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Decomposition Theorem (decomposition + theorem)

Distribution by Scientific Domains
Mathematics and Statistics57%

Selected Abstracts

Regular matroid decomposition via signed graphs,

JOURNAL OF GRAPH THEORY, Issue 1 2005
Jim Geelen
Abstract The key to Seymour's Regular Matroid Decomposition Theorem is his result that each 3-connected regular matroid with no R10 - or R12 -minor is graphic or cographic. We present a proof of this in terms of signed graphs. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 74,84, 2005 [source]

Generation of Arbitrary Lagrangian,Eulerian (ALE) velocities, based on monitor functions, for the solution of compressible fluid equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005
B. V. Wells
Abstract A moving mesh method is outlined based on the use of monitor functions. The method is developed from a weak conservation principle. From this principle a conservation law for the mesh position is derived. Using the Helmholtz decomposition theorem, this conservation law can be converted into an elliptic equation for a mesh velocity potential. The moving mesh method is discretized using standard finite elements. Once the mesh velocities are obtained an arbitrary Lagrangian,Eulerian (ALE) (Journal of Computational Physics 1974; 14:227) fluid solver is used to update the solution on the adaptive mesh. Results are shown for the compressible Euler equations of gas dynamics in one and two spatial dimensions. Two monitor functions are used, the fluid density (which corresponds to a Lagrangian description), and a function which includes the density gradient. A variety of test problems are considered. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A structure theorem for graphs with no cycle with a unique chord and its consequences

JOURNAL OF GRAPH THEORY, Issue 1 2010
Nicolas Trotignon
Abstract We give a structural description of the class ,, of graphs that do not contain a cycle with a unique chord as an induced subgraph. Our main theorem states that any connected graph in ,, is either in some simple basic class or has a decomposition. Basic classes are chordless cycles, cliques, bipartite graphs with one side containing only nodes of degree 2 and induced subgraphs of the famous Heawood or Petersen graph. Decompositions are node cutsets consisting of one or two nodes and edge cutsets called 1-joins. Our decomposition theorem actually gives a complete structure theorem for ,,, i.e. every graph in ,, can be built from basic graphs that can be explicitly constructed, and gluing them together by prescribed composition operations, and all graphs built this way are in ,,. This has several consequences: an ,,(nm) -time algorithm to decide whether a graph is in ,,, an ,,(n+ m) -time algorithm that finds a maximum clique of any graph in ,,, and an ,,(nm) -time coloring algorithm for graphs in ,,. We prove that every graph in ,, is either 3-colorable or has a coloring with , colors where , is the size of a largest clique. The problem of finding a maximum stable set for a graph in ,, is known to be NP-hard. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 31,67, 2010 [source]

Cell decomposition for P -minimal fields

MLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 5 2009
Marie-Hélène Mourgues
Abstract In [12], P. Scowcroft and L. van den Dries proved a cell decomposition theorem for p -adically closed fields. We work here with the notion of P -minimal fields defined by D. Haskell and D. Macpherson in [6]. We prove that a P -minimal field K admits cell decomposition if and only if K has definable selection. A preprint version in French of this result appeared as a prepublication [8] (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Proof of a decomposition theorem for symmetric tensors on spaces with constant curvature

ANNALEN DER PHYSIK, Issue 8 2008
N. Straumann
Abstract In cosmological perturbation theory a first major step consists in the decomposition of the various perturbation amplitudes into scalar, vector and tensor perturbations, which mutually decouple. In performing this decomposition one uses , beside the Hodge decomposition for one-forms , an analogous decomposition of symmetric tensor fields of second rank on Riemannian manifolds with constant curvature. While the uniqueness of such a decomposition follows from Gauss' theorem, a rigorous existence proof is not obvious. In this note we establish this for smooth tensor fields, by making use of some important results for linear elliptic differential equations. [source]

Perfect coloring and linearly ,-bound P6 -free graphs

JOURNAL OF GRAPH THEORY, Issue 4 2007
S. A. Choudum
Abstract We derive decomposition theorems for P6, K1 + P4 -free graphs, P5, K1 + P4 -free graphs and P5, K1 + C4 -free graphs, and deduce linear ,-binding functions for these classes of graphs (here, Pn (Cn) denotes the path (cycle) on n vertices and K1 + G denotes the graph obtained from G by adding a new vertex and joining it with every vertex of G). Using the same techniques, we also obtain an optimal ,-binding function for P5, C4 -free graphs which is an improvement over that given in [J. L. Fouquet, V. Giakoumakis, F. Maire, and H. Thuillier, 1995, Discrete Math, 146, 33,44.]. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 293,306, 2007 [source]

Decomposing kernels of iterated operators,a unified approach

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2007
Guangbin Ren
Abstract For any operator D acting in an Abelian group, we study the kernel of its iterates Dk and describe a general approach for decomposing it through the kernel of the operator D itself and some other given operators T1,,,Tk,1. Due to Almansi's famous theorem for polyharmonic functions the different types of decomposition are characterized in terms of strong, weak and restricted Almansi decomposition properties. Sufficient conditions are given for the existence of such decompositions. The case of the iterated Dirac operator (cf. Math. Meth. Appl. Sci. 2002; 25:1541,1552) follows as a special case. Several other special cases are discussed. Finally we prove corresponding decomposition theorems for the iterated weighted Laplacian (|x|,,)k, ,,(,,, 2), and the iterated Helmholtz type operator (,,,)k, ,,C. Copyright © 2006 John Wiley & Sons, Ltd. [source]