for use of the term homologous in reference to chromosomes Homologous chromosomes File Homology vertebrates.svg thumb 300px The principle of homology The biological derivation relationship shown by colors of the various bones in the forelimbs of four vertebrates is known as homology and was one of Darwin s arguments in favor of evolution. Homology forms the basis of organization for comparative biology . In 1843, Richard Owen defined homology as the same organ in different animals under every variety ... MK1888.png right thumb 350px Forelimb s in mammal s provide one example of homology. Homologous ... to a homologous protein, and to the gene DNA sequence encoding it. Etymology The word homology, coined ... homology due to inheritance from a common ancestor, and homoplasty , meaning homology due to other ... Press year 2004 isbn 0 415 28032 X page 198 ref Anatomical homology Image Homology.jpg thumb The wings ... s of male humans are homologous in this sense. Homology is different from analogy biology analogy ..., reversal, and convergence. ref Cf. Butler, A. B. Homology and Homoplasty. In Squire ... of organisms, Rolf Sattler emphasized that homology can also be partial. New structures ... R title Homology a continuing challenge journal Systematic Botany volume 9 pages 382 94 year 1984 doi 10.2307 2418787 issue 4 jstor 2418787 ref ref cite book author Sattler, R. chapter Homology, homeosis, and process morphology in plants editor Hall, Brian Keith title Homology the hierarchical basis ... structures in other phyla Discussions of homology commonly limit themselves to the limbs of tetrapod ... in several groups of arthropods, but add that ...the subject of head appendage homology among the arthropods ... See Deep homology . Determining homology Systematists identify two forms of homology primary homology ... homology is implied by parsimony analysis, where a character that only occurs once on a tree is taken ... potatoes Sequence homology This section is linked from Primary structure As with anatomical ... more details
Homologies are structural resonances ...between the different elements making up a socio cultural whole. Middleton 1990, p. 9 Examples include Alan Lomax s cantometrics , which Distinguishes ten musical styles, dealing most fully with Eurasian and Old European styles. These are correlated with sexual permissiveness, status of women, and treatment of children as the principal formative social influences. The musical styles are at the same time symbolic or expressive of such social influences, especially in the various musical communities of Spain and Italy, and are stable, persistent. Lomax states his expectation that further study and refinement of methods of measurement will increase our understanding of the relationships of musical style and culture in a way that Western European musical notation cannot adequately accomplish. Citation needed date November 2009 Richard Middleton 1990, p. 9 10 argues that such theories always end up in some kind of reductionism upwards , into an idealist cultural spirit, downwards , into economism, sociologism or technologism, or by circumnavigation , in a functionalist holism. However, he would like to hang on to the notion of homology in a qualified sense. For it seems likely that some signifying structures are more easily articulation sociology articulated to the interests of one group than are some others similarly, that they are more easily articulated to the interests of one group than to those of another. This is because, owing to the existence of what Paul Willis calls the objective possibilities and limitations of material and ideological structures, it is easier to find links and analogies between them in some cases than in others Willis 1978 198 201 . Source Middleton, Richard 1990 2002 . Studying Popular Music . Philadelphia Open University Press. ISBN 0 335 15275 9. Lomax, Alan 1959 . Folk Song Style. American Anthropologist 61 Dec. 1959 927 54. http www.alan lomax.com style cantometrics.html Lomax, Alan 1968 ... more details
In mathematics , a Homologymathematicshomology theory in algebraic topology is compactly supported if, in every degree n , the relative homology group H sub n sub X , A of every pair of spaces X , A is naturally isomorphic to the direct limit of the n th relative homology groups of pairs Y , B , where Y varies over compact subspace s of X and B varies over compact subspaces of A . Singular homology is compactly supported, since each singular chain is a finite sum of simplices , which are compactly supported. Strong homology is not compactly supported. If one has defined a homology theory over compact pairs, it is possible to extend it into a compactly supported homology theory in the wider category of Hausdorff pairs X , A with A closed in X , by defining that the homology of a Hausdorff pair X , A is the direct limit over pairs Y , B , where Y , B are compact, Y is a subset of X , and B is a subset of A . topology stub Category Homology theory ... more details
