Randić index is one of the most famous topological graph indices. The energy a was defined more than four decades ago for its molecular applications. classical modeling molecule as sum absolute values all eigenvalues adjacency matrix corresponding to graph. There are several other versions notion obtained using types matrices. In this paper, we introducing and investigating type Hadi RHE(G) G, ...

We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a...

ABSTRACT. We extend the notion of representation of a matroid to algebraic structures that we call skew partial fields. Our definition of such representations extends Tutte’s definition, using chain groups. We show how such representations behave under duality and minors, we extend Tutte’s representability criterion to this new class, and we study the generator matrices of the chain groups. An ...

*Correspondence: [email protected] 2School of Science, Zhejiang A&F University, Hangzhou, 311300, China Full list of author information is available at the end of the article Abstract Let S(G ) be the skew-adjacency matrix of an oriented graph G with n vertices, and let λ1,λ2, . . . ,λn be all eigenvalues of S(G ). The skew-spectral radius ρs(G ) of G is defined as max{|λ1|, |λ2|, . . . , |λn|}....

This paper shows that Cayley Transforms, which map Orthogonal and SkewSymmetric matrices, may be considered the extension to matrix field of the complex conformal mapping function f1(z) = 1− z 1 + x . Then, by using a set of real matrices which are, simultaneously, Orthogonal and Symmetric (the Ortho−Sym matrices), it similarly shows how to extend two complex conformal mapping functions (namely...

In this paper we consider numerical methods for computing functions of matrices being Hamiltonian and skew-symmetric. Analytic functions of this kind of matrices (i.e., exponential and rational functions) appear in the numerical solutions of orthosymplectic matrix differential systems when geometric integrators are involved. The main idea underlying the presented techniques is to exploit the sp...

We establish an identity for $$Ef\left( \varvec{Y}\right) - Ef\left( \varvec{X}\right) $$ , when $$\varvec{X}$$ and $$\varvec{Y}$$ both have matrix variate skew-normal distributions the function f satisfies some weak conditions. The characteristic of skew normal distribution is then derived. make use it to derive necessary sufficient conditions comparison under six different orders, such as usu...

We introduce a class of posets, which includes both ribbon posets (skew shapes) and $d$-complete such that their number linear extensions is given by determinant matrix whose entr...

In 1933 a family of skew Hadamard difference sets was described by Paley using matrix language and was called the Paley–Hadamard difference sets in the literature. During the last 70 years, no new skew Hadamard difference sets were found. It was conjectured that there are no further examples of skew Hadamard difference sets. This conjecture was proved to be true for the cyclic case in 1954, and...

Porous material such as metal-natural constructions and their particular partner poly-hydra are made up of inorganic clusters with no saturation exhibit great capability for utilization in the absorption gas ascending opening optics detecting biotechnology hardware. Cuboctahedral bi-metallic structure is an often-quoted example polyhedra class. In this study, we have calculated first second Zag...