Related papers: Approximate derivations of order $n$
This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…
D. Leviatan has investigated the behavior of the higher order derivatives of approximation polynomials of the differentiable function $f$ on $[-1,1]$. Especially, when $P_n$ is the best approximation of $f$, he estimates the differences…
Phase reduction is a commonly used techinque for analyzing stable oscillators, particularly in studies concerning synchronization and phase lock of a network of oscillators. In a widely used numerical approach for obtaining phase reduction…
A complete first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition.…
We characterize a closure of the set of dynamical-lexicographic orderings on $\mathrm{Homeo}_{+}{(\mathbb{R})}$ and prove the existence of orders outside of it.
In model-driven development, an ordered model transformation is a nested set of transformations between source and target classes, in which each transformation is governed by its own pre and post- conditions, but structurally dependent on…
We characterize the orderings of pairs of sets induced by several distances: Hamming, Jaccard, S\o rensen-Dice and Overlap. We also characterize these distances.
The main purpose of this paper is to investigate the stability problem of some functional equations that appear in the characterization problem of information measures.
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
It is a well-known empirical phenomenon that natural axiomatic theories are pre-well-ordered by consistency strength. Without a precise mathematical definition of "natural," it is unclear how to study this phenomenon mathematically. We will…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
The multidimensional chain rule formula for analytic functions and its generalisation to higher derivatives perfectly work in the algebraic setting in characteristic zero. In positive characteristic one runs into problems due to…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
We consider the time evolution of a one dimensional $n$-gradient continuum. Our aim is to construct and analyze discrete approximations in terms of physically realizable mechanical systems, called microscopic because they are living on a…
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…
This note is an introduction to the properties of stable polynomials in several variables with real or complex coefficients. These polynomials are defined in terms of where the polynomial is non-vanishing. We do not cover well-known topics…
A shift rule for the prefer-max De Bruijn sequence is formulated, for all sequence orders, and over any finite alphabet. An efficient algorithm for this shift rule is presented, which has linear (in the sequence order) time and memory…
In a previous paper (of which this is a prosecution) we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended…
First-order applicative term rewriting systems provide a natural framework for modeling higher-order aspects. In earlier work we introduced an uncurrying transformation which is termination preserving and reflecting. In this paper we…