. Standards File QR Code Structure Example 2.svg thumb Structure of a QR code, highlighting functional elements There are several standards in documents covering the physical encoding of QR Codes ref name qrstandard1 cite web url http www.denso wave.com qrcode qrstandard e.html title QR Code Standardization publisher Denso wave.com work QR Code.com accessdate 23 April 2009 ref October 1997 spaced ndash AIM Association for Automatic ... identification and data capture techniques spaced ndash Bar code symbology spaced ndash QR code now withdrawn br Defines QR code models 1 and 2 symbols. 1 September 2006 spaced ndash ISO IEC 18004 ... technology spaced ndash Automatic identification and data capture techniques spaced ndash QR Code 2005 bar code symbology specification br Defines QR code 2005 symbols, an extension of QR Code model 2. Does not specify how to read QR Code model 1 symbols, or require this for compliance. At the application ... 2009 ref The open source ZXing project maintains a list of QR Code data types. ref cite web url http ... time. As a result, the QR code has become a focus of advertising strategy, since it provides quick ... 11930.html ref ref http blogs.vancouversun.com 2012 01 04 tescos cool qr code advertising ... sales pitch may continue. Although initially used to track parts in vehicle manufacturing, QR Codes ... more details
company name QR National Limited logo Image QRNational.png 229px QRNational logo type Public traded ... chain management , line haul and rail yard terminal operations operating income Not provided by QR net income Not provided by QR num employees Not provided by QR divisions Bulk, Coal, Intermodal, Freight ... qrnational.com.au intl yes QR National Limited is one of the larger rail freight companies in Australia ... on 1 July 2010 when transport and logistics company QR Limited was split into two companies. Queensland ..., and remains owned by the Government. QR National owns the balance of the QR business above rail coal ... maintenance services. QR National was privatised by the Government through an initial public offering and the company was listed on the Australian Securities Exchange ASX on 22 November 2010. The QR National brand was established in the 2004 2005 financial year when QR s three freight business ... Magazine volume 23 issue 262 pages page 30 ref History The company grew out of QR s Coal and Freight Services Group, along with QR subsidiary Interail . In late June 2005, rail operator QR National ... Magazine volume 22 issue 256 pages page 36 ref which became a separate operating entity of QR National ... coal.asp title QRNational Coal About coal work About QRNational accessdate 2008 03 03 ref QR National ... coalfields in 2005, ref name coal and by November 2007 the QR National network covered the entire ... Freight News room Current News Articles 908expansion.asp title QR completes another ... date 12 October 2007 accessdate 2008 03 03 ref In July 2008 QR National took over the Melbourne ... s core passenger service responsibilities, and formed into a new company called QR National Limited ... QR s coal, freight and infrastructure businesses will be sold as an integrated enterprise, known as QR National Limited with headquarters in Brisbane . The new enterprise will control QR s coal business .... The QR rollingstock workshops at Redbank, Rockhampton and Townsville are also included ... more details
showitem.asp?interpret Quiet Riot&titel QR III&cat a title Quiet Riot QR III album accessdate 2011 ... left U.S. Billboard Hot 200 ref cite web url http www.billboard.com album quiet riot qr iii 13896 title QR III Quiet Riot accessdate 2011 09 08 work Billboard.com publisher Billboard magazine ref align ... producer References Reflist Quiet Riot DEFAULTSORT Qr 3 Category 1986 albums Category Quiet Riot albums ... more details
bassist Jimmy Johnson , who played bass on Stay with Me Tonight and Coppin a Feel . ref name QR cite ... Quiet Riot U.S. released album up to this point. ref name QR Paul Shortino and Sean McNabb later ... more details
more digits in inexact arithmetic such as floating point . Similarly, the QRdecomposition expresses A as QR with Q a unitary matrix and R an upper triangular matrix. The system Q Rx b is solved by Rx ... the LU solver, but no more digits are required in inexact arithmetic because the QRdecomposition is numerically stable . Decompositions related to solving systems of linear equations LU decomposition Applicable to square matrix A Decomposition math A LU math , where L is triangular matrix lower triangular and U is triangular matrix upper triangular Related the LDU decomposition LDU decomposition ... decomposition which can avoid extracting square roots. QRdecomposition Applicable to m by n matrix A Decomposition math A QR math where Q is an orthogonal matrix of size m by m , and R is an triangular matrix upper triangular matrix of size m by n Comment The QRdecomposition