uses see Mathematics disambiguation and Math disambiguation . File Euclid.jpg thumb Euclid , Greek ... . ref Mathematics from Greek language Greek m th ma , knowledge, study, learning is the study ... reasoning often provides insight or predictions. Through the use of abstraction mathematics abstraction and logic al reasoning , mathematics developed from counting , calculation , measurement ... mathematics has been a human activity for as far back as History of Mathematics written records exist. Logic Rigorous arguments first appeared in Greek mathematics , most notably in Euclid Euclid s Euclid s Elements Elements . Mathematics developed at a relatively slow pace until the Renaissance , when ... of Mathematics 1. Newton and Leibniz , BBC Radio 4 , 27 09 2010. ref Carl Friedrich Gauss 1777 1855 referred to mathematics as the Queen of the Sciences . ref name Waltershausen Waltershausen ref Benjamin Peirce 1809 1880 called mathematics the science that draws necessary conclusions . ref Peirce, p. 97. ref David Hilbert said of mathematics We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual ... , Basel, Birkh user 1992 . ref Albert Einstein 1879 1955 stated that as far as the laws of mathematics ... . ref name certain Mathematics is used throughout the world as an essential tool in many fields, including natural science , engineering , medicine , and the social sciences . Applied mathematics , the branch of mathematics concerned with application of mathematical knowledge to other fields ... in pure mathematics , or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. ref Peterson ref Etymology The word mathematics comes from ... of which mean to learn . The word mathematics in Greek came to have the narrower and more technical ... more details
Infobox journal title Homology, Homotopy and Applications cover abbreviation Homology, Homotopy Appl. discipline Algebraic topology editor nowrap 1 Gunnar Carlsson publisher International Press frequency Irregular history 1991 present impact 0.609 impact year 2009 url http intlpress.com hha index.html ISSN 1532 0073 eISSN 1532 0081 CODEN LCCN OCLC link1 http projecteuclid.org DPubS?service UI&version 1.0&verb Display&page past&handle euclid.hha&collection link1 name Online access Homology, Homotopy and Applications is a peer review peer reviewed mathematics journal published by International Press . Founded in 1991, the journal publishes articles on algebraic topology . The journal is indexed by Mathematical Reviews and Zentralblatt MATH . Its 2009 Mathematical Citation Quotient MCQ was 0.34, and its 2009 impact factor was 0.609. External links Official 1 http intlpress.com hha index.html Category Mathematics journals Category Publications established in 1991 Category English language journals Category International Press academic journals math journal stub ... more details
In mathematics , in the area of symplectic topology , relative contact homology is an invariant of spaces together with a chosen subspace. Namely, it is associated to a contact manifold and one of its Legendrian submanifold s. It is a part of a more general invariant known as Floer homology Symplectic field theory symplectic field theory , and is defined using pseudoholomorphic curves . Legendrian knots The simplest case yields invariants of Contact geometry Legendrian submanifolds Legendrian knots inside contact three manifold s. The relative contact homology has been shown to be a strictly more powerful invariant than the classical invariants , namely Thurston Bennequin number and rotation number within a class of smooth knots . Yuri Chekanov developed a purely combinatorial version of relative contact homology for Legendrian knots, i.e. a combinatorially defined invariant that reproduces the results of relative contact homology. Tamas Kalman developed a combinatorial invariant for loops of Legendrian knots, with which he detected differences between the fundamental group s of the space of smooth knots and of the space of Legendrian knots. Higher dimensional legendrian submanifolds In the work of Lenhard Ng , relative SFT is used to obtain invariants of smooth knots a knot or link inside a topological three manifold gives rise to a Legendrian torus inside a contact five manifold ... knot invariant from a combinatorial version of the zero th degree part of the homology. It has ... the unknot . See also Relative homology References Lenhard Ng , http front.math.ucdavis.edu math.SG 0412330 Conormal bundles, contact homology, and knot invariants . Tobias Ekholm, John Etnyre, Michael ... Homology . Yuri Chekanov, Differential Algebra of Legendrian Links . Inventiones Mathematicae 150 2002 , pp. 441 483. http front.math.ucdavis.edu math.GT 0407347 Contact homology and one parameter ... Category Homology theory Category Contact geometry ... more details
