相关论文: On the $r$-shifted central triangles of a Riordan …
In this paper we analyse the dynamics of a family of rational operators coming from a fourth-order family of root-finding algorithms. We first show that it may be convenient to redefine the parameters to prevent redundancies and…
Let $V$ denote a vector space with finite positive dimension. We consider a pair of linear transformations $A : V \to V$ and $A^* : V \to V$ that satisfy (i) and (ii) below: (i) There exists a basis for $V$ with respect to which the matrix…
A physical model which describes the CKM matrix is analyzed. The elements of such a matrix are field-strength renormalization factors. Each column gives the probability amplitude for the field operators of the coupled Lagrangian to create a…
Every regular N-gon defines a canonical family of regular polygons which are conforming to the bounds of the 'star polygons' determined by N. These star polygons are formed from truncated extended edges of the N-gon and the intersection…
We present a method to obtain families of lattice equations. Specifically we focus on two of such families, which include 3-parameters and their members are connected through B\"acklund transformations. At least one of the members of each…
We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent only for a limited range of parameters. However, when one…
We consider a parametrised family of Thue equations, \[ (x-G_1(n)\, y) \cdots (x-G_d(n)\, y) - y^d = \pm 1, \] which was first considered by Thomas to have an explicit set of solutions for parameters $n$ larger than some effectively…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
Ferroni and Larson gave a combinatorial interpretation of the braid Kazhdan-Lusztig polynomials in terms of series-parallel matroids. As a consequence, they confirmed an explicit formula for the leading Kazhdan-Lusztig coefficients of braid…
We study the singular values of certain triangular random matrices. When their elements are i.i.d. standard complex Gaussian random variables, the squares of the singular values form a biorthogonal ensemble, and with an appropriate change…
We consider $n\times n$ real-valued matrices $A = (a_{ij})$ satisfying $a_{ii} \geq a_{i,i+1} \geq \dots \geq a_{in} \geq a_{i1} \geq \dots \geq a_{i,i-1}$ for $i = 1,\dots,n$. With such a matrix $A$ we associate a directed graph $G(A)$. We…
We present and study two families of polynomials with coefficients in the center of the universal enveloping algebra. These polynomials are analogues of a determinant and a characteristic polynomial of a certain non-commutative matrix,…
We study multilinear generalized Radon transforms using a graph-theoretic paradigm that includes the widely studied linear case. These provide a general mechanism to study Falconer-type problems involving $(k+1)$-point configurations in…
On a Riemannian manifold we define a one-parameter family of Laplacians acting on sections of any bundle associated to the principal frame bundle via a representation, and show how various examples fit into this framework.
We defined two type $B$-sequences of Riordan arrays and present the $A$-sequence characterization and $Z$-sequence characterization of the Riordan matrices with two type $B$-sequences. The subgroups characterized by $A$-sequences and…
The author's idea of {\it algebraic compositeness} of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. i) For all fundamental particles of…
The exponential of an NxN matrix can always be expressed as a matrix polynomial of order N-1. In particular, a general group element for the fundamental representation of SU(N) can be expressed as a matrix polynomial of order N-1 in a…
For any real-valued $k > 1$, we consider the tree rooted at 0, where each positive integer $n$ has parent $\lfloor\frac{n}{k}\rfloor$. The average number of children per node is $k$, thus this definition gives a natural way to extend…
The higher rank numerical ranges of generic matrices are described in terms of the components of their Kippenhahn curves. Cases of tridiagonal (in particular, reciprocal) 2-periodic matrices are treated in more detail.
The rich analytic structure of hadronic form factors makes a theoretically consistent yet easily applicable parametrisation cumbersome. Consequently, most parametrisations are limited to reproducing the simplest analytic features sufficient…