provides an alternative ...In the mathematics mathematical discipline of linear algebra , a matrix decomposition is a factorization ... of linear equations math Ax b math , the matrix A can be decomposed via the LU decomposition . The LU decomposition factorizes a matrix into a lower triangular matrix L and an upper triangular matrix ... the LUP decomposition LUP decomposition is math A LUP math , where L is triangular matrix lower triangular ... decomposition exists for any square matrix A . When P is an identity matrix , the LUP decomposition reduces to the LU decomposition. If the LU decomposition exists, the LDU decomposition does too. ref ... the row echelon form without requiring any row interchanges, then P I , so an LU decomposition exists. LU reduction Block LU decomposition Rank factorization Cholesky decomposition Applicable ... A Decomposition math A U TU math , where U is upper triangular with positive diagonal entries Comment the Cholesky decomposition is a special case of the symmetric LU decomposition, with math L U T math . Comment the Cholesky decomposition is unique Comment the Cholesky decomposition is also applicable ... more details
wiktionary decompositionDecomposition is the biological process through which organic material is reduced. Decomposition may also refer to Chemical decomposition or analysis, in chemistry, is the fragmentation of a chemical compound into elements or smaller compounds Thermal decompositionDecomposition, spoilage of votes, see electoral fraud Mathematics Manifold decomposition , decomposition of manifolds JSJ decomposition , or toral decomposition , a decomposition of 3 manifolds Prime decomposition of integer s, see fundamental theorem of arithmetic for the mathematics or integer factorization for applications Prime decomposition in a commutative ring, see unique factorization domain Matrix decomposition , decomposition of matrices Vector decomposition , decomposition of vectors Helmholtz decomposition , decomposition of a vector field Lebesgue s decomposition theorem , decomposition of a measure Hahn decomposition of a measure space Hahn Jordan decomposition of a signed measure Doob decomposition theorem Doob decomposition of a discrete time sub or supermartingale Doob Meyer decomposition theorem Doob Meyer decomposition of a continuous time sub or supermartingale Semimartingale Decomposition of a semimartingale in a local martingale and a finite variation process Kunita Watanabe decomposition Kunita Watanabe or Galtchouk Kunita Watanabe decomposition in stochastic analysis F llmer Schweizer decomposition in mathematical finance decomposition of group representation s into irreducible representation s Lie group decompositions Computer science Decomposition computer science , or factoring, in computer science, refers to the process of breaking a complex problem down into easily understood and achievable parts Decomposition, in computer graphics , means spatial decomposition disambig cleanup date April 2012 Category Mathematical disambiguation cs Rozklad de Dekomposition es Descomposici n desambiguaci n fr D composition homonymie gl Descomposici n it Decomposizione ja ... more details
math U k 1 frac12 left gamma kU k frac1 gamma k U k 1 right math , k 0,1,2,... The QRdecomposition ...In mathematics , particularly in linear algebra and functional analysis , the polar decomposition of a matrix mathematics matrix or linear operator is a matrix decomposition factorization analogous to the Complex ... is called the complex sign of z . Quaternion polar decomposition The polar decomposition of quaternion ... polar decomposition math q t e ar . math Matrix polar decomposition The polar decomposition of a square complex matrix A is a matrix decomposition of the form math A UP , math where U is a unitary ..., the polar decomposition separates A into a component that stretches the space along a set of orthogonal axes, represented by P , and a rotation represented by U . The decomposition of the complex conjugate of math A math is given by math overline A overline U math math overline P math . This decomposition ... the corresponding polar decomposition of the determinant of A , since math det P r det A math and math ... value decomposition of A , A W V sup sup , one has math P V Sigma V , math math U W V , math ... . math This is known as the left polar decomposition, whereas the previous decomposition is known as the right polar decomposition. Left polar decomposition is also known as reverse polar decomposition ... write the polar decomposition as math A Q Phi Q Q Sigma Q , , math so A then thus also has a spectral decomposition math A Q Lambda Q , math with complex eigenvalues such that sup sup sup 2 sup ... n is a maximal compact subgroup of GL n , C . Bounded operators on Hilbert space The polar decomposition ... of a partial isometry and a non negative operator. The polar decomposition for matrices ... of a polar decomposition is a consequence of Douglas lemma Lemma If A , B are bounded operators ... U , which is unique if Ker A Ker U . Take P to be A A sup sup and one obtains the polar decomposition ... in general see example above . Alternatively, the polar decomposition can be shown using the operator ... more details
