Related papers: Order bounds for $C^2$-finite sequences
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…
This article introduces continuous $H^2$-nonconforming finite elements in two and three space dimensions which satisfy a strong discrete Miranda--Talenti inequality in the sense that the global $L^2$ norm of the piecewise Hessian is bounded…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
We consider the problem of deciding $\omega$-regular properties on infinite traces produced by linear loops. Here we think of a given loop as producing a single infinite trace that encodes information about the signs of program variables at…
A finite non-increasing sequence of positive integers $d = (d_1\geq \cdots\geq d_n)$ is called a degree sequence if there is a graph $G = (V,E)$ with $V = \{v_1,\ldots,v_n\}$ and $deg(v_i)=d_i$ for $i=1,\ldots,n$. In that case we say that…
Sequential pattern discovery is a well-studied field in data mining. Episodes are sequential patterns describing events that often occur in the vicinity of each other. Episodes can impose restrictions to the order of the events, which makes…
Finding integer solutions to norm form equations is a classical Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It is known that these solutions can be…
The calculus of finite differences is a solid foundation for the development of operations such as the derivative and the integral for infinite sequences. Here we showed a way to extend it for finite sequences. We could then define…
In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
We recall the definition and the properties of a moment sequence and recall that all real sequences that have a finite rank of its Hankel matrix (see definition in the sequel) satisfy a homogeneous linear equation with constant…
Let $G$ be a finite group. A sequence over $G$ means a finite sequence of terms from $G$, where repetition is allowed and the order is disregarded. A product-one sequence is a sequence whose elements can be ordered such that their product…
Separations among the first order logic ${\cal R}ing(0,+,*)$ of finite residue class rings, its extensions with generalized quantifiers, and in the presence of a built-in order are shown, using algebraic methods from class field theory.…
We discuss some aspects of the continuum limit of some lattice models, in particular the $2D$ $O(N)$ models. The continuum limit is taken either in an infinite volume or in a box whose size is a fixed fraction of the infinite volume…
Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the…
The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
We introduce a necessary and sufficient criterion for determining the existence and the values of ratio limits of complex sequences generated by arbitrary linear recurrences.
In this article, we establish global regularity results ($ C^{0,\gamma}$, $ C^{0,1} $ and $ C^{1}$ estimates) for a class of degenerate fully nonlinear equation on $ C^{2} $-domain. This corresponds to the boundary counterpart of the…
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…
A Lattice is a partially ordered set where both least upper bound and greatest lower bound of any pair of elements are unique and exist within the set. K\"{o}tter and Kschischang proved that codes in the linear lattice can be used for error…