In this paper, we obtain a comparison of Steklov eigenvalues and Laplacian on graphs discuss its rigidity. As applications the eigenvalues, Lichnerowicz-type estimates some combinatorial for graphs.

Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...

For Machine Learning (ML) classification problem, where a vector of x–observations (values of attributes) is mapped to a single y value (class label), a generalized Radon– Nikodym type of solution is proposed. Quantum–mechanics –like probability states ψ2(x) are considered and “Cluster Centers”, corresponding to the extremums of < yψ2(x) > / < ψ2(x) >, are found from generalized eigenvalues pro...

The abelian sandpile models feature a finite abelian group G generated by the operators corresponding to particle addition at various sites. We study the canonical decomposition of G as a product of cyclic groups G = Zd1 ×Zd2 ×Zd3 · · ·×Zdg where g is the least number of generators of G, and di is a multiple of di+1. The structure of G is determined in terms of the toppling matrix ∆. We constru...

In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.

An important problem in multi-label classification is to capture label patterns or underlying structures that have an impact on such patterns. One way of learning underlying structures over labels is to project both instances and labels into the same space where an instance and its relevant labels tend to have similar representations. In this paper, we present a novel method to learn a joint sp...

Let $G$ be a graph with eigenvalues $lambda_1(G)geqcdotsgeqlambda_n(G)$. In this paper we find all simple graphs $G$ such that $G$ has at most twelve vertices and $G$ has exactly two non-negative eigenvalues. In other words we find all graphs $G$ on $n$ vertices such that $nleq12$ and $lambda_1(G)geq0$, $lambda_2(G)geq0$ and $lambda_3(G)0$, $lambda_2(G)>0$ and $lambda_3(G)

Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...

In this paper, we define the symmetric hyperdeterminant, eigenvalues and E-eigenvalues of a real supersymmetric tensor. We show that eigenvalues are roots of a one-dimensional polynomial, and when the order of the tensor is even, E-eigenvalues are roots of another one-dimensional polynomial. These two one-dimensional polynomials are associated with the symmetric hyperdeterminant. We call them t...