In mathematics , Borel Moore homology or homology with closed support is a homology theory for locally compact space s, introduced by harvs txt last1 Borel author1 link Armand Borel last2 Moore author2 link John Coleman Moore year 1960 . For compact space s, the Borel Moore homology coincide with the usual singular homology , but for non compact spaces, it usually gives homology groups with better properties. Note There is an equivariant cohomology theory for spaces upon which a group math G math acts which is also called Borel cohomology and is defined as math H G X H EG times G X math . This is not related ... homology. They all coincide for spaces math X math that are homotopy equivalent to a finite CW complex ... math xi in C i T X , math its support mathematics support , math xi bigcup xi sigma neq 0 sigma ... limit of math C i T X math under refinements of math T math . The boundary map of simplicial homology ... math dots to C i 1 X to C i X to C i 1 X to dots math is a chain complex . The Borel Moore homology of X is defined to be the homology of this chain complex. Concretely, math H BM i X Ker partial ... math be a compactification mathematics compactification of math X math such that the pair math bar X ... H BM i X H i bar X , bar X setminus X , math where in the right hand side, usual relative homology ... in the right hand side, hypercohomology is meant. Properties Borel Moore homology is not homotopy ... mathbb R math for math i n math . Borel Moore homology is a covariant functor with respect to proper ... Y cup infty math are the one point compactifications. Using the definition of Borel Moore homology via ... to H BM i 1 F to dots math . One of the main reasons to use Borel Moore homology is that for every ... triangulation. In fact, in Borel Moore homology, one can define a fundamental class for arbitrary ... John C. title Homology theory for locally compact spaces url http projecteuclid.org euclid.mmj ... 137 159 Category Homology theory Category Sheaf theory ... more details
In biology, a Src homology domain is one of the two small protein binding domains found in the Src gene Src oncoprotein . Homologs of both the SH2 domain Src homology 2 and SH3 domain Src homology 3 domains are found in numerous other proteins. protein stub cell biology stub Category Protein domains ... more details
Pfam box Symbol Syja N Name SacI homology domain image width caption Pfam PF02383 InterPro IPR002013 SMART Prosite PS50275 SCOP TCDB OPM family OPM protein SacI homology domain is a Protein family family of evolutionarily related proteins . ref name pmid9388224 cite journal author Nemoto Y, Arribas M, Haffner C, DeCamilli P title Synaptojanin 2, a novel synaptojanin isoform with a distinct targeting domain and expression pattern journal J. Biol. Chem. volume 272 issue 49 pages 30817 21 year 1997 month December pmid 9388224 doi 10.1074 jbc.272.49.30817 url issn ref This Pfam family represents a protein domain which shows homology to the yeast protein SacI UniProt P32368 . The SacI homology domain is most notably found at the amino terminal of the inositol 5 phosphatase synaptojanin . Synaptic vesicles are recycled with remarkable speed and precision in nerve terminals. A major recycling pathway involves clathrin mediated endocytosis at endocytic zones located around sites of release. Different accessory proteins linked to this pathway have been shown to alter the shape and composition of lipid membranes, to modify membrane coat protein interactions, and to influence actin polymerization. These include the GTPase dynamin , the lysophosphatidic acid acyl transferase endophilin , and the phosphoinositide phosphatase synaptojanin. ref name PUB00006604 cite journal author Cox DN, Chao A, Baker J, Chang L, Qiao D, Lin H title A novel class of evolutionarily conserved genes defined by piwi are essential for stem cell self renewal journal Genes Dev. volume 12 issue 23 pages 3715 3727 year 1998 pmid 9851978 doi 10.1101 gad.12.23.3715 pmc 317255 ref The recessive suppressor of secretory defect in yeast Golgi and yeast actin function belongs to this family. This protein may be involved in the coordination of the activities of the secretory pathway and the actin cytoskeleton. Human synaptojanin which may be localised on coated endocytic intermediates in nerve terminals also belongs ... more details
