Global ETD Search

1	Witten Laplacian Methods For Critical Phenomena Lo, Assane January 2007 (has links) It is well known that very few models of interacting systems particularly those in dimension higher than two, can be solved exactly. The mean-field treatment is the first step in approximate calculations for such models. Although mean-field approximation leads to sufficiently accurate results of the thermodynamic properties of these systems away from critical points, most often it fails miserably close to the critical points. In this thesis, we propose to study direct methods (not based on any mean-field type approximations) for proving the exponential decay of the two point-correlation functions and the analyticity of the pressure (free energy per unit volume) for models of Kac type. The methods are based on the Helffer-SjÃ¶strand formula for the covariance in terms of Witten's Laplacians. Witten Laplacians Correlations Analyticity Pressure
2	Mean Eigenvalue Counting Function Bound for Laplacians on Random Networks Samavat, Reza 22 January 2015 (has links) (PDF) Spectral graph theory widely increases the interests in not only discovering new properties of well known graphs but also proving the well known properties for the new type of graphs. In fact all spectral properties of proverbial graphs are not acknowledged to us and in other hand due to the structure of nature, new classes of graphs are required to explain the phenomena around us and the spectral properties of these graphs can tell us more about the structure of them. These both themes are the body of our work here. We introduce here three models of random graphs and show that the eigenvalue counting function of Laplacians on these graphs has exponential decay bound. Since our methods heavily depend on the first nonzero eigenvalue of Laplacian, we study also this eigenvalue for the graph in both random and nonrandom cases. spektrale Graphentheorie zufällige Graphen Laplacians Spectral Graph theory Random Graphs Laplacians ddc:515 Spektraltheorie Zufallsgraph Operator
3	Mean Eigenvalue Counting Function Bound for Laplacians on Random Networks Samavat, Reza 15 December 2014 (has links) Spectral graph theory widely increases the interests in not only discovering new properties of well known graphs but also proving the well known properties for the new type of graphs. In fact all spectral properties of proverbial graphs are not acknowledged to us and in other hand due to the structure of nature, new classes of graphs are required to explain the phenomena around us and the spectral properties of these graphs can tell us more about the structure of them. These both themes are the body of our work here. We introduce here three models of random graphs and show that the eigenvalue counting function of Laplacians on these graphs has exponential decay bound. Since our methods heavily depend on the first nonzero eigenvalue of Laplacian, we study also this eigenvalue for the graph in both random and nonrandom cases. info:eu-repo/classification/ddc/515 ddc:515 Spektraltheorie; Zufallsgraph; Operator
4	Graph Laplacians, Nodal Domains, and Hyperplane Arrangements Biyikoglu, Türker, Hordijk, Wim, Leydold, Josef, Pisanski, Tomaz, Stadler, Peter F. 08 November 2018 (has links) Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. Here we investigate their so-called nodal domains, i.e. the connected components of the maximal induced subgraphs of G on which an eigenvector ψ does not change sign. An analogue of Courant's nodal domain theorem provides upper bounds on the number of nodal domains depending on the location of ψ in the spectrum. This bound, however, is not sharp in general. In this contribution we consider the problem of computing minimal and maximal numbers of nodal domains for a particular graph. The class of Boolean Hypercubes is discussed in detail. We find that, despite the simplicity of this graph class, for which complete spectral information is available, the computations are still non-trivial. Nevertheless, we obtained some new results and a number of conjectures. info:eu-repo/classification/ddc/510.72 ddc:510.72
5	Hypernode graphs for learning from binary relations between sets of objects / Un modèle d'hypergraphes pour apprendre des relations binaires entre des ensembles d'objets Ricatte, Thomas 23 January 2015 (has links) Cette étude a pour sujet les hypergraphes. / This study has for subject the hypergraphs. Hypergraphes Laplaciens de graphe Noyaux de graphe Apprentissage spectral Apprentissage semi-supervisé Algorithmes de skill rating Hypergraphs Graph laplacians Graph kernels Spectral learning Semi-supervised learning Skill rating algorithms
6	Наилучшее приближение оператора Лапласа ограниченными операторами в пространстве L2 : магистерская диссертация / The best approximation of the Laplacian by bounded operators in the space L2 Сокольский, С. А., Sokol’skii, S. A. January 2019 (has links) Рассматривается задача о наилучшем приближении оператора Лапласа первого порядка линейными ограниченными операторами с нормой, не превосходящей заданного числа, в пространстве L2(Rn) на классе функций, норма второй степени оператора Лапласа которых ограничена. Также в ходе решения этой задачи получена точная оценка нормы оператора Лапласа первого порядка через норму оператора Лапласа второго порядка и норму функции в пространстве L2(Rn). / We consider the problem of the best approximation of the first order Laplace operator by linear bounded operators with norm not exceeding a given number in the space L2(Rn) on the class of functions with a bounded norm of the second degree of the Laplace operator. We also obtain an exact estimate for the norm of the first order Laplace operator in terms of the norm of the second order Laplace operator and the norm of the function in the space L2(Rn). ЗАДАЧА СТЕЧКИНА MASTER'S THESIS FIRST AND SECOND ORDER LAPLACIANS STECHKIN PROBLEM KOLMOGOROV INEQUALITY

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