Related papers: The generalized recurrent set and strong chain rec…
I consider general reflection coefficients for arbitrary one-dimensional whole line differential or difference operators of order $2$. These reflection coefficients are semicontinuous functions of the operator: their absolute value can only…
The asynchronous systems f are multi-valued functions, representing the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In real time, they map an 'admissible input' function…
Extensions of equivalent representations of gravity are discussed in the metric-affine framework. First, we focus on: (i) General Relativity, based upon the metric tensor whose dynamics is given by the Ricci curvature scalar $R$; (ii) the…
In commutative algebra, the theory of Gr\"obner bases enables one to compute in any finitely generated algebra over a given computable field. For non-finitely generated algebras however, other methods have to be pursued. For instance, it…
Given a dynamical system $(X,T)$ and a family $\mathsf{I}\subseteq \mathcal{P}(\omega)$ of "small" sets of nonnegative integers, a point $x \in X$ is said to be $\mathsf{I}$-strong universal if for each $y \in X$ there exists a subsequence…
We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$-flat chain admits a decomposition in set-indecomposable sub-chains. This generalizes the decomposition of sets of finite…
We study a combinatorial object, which we call a GRRS (generalized reflection root system); the classical root systems and GRSs introduced by V. Serganova are examples of finite GRRSs. A GRRS is finite if it contains a finite number of…
The class of recurrent mixture density networks is an important class of probabilistic models used extensively in sequence modeling and sequence-to-sequence mapping applications. In this class of models, the density of a target sequence in…
An algorithm for calculating two-loop propagator type Feynman diagrams with arbitrary masses and external momentum is proposed. Recurrence relations allowing to express any scalar integral in terms of basic integrals are given. A minimal…
Let (F_n^{(k)})_{n\geq -(k-2)} be the k-generalized Fibonacci sequence, defined as the linear recurrence sequence whose first k terms are \(0, 0, \ldots, 0, 1\), and whose subsequent terms are determined by the sum of the preceding k terms.…
In regular dynamics, discrete maps are model presentations of discrete dynamical systems, and they may approximate continuous dynamical systems. Maps are used to investigate general properties of dynamical systems and to model various…
Let $A$ be a unital algebra over a field $F$ with $\operatorname*{char} (F)\neq2$. In this paper we introduce a new concept of a generalized Jordan derivation, covering Jordan centralizers and Jordan derivations, as follows: a linear map…
This study involves definitions for multiple-counting regular and summation sequences of rho. My paper introduces and proves recurrent relationships for multiple-counting sequences and shows their association with Fermat's little theorem. I…
Some known constraints on Renormalization Group flow take the form of inequalities: in even dimensions they refer to the coefficient $a$ of the Weyl anomaly, while in odd dimensions to the sphere free energy $F$. In recent work…
The mining of frequent subgraphs from labeled graph data has been studied extensively. Furthermore, much attention has recently been paid to frequent pattern mining from graph sequences. A method, called GTRACE, has been proposed to mine…
The goal of this article is to study some basic algebraic and combinatorial properties of "generalized $n$-series" over a commutative ring $R$, which are functions $s: \mathbf{Z}_{\geq 0} \to R$ satisfying a mild condition. A special…
In Symmetric Teleparallel General Relativity, gravity is attributed to the non-metricity. The so-called "coincident gauge" is usually taken in this theory so that the affine connection vanishes and the metric is the only fundamental…
We develop a general spectral framework to analyze quantum fractional revival in quantum spin networks. In particular, we introduce generalizations of the notions of cospectral and strongly cospectral vertices to arbitrary subsets of…
It is natural for probabilistic programs to use conditionals to express alternative substructures in models, and loops (recursion) to express repeated substructures in models. Thus, probabilistic programs with conditionals and recursion…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…