Pfam box Symbol CH Name Calponin homology CH domain image 2RR8.pdb.jpg width caption Solution structure of calponin homology domain of IQGAP1 ref name pmid20644981 PDB 2RR8 cite journal author Umemoto R, Nishida N, Ogino S, Shimada I title NMR structure of the calponin homology domain of human IQGAP1 and its implications for the actin recognition mode journal J. Biomol. NMR volume 48 issue 1 pages 59 64 year 2010 month September pmid 20644981 doi 10.1007 s10858 010 9434 8 url issn ref Pfam PF00307 InterPro IPR001715 SMART CH Prosite PDOC00019 SCOP 1aoa TCDB OPM family OPM protein PDB PDB3 1sjj B 33 136 PDB3 1tjt A 46 149 PDB3 1wku A 46 149 PDB3 1sh5 B 186 293 PDB3 1sh6 A 186 293 PDB3 1mb8 A 180 282 PDB3 1dxx A 16 119 PDB3 1qag B 32 135 PDB3 1rt8 A 386 495 PDB3 1pxy B 393 498 PDB3 1aoa 121 236 PDB3 1wyp A 29 132 PDB3 1h67 A 29 132 PDB3 1wyn A 29 132 PDB3 1ujo A 25 138 PDB3 1wym A 25 137 PDB3 1wyr A 4 111 PDB3 1p2x A 42 148 PDB3 1p5s A 42 148 PDB3 1bkr A 174 278 PDB3 1aa2 174 278 PDB3 1wyq A 178 281 PDB3 1bhd A 151 254 PDB3 1wyl A 509 612 PDB3 1wjo A 517 624 PDB3 1wyo A 15 116 PDB3 1vka B 15 116 PDB3 1ueg A 15 116 PDB3 1pa7 A 15 116 Calponin homology actin binding domain or CH domain is a superfamily of actin binding domains found in both cytoskeletal proteins and signal transduction proteins. ref name PUB00001696 cite journal author Saraste M, Castresana J title Does Vav bind to F actin through a CH domain? journal FEBS Lett. volume 374 issue 2 pages 149 151 year 1995 pmid 7589522 doi 10.1016 0014 5793 95 01098 Y ref It comprises the following groups of actin binding domains Actinin type including spectrin, fimbrin, ABP 280 Calponin type A comprehensive review of proteins containing this type of actin binding domains is given in. ref name PUB00004975 cite journal author Hartwig ... cite journal author Saraste M, Carugo KD, Banuelos S title Crystal structure of a calponin homology ... nsb0397 175 ref Examples Human genes encoding calponin homology domain containing proteins include ... more details
Pfam box Symbol RHD Name Rel homology domain RHD image 1SVC.png width caption Top view of the crystallographic structure of a homodimer of the NFKB1 protein green and magenta bound to DNA brown . ref name pmid7830764 PDB 1SVC cite journal author M ller CW, Rey FA, Sodeoka M, Verdine GL, Harrison SC title Structure of the NF kappa B p50 homodimer bound to DNA journal Nature volume 373 issue 6512 pages 311 7 year 1995 month January pmid 7830764 doi 10.1038 373311a0 url ref Pfam PF00554 InterPro IPR011539 SMART PROSITE PDOC00924 SCOP 1svc TCDB OPM family OPM protein CDD cd07827 PDB PDB2 1a02 , PDB2 1a3q , PDB2 1a66 , PDB2 1bvo , PDB2 1gji , PDB2 1ikn , PDB2 1imh , PDB2 le5 , PDB2 le9 , PDB2 1lei , PDB2 1nfa , PDB2 1nfi , PDB2 1nfk , PDB2 1ooa , PDB2 1owr , PDB2 1p7h , PDB2 1pzu , PDB2 1ram , PDB2 1s9k , PDB2 1svc , PDB2 1uur , PDB2 1uus , PDB2 1vkx , PDB2 2as5 , PDB2 2ram The Rel homology domain RHD is a protein domain found in a family of eukaryotic transcription factor s, which includes NF B , NFAT , among others. Some of these transcription factors appear to form multi protein DNA bound complexes. ref name pmid9794820 cite journal author Wolberger C title Combinatorial transcription factors journal Curr. Opin. Genet. Dev. volume 8 issue 5 pages 552 9 year 1998 month October pmid 9794820 doi 10.1016 S0959 437X 98 80010 5 url ref Phosphorylation of the RHD appears to play a role in the regulation of some of these transcription factors, acting to modulate the expression of their target genes. ref name pmid15516339 cite journal author Anrather J, Racchumi G, Iadecola C title cis acting, element specific transcriptional activity of differentially phosphorylated nuclear factor kappa B journal J. Biol. Chem. volume 280 issue 1 pages 244 52 year 2005 month January pmid 15516339 doi 10.1074 jbc.M409344200 url ref The RHD is composed of two immunoglobulin like beta barrel subdomains that grip the DNA in the major groove. The N terminus N terminal specificity domain resembles ... more details
