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981.
Jason J. Molitierno 《Linear and Multilinear Algebra》2018,66(6):1153-1170
In this paper, we use graph theoretic properties of generalized Johnson graphs to compute the entries of the group inverse of Laplacian matrices for generalized Johnson graphs. We then use these entries to compute the Zenger function for the group inverse of Laplacian matrices of generalized Johnson graphs. 相似文献
982.
In this paper, we establish a tight sufficient condition for the Hamiltonicity of graphs with large minimum degree in terms of the signless Laplacian spectral radius and characterize all extremal graphs. Moreover, we prove a similar result for balanced bipartite graphs. Additionally, we construct infinitely many graphs to show that results proved in this paper give new strength for one to determine the Hamiltonicity of graphs. 相似文献
983.
984.
Caffarelli and Silvestre [Comm. Part. Diff. Eqs., 32, 1245–1260(2007)] characterized the fractional Laplacian(-Δ)~s as an operator maps Dirichlet boundary condition to Neumann condition via the harmonic extension problem to the upper half space for 0 s 1. In this paper, we extend this result to all s 0. We also give a new proof to the dissipative a priori estimate of quasi-geostrophic equations in the framework of L~p norm using the Caffarelli–Silvestre's extension technique. 相似文献
985.
R. K. Mohanty 《Numerical Methods for Partial Differential Equations》2010,26(4):931-944
In this article, using coupled approach, we discuss fourth order finite difference approximation for the solution of two dimensional nonlinear biharmonic partial differential equations on a 9‐point compact stencil. The solutions of unknown variable and its Laplacian are obtained at each internal grid points. This discretization allows us to use the Dirichlet boundary conditions only and there is no need to discretize the derivative boundary conditions. We require only system of two equations to obtain the solution and its Laplacian. The proposed fourth order method is used to solve a set of test problems and produce high accuracy numerical solutions. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
986.
本文刻画取得给定阶数和独立数连通图的谱半径最大值的图的结构,对特殊独立数也给出取得最小谱半径图的结构. 相似文献
987.
The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In our recent work, we have determined the graphs with maximal Laplacian spreads among all trees of fixed order and among all unicyclic graphs of fixed order, respectively. In this paper, we continue the work on Laplacian spread of graphs, and prove that there exist exactly two bicyclic graphs with maximal Laplacian spread among all bicyclic graphs of fixed order, which are obtained from a star by adding two incident edges and by adding two nonincident edges between the pendant vertices of the star, respectively. 相似文献
988.
Mihai N. Pascu 《Transactions of the American Mathematical Society》2002,354(11):4681-4702
We introduce a new type of coupling of reflecting Brownian motions in smooth planar domains, called scaling coupling. We apply this to obtain monotonicity properties of antisymmetric second Neumann eigenfunctions of convex planar domains with one line of symmetry. In particular, this gives the proof of the hot spots conjecture for some known types of domains and some new ones.
989.
Perron components and algebraic connectivity for weighted graphs 总被引:8,自引:0,他引:8
The algebraic connectivity of a connected graph is the second-smallest eigenvalue of its Laplacian matrix, and a remarkable result of Fiedler gives information on the structure of the eigenvectors associated with that eigenvalue. In this paper, we introduce the notion of a perron component at a vertex in a weighted graph, and show how the structure of the eigenvectors associated with the algebraic connectivity can be understood in terms of perron components. This leads to some strengthening of Fiedler's original result, gives some insights into weighted graphs under perturbation, and allows for a discussion of weighted graphs exhibiting tree-like structure. 相似文献
990.
E. M. E. Zayed 《数学学报(英文版)》1997,13(3):337-346
This paper is devoted to asymptotic formulae for functions related with the spectrum of the negative Laplacian in two and
three dimensional bounded simply connected domains with impedance boundary conditions, where the impedances are assumed to
be discontinuous functions. Moreover, asymptotic expressions for the difference of eigenvalues related to the impedance problems
with different impedances are derived. Further results may be obtained. 相似文献