Spatial autocorrelation, of which Geary’s c has traditionally been a popular measure, is fundamental to spatial science. This paper provides new perspective on c. We discuss this using concepts from spectral graph theory/linear algebraic theory. More precisely, we provide three types representations for it: (a) Laplacian representation, (b) Fourier transform and (c) Pearson’s correlation coeffi...

in the present study, a spectral finite element method is developed for free and forced transverse vibration of levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. in the first step, the governing out-of-plane differential equations are tr...

Recently we generalized the max algebra system to the class of nonnegative  tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and i...

Many approaches to analyzing the structure of a musical recording involve detecting sequential patterns within a selfsimilarity matrix derived from time-series features. Such patterns ideally capture repeated sequences, which then form the building blocks of large-scale structure. In this work, techniques from spectral graph theory are applied to analyze repeated patterns in musical recordings....

Despite of the extreme success of the spectral graph theory, there are relatively few papers applying spectral analysis to hypergraphs. Chung first introduced Laplacians for regular hypergraphs and showed some useful applications. Other researchers treated hypergraphs as weighted graphs and then studied the Laplacians of the corresponding weighted graphs. In this paper, we aim to unify these ve...

What Is Spectral Theory? By spectral theory we mean the theory of structure of certain bounded linear operators on a Hilbert space. In a broader sense, the history of spectral theory goes way back to the nineteenth century, when the objects of study used to be infinite systems of linear equations and integral equations. The subject was revolutionized in the late 1920s by von Neumann, when he de...