In mathematics , Jordan decomposition may refer to Hahn decomposition theorem , and the Jordan decomposition of a measure Jordan normal form of a matrix Jordan Chevalley decomposition of a matrix Deligne Lusztig theory , and its Jordan decomposition of a character of a finite group of Lie type The Jordan H lder theorem , about decompositions of finite group s. mathdab ... more details
In mathematics , the term cycle decomposition can mean In graph theory , a Cycle decomposition graph theory cycle decomposition is a partitioning of the vertices of a graph into subsets, such that the vertices in each subset lie on a Cycle graph theory cycle . In group theory , a Cycle decomposition group theory cycle decomposition is a useful convention for expressing a permutation in terms of its constituent cycles. mathdab ... more details
Decomposition method is a generic term for solutions of various problems and design of algorithms in which the basic idea is to decompose the problem into subproblems. The term may specifically refer to one of the following. Decomposition method constraint satisfaction in constraint satisfaction Decomposition method in multidisciplinary design optimization Adomian decomposition method , a non numerical method for solving nonlinear differential equations Domain decomposition methods in mathematics, numerical analysis, and numerical partial differential equations Cholesky decomposition method disambig ... more details
Orphan date June 2011 Abiotic decomposition or abiotic degradation is degradation of a substance by chemical or physical processes, for example hydrolysis , redox reduction and oxidation . ref Water Quality Vocabulary. ISO 6107 6 1994 ref References reflist See also Biotic decomposition Chemical decomposition DEFAULTSORT Abiotic Decomposition Category Biodegradation ... more details
decomposition Matrix decompositionQRdecomposition LU Reduction References reflist Citation ...In linear algebra , LU decomposition also called LU factorization factorizes a matrix mathematics matrix ... includes a permutation matrix as well. LU decomposition is a key step in several fundamental numerical ... . LU decomposition was introduced by mathematician Alan Turing ref citation first1 David last1 Poole ... Thomson Brooks Cole place Canada isbn 0 534 99845 3 . ref . Definitions File LDU decomposition of Walsh 16.svg thumb 300px LDU decomposition of a Walsh matrix Let A be a square matrix. An LU decomposition is a decomposition of the form math A LU, , math where L is a lower triangular matrix and U ... below the diagonal. For example, for a 3 by 3 matrix A , its LU decomposition looks like this math ... decomposition is commonly used. An LUP decomposition also called a LU decomposition with partial Pivot element pivoting is a decomposition of the form math PA LU, , math where L and U are again lower ... 2012 . This makes LUP decomposition a useful technique in practice. An LU decomposition with full ..., and Q is a permutation matrix that reorders the columns of A . An LDU decomposition is a decomposition ... bmatrix begin bmatrix u 11 & u 12 0 & u 22 end bmatrix . math One way to find the LU decomposition ... to find the unique LU decomposition, it is necessary to put some restriction on L and U matrices. For example ... decomposition above yields math begin bmatrix 4 & 3 6 & 3 end bmatrix begin bmatrix 1 & 0 ... of L . That is, we can write A as math A L L . , math This decomposition is called the Cholesky decomposition . The Cholesky decomposition always exists and is unique. Furthermore, computing the Cholesky decomposition is more efficient and numerical stability numerically more stable than computing ... algorithm for obtaining LU decomposition has also been extended to this most general case harv Okunev Johnson 1997 . Algorithms The LU decomposition is basically a modified form of Gaussian elimination ... more details
Unreferenced stub auto yes date December 2009 Vector decomposition refers to decomposing a Vector geometric vector of R sup n sup into several vectors, each linearly independent in mutually distinct directions in the n dimensional space . Vector decomposition in two dimensions In two dimensions, a vector can be decomposed in many ways. In the Cartesian coordinate system , the vector is decomposed into a portion along the math hat x math or math hat i math and the math hat y math or math hat j math directions. One of the most common situations is when given a vector with magnitude and direction or given in polar coordinate system polar form , it can be converted into the Vector geometric Addition and subtraction sum of two perpendicular vectors or converted to a Cartesian coordinate . Application in physics Vector decomposition is used in physics to help adding vectors and hence solve many mechanical problems involving force , work physics work , momentum , etc. See also coordinate system Helmholtz decompositiondecomposition of a vector field DEFAULTSORT Vector Decomposition Category Introductory physics Phys stub ... more details
