Global ETD Search

1	Normal and Δ-Normal Configurations in Toric Algebra Solus, Liam 17 June 2011 (has links) No description available. Mathematics toric algebra normal toric varieties triangulations normal configurations &916 -normal configurations unimodular unimodular triangulations unimodular coverings toric ideals regular unimodular triangulations
2	Unimodular Covers and Triangulations of Lattice Polytopes v.Thaden, Michael 17 June 2008 (has links) Diese Arbeit befasst sich mit der unimodularen Überdeckung und Triangulierung von Gitterpolytopen. Zentral ist in diesem Zusammenhang die Angabe einer möglichst guten oberen Schranke c0, so dass die Vielfachen cP eines Polytopes P für alle c>c0 eine unimodulare Überdeckung besitzen. Bruns und Gubeladze haben erstmals die Existenz einer solchen Schranke nachgewiesen und konnten sogar explizit eine solche in Abhängigkeit von der Dimension des Polytopes angeben. Allerdings war diese Schranke super-exponentiell. In dieser Arbeit wird nun u.a. eine polynomielle obere Schranke hergeleitet. Unimodular Covers Unimodular Triangulations Lattice Polytopes Gitterpolytope 52B20 52C07 52C17 32B25 11H06 27 - Mathematik ddc:510
3	Contributions à la théorie des espaces de fonctions : singularités et relèvements / Contributions to the theory of functional spaces : singularities and liftings Molnar, Ioana 24 June 2014 (has links) Dans cette thèse nous étudions quelques aspects des certains espaces de fonctions. D’une part nous nous intéressons aux singularités des applications W^{1,n} à valeurs dans la sphère unité S^n, et d’autre part, aux relèvements des applications W^{s,p} à valeurs dans le cercle S^1.La première partie concerne le problème de minimisation d’une énergie de type Dirichlet à poids. Les fonctions admissibles sont les fonctions continues hors d’un ensemble singulier donné prescrit par le bord d’un courant rectifiable. Nous obtenons la formule exacte, résultat qui améliore celui d’Alberto, Baldi et Orlando (2003). Il s’agit aussi d’une généralisation des résultats obtenus précédemment par Brezis, Coron, Lieb (1986), Almgren, Browder, Lieb (1988).La deuxième partie porte sur le meilleur contrôle des phases des applications uni-modulaires et elle se repose sur les travaux de Bourgain, Brezis, Mironescu (2000, 2002). A l’aide de quelques méthodes connues et des méthodes nouvelles, nous étudions des estimations optimales des semi-normes W^{s,p} des relèvements selon les différentes valeurs de s et de p. Nous obtenons aussi une nouvelle caractérisation de W^{s,p} pour s<1 en termes de semi-norme dyadique / In this thesis we study some aspects of certain functional spaces. On the one hand we focus on the singularities of maps W^{1, n} with values in the unit sphere S^n, and secondly, on liftings of maps W^{s, p} with values in the circle S^1.The first part concerns the minimization problem of a weighted Dirichlet energy. Admissible maps are functions which are continuous functions outside a given singular set prescribed by the boundary of a rectifiable current. We obtain the exact formula, which improves the result of Alberto, Baldi and Orlando (2003). In the same time, we generalize some results previously obtained by Brezis, Coron, Lieb (1986), Almgren, Browder, Lieb (1988).The second part focuses on the best control of unimodular maps and it is based on the work of Bourgain, Brezis, Mironescu (2000, 2002). Using some known methods and some new ones, we study optimal estimates of seminorms W^{s, p} of liftings, for different values of s and p. We also obtain a new characterization of the space W^{s, p} for s<1 in terms of dyadic seminorm Applications unimodulaires Estimations optimales Relèvement Jacobien distributionnel Construction dipôle Courant rectifiable Dipole construction Rectifiable currents Optimal estimates Unimodular maps Lifting Distributional jacobian 510
4	Divisors on graphs, binomial and monomial ideals, and cellular resolutions Shokrieh, Farbod 27 August 2014 (has links) We study various binomial and monomial ideals arising in the theory of divisors, orientations, and matroids on graphs. We use ideas from potential theory on graphs and from the theory of Delaunay decompositions for lattices to describe their minimal polyhedral cellular free resolutions. We show that the resolutions of all these ideals are closely related and that their Z-graded Betti tables coincide. As corollaries, we give conceptual proofs of conjectures and questions posed by Postnikov and Shapiro, by Manjunath and Sturmfels, and by Perkinson, Perlman, and Wilmes. Various other results related to the theory of chip-firing games on graphs also follow from our general techniques and results. Graph Divisors Chip-firing Potential theory Green's function Grobner theory Hyperplane arrangement Lattice Delaunay decomposition Totally unimodular
5	Termodynamika prostoročasu: nový pohled z kvantové oblasti / Thermodynamics of spacetime: A new perspective from the quantum realm Liška, Marek January 2020 (has links) The main result of the thesis is the derivation of quantum phenomenological gravi- tational dynamics from the thermodynamics of local causal diamonds. By taking into account logarithmic corrections to entropy implied by quantum gravity effects, we derive new gravitational equations of motion which incorporate quantum corrections. The re- sulting theory appears to be a direct generalisation of the classical unimodular gravity instead of the general relativity. Upon obtaining the equations, we discuss their prop- erties and possible implications. As by-products, we also present a novel derivation of the Einstein equations from the thermodynamics of causal diamonds and a derivation of the logarithmic corrections to black hole entropy from the existence of minimal re- solvable area. Apart from the new results, we also provide an extensive review of the thermodynamics of local causal horizons. 1
