Related papers: Properties of the Hyper-Wiener index as a local fu…
We define an affine structure on $\ltwor\oplus...\oplus\ltwor$ and, following some ideas developed in \cite{Dut1}, we construct a local trace function for this situation. This trace function is a complete invariant for a shift invariant…
This work is dedicated to the development of the theory of Fourier hyperfunctions in one variable with values in a complex non-necessarily metrisable locally convex Hausdorff space $E$. Moreover, necessary and sufficient conditions are…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
Index theory has had profound impact on many branches of mathematics. In this note we discuss the context for a new kind of index theorem. We begin, however, with some operator theoretic results. In [11] Berger and Shaw established that…
The Wallenius distribution is a generalisation of the Hypergeometric distribution where weights are assigned to balls of different colours. This naturally defines a model for ranking categories which can be used for classification purposes.…
In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in the context of both type 1 and type 2 unitary…
In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…
Generalized integral formulas involving the generalized Bessel-Maitland function are considered and it expressed in terms of generalized Wright hypergeometric functions. By assuming appropriate values of the parameters in the main results,…
The spectral graph theory provides an algebraical approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the…
The Wiener index of a connected graph is the sum of the distances between all pairs of vertices in the graph. It was conjectured that the Wiener index of an $n$-vertex maximal planar graph is at most $\lfloor\frac{1}{18}(n^3+3n^2)\rfloor$.…
We study the local functor of points (which we call the Weil-Berezin functor) for smooth supermanifolds, providing a characterization, representability theorems and applications to differential calculus.
Let $G$ be a finite, connected, undirected, and simple graph and $W$ be a set of vertices in $G$. A representation multiset of a vertex $u$ in $V(G)$ with respect to $W$ is defined as the multiset of distances between $u$ and the vertices…
The Hirsch function of a given continuous function is a new function depending on a parameter. It exists provided some assumptions are satisfied. If this parameter takes the value one, we obtain the well-known h-index. We prove some…
On the background of Zhang's local Gross-Zagier formulae for GL(2), we study some p-adic problems. The local Gross-Zagier formulae give identities of very special local geometric data (local linking numbers) with certain local Fourier…
For any natural number n, the Hurwitz graph $\mathcal{H}(S_n )$ has vertices corresponding to reduced words of the cycle $(1 . . . n)$ in terms of transpositions in $S_n$, and has edges corresponding to local shifts. This graph is known to…
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
Let G be a simple connected graph having vertex set V and edge set E. The vertex-set and edge-set of G denoted by V(G) and E(G), respectively. The length of the smallest path between two vertices is called the distance. Mathematical…
In recent years several compressed indexes based on variants of the Burrows-Wheeler transformation have been introduced. Some of these index structures far more complex than a single string, as was originally done with the FM-index…
The Hirsch index (commonly referred to as h-index) is a bibliometric indicator which is widely recognized as effective for measuring the scientific production of a scholar since it summarizes size and impact of the research output. In a…
Consider a random matrix of the form $W_n = M_n + D_n$, where $M_n$ is a Wigner matrix and $D_n$ is a real deterministic diagonal matrix ($D_n$ is commonly referred to as an external source in the mathematical physics literature). We study…