Related papers: Properties of the Hyper-Wiener index as a local fu…
Fullerenes are molecules in the form of cage-like polyhedra, consisting solely of carbon atoms. Fullerene graphs are mathematical models of fullerene molecules. The transmission of a vertex $v$ of a graph is the sum of distances from $v$ to…
We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…
A nonlocal vector calculus was introduced in [2] that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A generalization is developed that provides a more general setting for…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
Indices of vector fields on (complex analytic) singular varieties have been considered by various authors from several different viewpoints. All these indices coincide with the classical local index of Poincar\'e-Hopf when the ambient…
Teminal Wiener index is one of the commonly used topological index in mathematical chemistry. If two or more chemical compounds have the same terminal Wiener index then they will have similar physico-chemical properties. In this work we…
We present a list of formulae useful for Weyl-Heisenberg integral quantizations, with arbitrary weight, of functions or distributions on the plane. Most of these formulae are known, others are original. The list encompasses particular cases…
This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…
We discuss the local index theorem for cofinite Riemann surfaces in a pedagogical way, from a more computational perspective. Given a cofinite Riemann surface $X$, let $\Delta_n$ be the $n$-Laplacian and let $N_n$ be the Gram matrix of a…
The fundamental set of solutions of the generalized hypergeometric differential equation in the neighborhood of unity has been built by N{\o}rlund in 1955. The behavior of the generalized hypergeometric function in the neighborhood of unity…
The Whittaker function and its diverse extensions have been actively investigated. Here we introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function $\Phi_{p,v}$ and investigate some of…
The Wiener index of a graph is the sum of all the distances between any pair of vertices. We aim to describe graphs which minimize the Wiener index among all unicyclic graphs with fixed girth and given degree sequence. Depending on where…
Wiener index and Harary index are two classic and well-known topological indices for the characterization of molecular graphs. Recently, Yu et al. \cite{YYSX} established some sufficient conditions for a graph to be pancyclic in terms of…
The edge-Wiener index $W_e(G)$ of a connected graph $G$ is the sum of distances between all pairs of edges of $G$. A connected graph $G$ is said to be a cactus if each of its blocks is either a cycle or an edge. Let $\mathcal{G}_{n,t}$…
This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statistical literature and are useful when dealing with the…
Indices of singular points of a vector field or of a 1-form on a smooth manifold are closely related with the Euler characteristic through the classical Poincar\'e--Hopf theorem. Generalized Euler characteristics (additive topological…
In this paper, we study the Steiner hyper-Wiener index of a graph, which is obtained from the standard hyper-Wiener index by replacing the classical graph distance with the Steiner distance. It is shown how this index is related to the…
H-measures and semiclassical (Wigner) measures were introduced in earlyn 1990s and since then they have found numerous applications in problems involving $\mathrm{L}^2$ weakly converging sequences. Although they are similar objects, neither…
The delta interaction at a vertex generalizes the Robin (generalized Neumann) boundary condition on an interval. Study of a single vertex with N infinite leads suffices to determine the localized effects of such a vertex on densities of…
Kuznetsov et al. (2011) and Kuznetsov and Pardo (2013) introduced the family of Hypergeometric L\'evy processes. They appear naturally in the study of fluctuations of stable processes when one analyses stable processes through the theory of…