6	Fast Order Basis and Kernel Basis Computation and Related Problems Zhou, Wei 28 November 2012 (has links) In this thesis, we present efficient deterministic algorithms for polynomial matrix computation problems, including the computation of order basis, minimal kernel basis, matrix inverse, column basis, unimodular completion, determinant, Hermite normal form, rank and rank profile for matrices of univariate polynomials over a field. The algorithm for kernel basis computation also immediately provides an efficient deterministic algorithm for solving linear systems. The algorithm for column basis also gives efficient deterministic algorithms for computing matrix GCDs, column reduced forms, and Popov normal forms for matrices of any dimension and any rank. We reduce all these problems to polynomial matrix multiplications. The computational costs of our algorithms are then similar to the costs of multiplying matrices, whose dimensions match the input matrix dimensions in the original problems, and whose degrees equal the average column degrees of the original input matrices in most cases. The use of the average column degrees instead of the commonly used matrix degrees, or equivalently the maximum column degrees, makes our computational costs more precise and tighter. In addition, the shifted minimal bases computed by our algorithms are more general than the standard minimal bases. polynomial matrix computation algorithm complexity computer algebra order basis kernel basis linear system solving matrix inverse determinant unimodular completion Popov form Hermite form column reduced form GCD matrix GCD rank rank profile column basis Computer Science
7	Fast Order Basis and Kernel Basis Computation and Related Problems Zhou, Wei 28 November 2012 (has links) In this thesis, we present efficient deterministic algorithms for polynomial matrix computation problems, including the computation of order basis, minimal kernel basis, matrix inverse, column basis, unimodular completion, determinant, Hermite normal form, rank and rank profile for matrices of univariate polynomials over a field. The algorithm for kernel basis computation also immediately provides an efficient deterministic algorithm for solving linear systems. The algorithm for column basis also gives efficient deterministic algorithms for computing matrix GCDs, column reduced forms, and Popov normal forms for matrices of any dimension and any rank. We reduce all these problems to polynomial matrix multiplications. The computational costs of our algorithms are then similar to the costs of multiplying matrices, whose dimensions match the input matrix dimensions in the original problems, and whose degrees equal the average column degrees of the original input matrices in most cases. The use of the average column degrees instead of the commonly used matrix degrees, or equivalently the maximum column degrees, makes our computational costs more precise and tighter. In addition, the shifted minimal bases computed by our algorithms are more general than the standard minimal bases. polynomial matrix computation algorithm complexity computer algebra order basis kernel basis linear system solving matrix inverse determinant unimodular completion Popov form Hermite form column reduced form GCD matrix GCD rank rank profile column basis Computer Science
8	On Weak Limits and Unimodular Measures Artemenko, Igor 14 January 2014 (has links) In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation, sometimes referred to as the intrinsic mass transport principle. The so-called law of a finite graph is an example of a unimodular measure. We say that a measure is sustained by a countable graph if the set of rooted connected components of the graph has full measure. We demonstrate several new results involving sustained unimodular measures, and provide thorough arguments for known ones. In particular, we give a criterion for unimodularity on connected graphs, deduce that connected graphs sustain at most one unimodular measure, and prove that unimodular measures sustained by disconnected graphs are convex combinations. Furthermore, we discuss weak limits of laws of finite graphs, and construct counterexamples to seemingly reasonable conjectures. tree automorphism group ball path connected component rooted birooted graph Cayley converges weakly extreme point mass transport principle involution invariance law neighbourhood orbit rigid subgraph unimodular unimodularity vertex-transitive walk weak limit weak convergence probability measure barred binary tree bi-infinite path first ancestor judicial lawless negligible stabilizer sustained strictly sustained random graph
9	On Weak Limits and Unimodular Measures Artemenko, Igor January 2014 (has links) In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation, sometimes referred to as the intrinsic mass transport principle. The so-called law of a finite graph is an example of a unimodular measure. We say that a measure is sustained by a countable graph if the set of rooted connected components of the graph has full measure. We demonstrate several new results involving sustained unimodular measures, and provide thorough arguments for known ones. In particular, we give a criterion for unimodularity on connected graphs, deduce that connected graphs sustain at most one unimodular measure, and prove that unimodular measures sustained by disconnected graphs are convex combinations. Furthermore, we discuss weak limits of laws of finite graphs, and construct counterexamples to seemingly reasonable conjectures. tree automorphism group ball path connected component rooted birooted graph Cayley converges weakly extreme point mass transport principle involution invariance law neighbourhood orbit rigid subgraph unimodular unimodularity vertex-transitive walk weak limit weak convergence probability measure barred binary tree bi-infinite path first ancestor judicial lawless negligible stabilizer sustained strictly sustained random graph

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