Benders decomposition alternatively, Benders s decomposition is a technique in mathematical programming that allows the solution of very large linear programming problems that have a special block structure . This structure often occurs in applications such as stochastic programming . As it progress towards a solution, Benders decomposition adds new constraints , so the approach is called row generation row generation . In contrast, Dantzig Wolfe decomposition uses column generation column generation . References J. F. Benders, Partitioning procedures for solving mixed variables programming problems, Numer. Math. 4, 3 Sept. 1962 , pp. 238 252. http www.springerlink.com content g203830n1gm58w73 fulltext.pdf cite book last Lasdon first Leon S. title Optimization theory for large systems publisher Dover Publications, Inc. location Mineola, New York year 2002 edition reprint of the 1970 Macmillan pages xiii 523 MR 1888251 See also FortSP solver uses Benders decomposition for solving stochastic programming problems Category Mathematical optimization Category Decomposition methods fr D composition de Benders ... more details
In mathematics , the JSJ decomposition , also known as the toral decomposition , is a topological construct given by the following theorem Irreducible mathematics Irreducible Orientability orientable closed i.e., compact and without boundary 3 manifold s have a unique up to homotopy isotopy minimal collection of disjointly Embedding embedded incompressible surface incompressible torus tori such that each component of the 3 manifold obtained by cutting along the tori is either atoroidal or Seifert fibered . The acronym JSJ is for William Jaco , Peter Shalen , and Klaus Johannson . The first two ... of the JSJ decomposition states A closed irreducible orientable 3 manifold M has a submanifold ... is a union of tori that are almost the same as the tori appearing in the JSJ decomposition. However there is a subtle difference if one of the tori in the JSJ decomposition is non separating ... submanifold is also sometimes called the JSJ decomposition, though it may have more tori than the JSJ decomposition defined in the introduction. Warning the JSJ decomposition is not quite the same as the decomposition in the geometrization conjecture , because some of the pieces in the JSJ decomposition might not have finite volume geometric structures. For example, the mapping torus of an Anosov map of a torus has a finite volume sol structure, but its JSJ decomposition cuts it open ... no finite volume geometric structure. See also Geometrization conjecture Manifold decomposition Satellite ... JSJ Decomposition of 3 manifolds This lecture gives a brief introduction to Seifert fibered 3 manifolds and provides the existence and uniqueness theorem of Jaco, Shalen, and Johannson for the JSJ decomposition ... to Construct the JSJ Decomposition of a 3 manifold. An algorithm is given for constructing the JSJ decomposition of a 3 manifold and deriving the Seifert invariants of the Characteristic submanifold ... Press, New York London, 1979. Jaco, William Shalen, Peter B. A new decomposition theorem for irreducible ... more details
of microbial proliferation within the body. Microbiology of decomposition is the study of all microorganisms ... organic matter is broken down and reduced to its original elements. Decomposition microbiology can be divided between two fields of interest decomposition of plant materials decomposition of cadavers and carcasses. The decomposition of plant materials is commonly studied in order to understand the cycling .... Plant material decomposition is also often referred to as composting. The decomposition of cadavers and carcasses has become an important field of study within forensic taphonomy . Decomposition microbiology ... and moisture levels. During decomposition, microorganisms require oxygen for their respiration. If anaerobic conditions dominate the decomposition environment, microbial activity will be slow and thus decomposition will be slow. Appropriate moisture levels are required for microorganisms to proliferate ... to take part in decomposition. In wet environments, anaerobic conditions will develop and decomposition can also be considerably slowed down. Decomposing microorganisms also require the appropriate plant substrates in order to achieve good levels of decomposition. This usually translates ... is thought to be approximately 30 1. As in any microbial process, the decomposition of plant litter ... decomposition during the winter months where snow cover occurs as temperatures are too low ... volume 26 issue 10 pages 47 50 ref Decomposition microbiology of cadavers and carcasses The decomposition ... clandestine graves. Decomposition microbiology as applied to forensic taphonomy can be divided into 2 groups of studies microorganisms from within the body microorganisms from the decomposition ..., red or black depending on 1 where the color changes are observed and 2 how far along within the decomposition ... Aspects of Decomposition isbn 9780849394348 ref Proliferation of bacteria throughout the body ... title Decomposition chemistry of human remains a new methodology for determining post mortem interval ... more details