Image evh.png thumb 350px right Domain organisation of EVH proteins ENA VASP Homology proteins or EVH proteins are a family of closely related proteins involved in cell motility in vertebrate and invertebrate animals. EVH proteins are modular proteins that are involved in actin polymerisation, as well as interaction with other proteins. Within the cell, Ena VASP proteins are found at the leading edge of Lamellipodia and at the tips of filopodia . ref name pmid19494122 cite journal author Bear and Gertler title Ena VASP towards resolving a controversy at the barbed end journal J Cell Sci year 2009 pmid 19494122 pmc 2723151 doi 10.1242 jcs.038125 last2 Gertler first2 FB volume 122 issue Pt 12 pages 1947 53 ref Ena, the founding member of the family was discovered in a Drosophila melanogaster drosophila genetic screen for mutations that act as Dominance genetics dominant suppressors of the Abl gene abl non receptor tyrosine kinase . Invertebrate animals have one Ena homologue, whereas mammals have three, in mice named Mena, VASP, and Evl. Ena VASP proteins promote the spatially regulated actin polymerization required for efficient chemotaxis in responsive to attractive and repulsive guidance cues. Mice lacking functional copies of all three family members display pleiotropic phenotypes including exencephaly , edema , failures in neurite formation, and embryonic lethality. A sub domain of EVH is the EVH1 domain . References reflist Category EVH domain Category Protein domains Category Proteins Category Cell movement Category Cytoskeleton Category Cell biology Molecular cell biology stub ... more details
ref name pmid7890802 cite journal author Ingley E, Hemmings BA title Pleckstrin homology PH domains ..., Hyv nen M title Pleckstrin homology domains a fact file journal Curr. Opin. Struct. Biol. volume 5 ... Yao L, Kawakami Y, Kawakami T title The pleckstrin homology domain of Bruton tyrosine kinase interacts ... SD, Lemmon MA title Genome wide analysis of membrane targeting by S. cerevisiae pleckstrin homology ... more details
unreferenced date March 2008 Homology directed repair HDR is a mechanism in cell biology cells to repair double strand DNA lesions. This repair mechanism can only be used by the cell when there is a homologue piece of DNA present in the Cell nucleus nucleus , mostly in G2 and S phase of the cell cycle . When the homologue DNA piece is absent, another process called non homologous end joining NHEJ can take place instead. Cancer Suppression HDR is important for suppressing the formation of cancer . HDR maintains the genomic stability by repairing the broken DNA strand, assumed error free because of the use of a template. When a double strand DNA lesion is repaired by NHEJ there is no validating DNA template present which may result in a non original DNA strand formation with loss of information. A different nucleotide sequence in the DNA strand results in a different protein expressed in the cell. This protein may malfunction by which processes in the cell may fail. When, for example, a receptor of the cell that can receive a signal to stop dividing malfunctions, the cell ignores the signal and keeps dividing and can form a cancer. An example for the essence of HDR is the fact that the mechanism is conserved throughout evolution . The HDR mechanism has also been found in more simple organism s, like in yeast . Biological Pathway The pathway of HDR is not totally enlightened yet March 2008 . Though there are a lot of experimental results which point to the validity of certain models. Generally accepted is the phosphorylation of histone H2AX noted as H2AX within seconds after occurrence of the damage. H2AX is phosphorylated widely in the surrounding area of the damage and not only at the precise location. Therefore H2AX is suggested to function as an adhesive component to attract proteins to the damaged location. A variety of research groups suggest that the phosphorylation of H2AX is done by ATM and ATR in cooperation with MDC1. Before or meanwhile H2AX is involved in the repair ... more details
There are many terms in mathematics that begin with cyclic Cyclic chain rule , for derivatives, used in thermodynamics Cyclic code , linear codes closed under cyclic permutations Cyclic convolution , a method of combining periodic functions Cycle decomposition graph theory Cycle decomposition group theory Cyclic extension , a field extension with cyclic Galois group Cycle graph or cyclic graph is a connected, 2 regular graph Cycle graph algebra , a diagram representing the cycles determined by taking powers of group elements Circulant graph , a graph whose adjacency matrix is circulant Cycle graph theory , a nontrivial path from a node to itself Cyclic group , a group generated by a single element Cyclic homology , an approximation of K theory used in non commutative differential geometry Cyclic module , a module generated by a single element Cyclic notation , a way of writing permutations Cyclic number , a number such that cyclic permutations of the digits are successive multiples of the number Cyclic order , a binary relation for doubly linked lists Cyclic permutation , a permutation with one nontrivial orbit Cyclic polygon , a polygon which can be given a circumscribed circle Cyclic shift , also known as circular shift Cyclic symmetry , n fold rotational symmetry of 3 dimensional space See also Cycle disambiguation Cycle mathematics Category Mathematics related lists sv Cyklisk matematik ... more details
