Related papers: On the facet ideal of an expanded simplicial compl…

Self-similar sets require a separation condition to admit a nice mathematical structure. The classical open set condition (OSC) is difficult to verify. Zerner proved that there is a positive and finite Hausdorff measure for a weaker…

In a local Cohen-Macaulay ring $(A, \mathrm{m})$, we study the Hilbert function of an $\mathrm{m}$-primary ideal $I$ whose reduction number is two. It is a continuous work of the papers of Huneke, Ooishi, Sally, and Goto-Nishida-Ozeki. With…

We introduce a new family of pure simplicial complexes, called the $r$-co-connected complex of $G$ with respect to $A$, $\Sigma_r(A,G)$, where $r\geq 1$ is a natural number, $G$ is a simple graph, and $A$ is a subset of vertices.…

Associated to a simple undirected graph $G$ is a simplicial complex $\Delta_G$ whose faces correspond to the independent sets of $G$. A graph $G$ is called vertex decomposable if $\Delta_G$ is a vertex decomposable simplicial complex. We…

The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the P\"oschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of…

We prove that an iterative derivation $\delta_F$ on a field $F$ can be extended to an iterative derivation $\delta_A$ on a central simple $F-$algebra $A$ if the characteristic of $F$ does not divide the exponent of $A$ in the Brauer group…

In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $t\geq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we prove that it can be obtained from a Buchsbaum…

Given any finite simplicial complex \Delta, we show how to construct a new simplicial complex \Delta_{\chi} that is balanced and vertex decomposable. Moreover, we show that the h-vector of the simplicial complex \Delta_{\chi} is precisely…

We prove a generalization of the Expander Mixing Lemma for arbitrary (finite) simplicial complexes. The original lemma states that concentration of the Laplace spectrum of a graph implies combinatorial expansion (which is also referred to…

Let R be a commutative ring with unity, M be an unitary R-module and {\Gamma} be a simple graph. This research article is an interplay of combinatorial and algebraic properties of M . We show a combinatorial object completely determines an…

Using the theory of self-adjoint extensions, we study the relativistic spectral properties of the Landau operator with $\delta$ and $\delta '$ interactions on a cylinder of radius $R$ for a charged spin particle system, formally given by…

Let $G$ be a simple graph on the vertex set $[n]$ and $J_G$ be the corresponding binomial edge ideal. Let $G=v*H$ be the cone of $v$ on $H$. In this article, we compute all the Betti numbers of $J_G$ in terms of Betti number of $J_H$ and as…

Let I=I(D) be the edge ideal of a weighted oriented graph D. We determine the irredundant irreducible decomposition of I. Also, we characterize the associated primes and the unmixed property of I. Furthermore, we give a combinatorial…

Let $I$ be a homogeneous ideal in the polynomial ring $R = k[z_1, \cdots, z_n]$ , where $k$ is an algebraically closed field of characteristic zero. Macaulay's Theorem provides constraints on the Hilbert function of $I$ or $R/I$ from one…

An explicit formula is obtained for the generalized Macdonald functions on the $N$-fold Fock tensor spaces, calculating a certain matrix element of a composition of several screened vertex operators. As an application, we prove the…

We study theta functions of a Riemann surface of genus g from the view point of tau function of a hierarchy of soliton equations. We study two kinds of series expansions. One is the Taylor expansion at any point of the theta divisor. We…

In this paper, we explore the inflationary dynamics of the $\beta$-exponential potential model, where a scalar field couples to quadratic $(R + R^2)$ gravity. In this model, the inflaton is the field that determines the size of the extra…

By using a bottom-up reconstruction technique for non-minimally coupled scalar-tensor theories, we realize the Einstein frame attractor cosmologies in the $\Omega (\phi)$-Jordan frame. For our approach, what is needed for the reconstruction…

The face ring of a simplicial complex modulo m generic linear forms is shown to have finite local cohomology if and only if the link of every face of dimension m or more is `nonsingular', i.e., has the homology of a wedge of spheres of the…

We study pseudospectral and spectral functions for Hamiltonian system $Jy'-B(t)=\lambda\Delta(t)y$ and differential equation $l[y]=\lambda\Delta(t)y$ with matrix-valued coefficients defined on an interval $\mathcal{I}=[a,b)$ with the…