Unreferenced date March 2009 In semi Riemannian geometry , the Bel decomposition , taken with respect to a specific timelike congruence , is a way of breaking up the Riemann tensor of a pseudo Riemannian manifold into four pieces. It was introduced in 1959 by the physicist Lluis Bel . This decomposition is particularly important in general relativity . This is the four dimensional case of Lorentzian manifold s, for which there are only three pieces with particularly simple properties, which have individual physical interpretations. See also Electrogravitic tensor Magnetogravitic tensor Ricci decomposition Topogravitic tensor Category Lorentzian manifolds Category Tensors in general relativity relativity stub ... more details
In geometric topology , a cellular decomposition G of a manifold M is a decomposition of M as the disjoint union of cells. The quotient space M G has points that correspond to the cells of the decomposition. There is a natural map from M to M G , which is given the quotient topology. A fundamental question is whether M is homeomorphic to M G . Bing s dogbone space is an example with M equal to R sup 3 sup not homeomorphic to M G . See also CW complex References Citation last1 Daverman first1 Robert J. title Decompositions of manifolds url http www.ams.org bookstore getitem item chel 362.h publisher AMS Chelsea Publishing, Providence, RI isbn 978 0 8218 4372 7 mr 2341468 year 2007 page 22 Category Geometric topology ... more details
In mathematics, a Remak decomposition , introduced by harvs txt last Remak authorlink Robert Remak mathematician year 1911 , is a decomposition of an abelian group or similar object into a finite direct sum of indecomposable objects. The Krull Schmidt theorem gives conditions for a Remak decomposition to exist and for its factors to be unique. References Citation last1 Remak first1 Robert title ber die Zerlegung der endlichen Gruppen in direkte unzerlegbare Faktoren url http resolver.sub.uni goettingen.de purl?GDZPPN00216731X language German doi 10.1515 crll.1911.139.293 id JFM 42.0156.01 year 1911 journal Journal f r die reine und angewandte Mathematik issn 0075 4102 volume 139 pages 293 308 Category Group theory Category Module theory ... more details
1 Type of decomposition M How it is decomposed The pieces How they are combined Triangulation topology ... simplices Glue together pairs of codimension one faces JSJ decomposition Jaco Shalen Johannson torus decomposition Irreducible mathematics Irreducible , orientable , Compact space compact 3 manifold ... Adjunction space Union along their boundary, using the trivial homeomorphism Prime decomposition 3 manifold Prime decomposition Essentially surfaces and 3 manifold . The decomposition is unique when ... Handle decomposition Any compact smooth manifold smooth n manifold and the decomposition is never unique ... 3 balls Disk decomposition Certain Compact space compact , orientable 3 manifold s Sutured manifold ...... Ball mathematics Topology 3 balls Open book decomposition Any Closed manifold closed orientable 3 ... Manifold Decomposition Category Geometric topology ... more details
Unreferenced stub auto yes date December 2009 In fluid dynamics and the theory of turbulence , Reynolds decomposition is a mathematical technique to separate the average and fluctuating parts of a quantity. For example, for a quantity math scriptstyle u math the decomposition would be math u x,y,z,t overline u x,y,z u x,y,z,t math where math scriptstyle overline u math denotes the time average of math scriptstyle u , math often called the steady component , and math u , math the fluctuating part or perturbations . The perturbations are defined such that their time average equals zero. This allows us to simplify the Navier Stokes equations by substituting in the sum of the steady component and perturbations to the velocity profile and taking the mean value. The resulting equation contains a nonlinear term known as the Reynolds stresses which gives rise to turbulence . See also Reynolds averaged Navier Stokes equations Turbulence DEFAULTSORT Reynolds Decomposition Category Turbulence Fluiddynamics stub nn Reynolds dekomponering ... more details
Encyclopedia
top