self immersion mathematics immersion . Pathological properties Solenoids are compact space ... connected . This is reflected in their pathological mathematics pathological behavior with respect to various homology theories , in contrast with the standard properties of homology for simplicial complex es. In ech cohomology ech homology , one can construct a non exact long exact sequence long homology sequence using a solenoid. In Steenrod style homology theories, the 0th homology group of a solenoid ... about solenoids arxiv 1201.2647 DEFAULTSORT Solenoid Mathematics Category Topological groups Category ... more details
Merge to Mathematics Fields of mathematics date September 2011 multiple issues confusing September 2010 refimprove September 2010 Mathematics has become a vastly diverse subject over History of mathematics history , and there is a corresponding need to categorize the different areas of mathematics . A number ... due in part to the different purposes they serve. In addition, as mathematics evolves ... the most active, which straddle the boundary between different areas. A traditional division of mathematics is into pure mathematics , mathematics studied for its intrinsic interest, and applied mathematics , mathematics which can be directly applied to real world problems. ref For example the Encyclop dia Britannica Eleventh Edition groups its mathematics articles as Pure, Applied, and Biographies ... ED9A945 . ref This division is not always clear and many subjects have been developed as pure mathematics to find unexpected applications later on. Broad divisions, such as discrete mathematics and computational mathematics , have emerged more recently. Classification systems The Mathematics Subject ... MATH . Many mathematics journals ask authors to label their papers with MSC subject codes. The MSC divides mathematics into over 60 areas, with further subdivisions within each area. In the Library of Congress Classification , mathematics is assigned the subclass QA within the class Q Science . The LCC defines Library of Congress Classification Class Q Science QA Mathematics broad divisions ... 500 Science Dewey Decimal Classification assigns mathematics to division 510, with subdivisions for Algebra ... & applied mathematics . The http arxiv.org archive math Categories within Mathematics list .... Mathematics of Computing. MathOverflow has a http mathoverflow.net tags tag system . Mathematics book publishers such as Springer Science Business Media Springer http www.springer.com mathematics?SGWID ... other subject item1521 ?site locale en GB Browse Mathematics and statistics and the American ... more details
has at least one fixed point mathematics fixed point we don t require the map to be bijective or even ... one. See also Unit disk , a disk with radius one Annulus mathematics Ball mathematics , the usual ... Disk Mathematics Category Euclidean geometry Category Rigid bodies ar bs Krug ca Disc ... more details
saved book title Mathematics subtitle An overview cover image Math.svg cover color Mathematics Main article Mathematics Supporting articles History of mathematics Mathematical beauty Mathematical notation Mathematical proof Areas of mathematics Glossary of areas of mathematics Category Wikipedia books on mathematicsMathematics ... more details
Wiktionarypar mathematicsMathematics is the body of knowledge justified by deductive reasoning about abstract structures, starting from axioms and definitions. Mathematics may also refer to Mathematics producer , a hip hop producer Mathematics album Mathematics album , an album by the band The Servant Mathematics song Mathematics song , a song by Mos Def Mathematics Cherry Ghost song Mathematics Cherry Ghost song , a song by Cherry Ghost Mathematics , a song by Little Boots from Hands Little Boots album Hands Mathematics Magazine , a publication of the Mathematical Association of America See also Category Mathematics Portal Mathematics Math disambiguation Mathematica disambiguation disambig fr Math homonymie it Mathematics lv Mathematics ... more details
