Results 51 to 60 of about 67,630 (266)

Variation of sum of two largest eigenvalues of the distance matrices of four-leaf graph

Journal of Hebei University of Science and Technology, 2020
In order to accurately obtain the extremum of the distance eigenvalues of fowr-leaf graphs under tow graph transformations in any case, two graph transformations of four-leaf graphs and the results of the above problems were given by using the properties
Zhe LYU, Yubin GAO
doaj   +1 more source

Spectral Convergence of the connection Laplacian from random samples

, 2015
Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction.
Singer, Amit, Wu, Hau-tieng
core   +1 more source

Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues [PDF]

, 2018
We present two graph quantities Psi(G,S) and Psi_2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues, lambda(G,S) and lambda_2(G), respectively.
Miller, Gary L., Walkington, Noel J., Wang, Alex L.   +2 more
core   +2 more sources

Unified spectral bounds on the chromatic number

, 2014
One of the best known results in spectral graph theory is the following lower bound on the chromatic number due to Alan Hoffman, where mu_1 and mu_n are respectively the maximum and minimum eigenvalues of the adjacency matrix: chi >= 1 + mu_1 / (- mu_n).
Elphick, Clive, Wocjan, Pawel
core   +2 more sources

Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods [PDF]

, 2010
We consider Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way.
Borisov, D., Cardone, G.
core   +2 more sources

Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver

International Journal for Numerical Methods in Fluids, EarlyView.
A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
wiley   +1 more source

Eigenvalues of collapsing domains and drift Laplacians

, 2012
By introducing a weight function to the Laplace operator, Bakry and \'Emery defined the "drift Laplacian" to study diffusion processes. Our first main result is that, given a Bakry-\'Emery manifold, there is a naturally associated family of graphs whose ...
Lu, Zhiqin, Rowlett, Julie
core   +1 more source

Diameter vs. Laplacian eigenvalue distribution

The Electronic Journal of Linear Algebra
Let $G$ be a simple graph of order $n$. It is known that any Laplacian eigenvalue of $G$ belongs to the interval $[0,n]$. For an interval $I\subseteq [0, n]$, denote by $m_GI$ the number of Laplacian eigenvalues of $G$ in $I$, counted with multiplicities. Let $d$ be the diameter of $G$. If $2\le d\le n-4$, we show that $m_G[n-d,n]\le n-d+2$, and it may
Leyou Xu, Bo Zhou
openaire   +2 more sources

Shape Derivatives of the Eigenvalues of the De Rham Complex for Lipschitz Deformations and Variable Coefficients: Part I

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We study eigenvalue problems for the de Rham complex on varying three‐dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non‐constant coefficients. We provide Hadamard‐type formulas for the shape derivatives under weak regularity assumptions on the domain and its ...
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron   +2 more
wiley   +1 more source

Two Laplacian energies and the relations between them / Две энергии Лапласа и их соотношение / Dve Laplasove energije i odnosi među njima [PDF]

Vojnotehnički Glasnik, 2020
Introduction/purpose: The Laplacian energy (LE) is the sum of absolute values of the terms μi-2m/n, where μi, i=1,2,…,n, are the eigenvalues of the Laplacian matrix of the graph G with n vertices and m edges. In 2006, another quantity Z was introduced,
Ivan Gutman
doaj   +1 more source