with the fixed submanifold. Such perturbations do not affect the Homologymathematicshomology ...Refimprove date December 2009 In mathematics , transversality is a notion that describes how spaces can intersect transversality can be seen as the opposite of tangent tangency , and plays a role in general position . It formalizes the idea of a generic intersection in differential topology . It is defined by considering the linearizations of the intersecting spaces at the points of intersection. Definition Image Sphere transverse.svg thumb Transverse curves on the surface of a sphere Image Sphere nontransverse.svg thumb Non transverse curves on the surface of a sphere Two submanifold s of a given finite dimensional smooth manifold are said to intersect transversally if at every point of Intersection set theory intersection , their separate tangent spaces at that point together generate the tangent space of the ambient manifold at that point. ref Guillemin and Pollack 1974, p.30. ref Manifolds that do not intersect are vacuously transverse. If the manifolds are of complementary dimension i.e., their dimensions add up to the dimension of the ambient space , the condition means that the tangent space to the ambient manifold is the direct sum of the two smaller tangent spaces. If an intersection is transverse, then the intersection will be a submanifold whose codimension is equal to the sums of the codimensions of the two manifolds. In the absence of the transversality condition the intersection may fail to be a submanifold, having some sort of Mathematical singularity singular point ... mathematics immersion s at their point of intersection, as happens in the case of embedded submanifolds ... to a bilinear intersection product on homology classes of any dimension, which is Poincar dual to the cup ... of the base of codimension equal to the rank of the vector bundle, and its homology class ... 2. DEFAULTSORT Transversality Mathematics Category Differential topology Category Calculus of variations ... more details
operator on the homologymathematicshomology of M . More generally, a boundary operator can be defined ...In mathematics , more particularly in functional analysis , differential topology , and geometric measure theory , a k current in the sense of Georges de Rham is a linear functional functional on the space of compactly supported differential form differential k forms , on a smooth manifold M . Formally currents behave like Schwartz distribution s on a space of differential forms. In a geometric setting, they can represent integration over a submanifold, generalizing the Dirac delta function , or more generally even directional derivative s of delta functions multipole s spread out along subsets of M . Definition Let math scriptstyle Omega c m mathbb R n math denote the space of smooth m forms with compact support on math mathbb R n math . A current is a linear functional on math scriptstyle Omega c m mathbb R n math which is continuous in the sense of distribution mathematics distribution s. Thus a linear functional math T colon Omega c m mathbb R n to mathbb R math is an m current if it is continuous function continuous in the following sense If a sequence math omega k math of smooth forms, all supported in the same compact set, is such that all derivatives of all their coefficients tend uniformly to 0 when math k math tends to infinity, then math T omega k math tends to 0. The space math scriptstyle mathcal D m math of m dimensional currents on sup n sup is a real number real vector space with operations defined by math T S omega T omega S omega , qquad lambda T omega lambda T omega . math Multiplication by a constant scalar mathematics scalar represents a change in the multiplicity ... Integral Integration over a compact rectifiable set rectifiable orientation mathematics oriented submanifold ... several norm mathematics norms on subspaces of the space of all currents. One such norm is the mass ... Yang first2 Xiaoping title Geometric Measure Theory An Introduction series Advanced Mathematics Bejing ... more details
Folk mathematics can mean The mathematical folklore that circulates among mathematicians The informal mathematics used in everyday life, as studied in ethno cultural studies of mathematics. disambig Category Mathematical disambiguation ... more details
Italic title Mathematics of Computation ref http www.ams.org mcom aboutmcom.html Mathematics of Computation Journal overview , retrieved April 2007 ref is a quarterly mathematics journal focused on computational mathematics that is published by the American Mathematical Society . It was established in 1943. The articles in all volumes older than five years are available electronically free of charge. ref http www.ams.org jourcgi jrnl toolbar nav mcom all Mathematics of Computation Archive ref References reflist Category Mathematics journals Category Quarterly journals sci journal stub ... more details
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