相关论文: Finitary Codes, a short survey

In domain theory every finite computable object can be represented by a single mathematical object instead of a set of objects, using the notion of finitary-basis. In this article we report on our effort to formalize domain theory in Coq in…

In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.

Fractional action-like variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multi-dimensional fractional action-like problems of the calculus of variations.

This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…

In the last years a lot of work has been concentrated on the study of the behaviour at infinity of polynomial maps. This behaviour can be very complicated, therefore the main idea was to find special classes of polynomial maps which have,…

We prove that the finiteness of a finitely generated category of irreducible algebraic varieties over a field of characteristic zero is decidable. We also obtain a Burnside finiteness criterion for such a category, with applications to…

Helicity plays a unique role as an integral invariant of a dynamical system. In this paper, the concept of helicity in the general setting of Hamiltonian dynamics is discussed. It is shown, through examples, how the conservation of overall…

The dominant rational maps of finite degree from a fixed variety to varieties of general type, up to birational isomorphisms, form a finite set. This has been known as the Iitaka-Severi conjecture, and is nowdays an established result, in…

We introduce the notion of residual finiteness for categories. In analogy with the group-theoretic setting, we prove that free categories and finitely generated subcategories of finite-dimensional vector spaces are residually finite.…

We discuss algorithms applicable to the numerical solution of second-order ordinary differential equations by finite-differences. We make particular reference to the solution of the dissipative particle dynamics fluid model, and present…

The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…

In this survey the role of implications of positive formulas -- finitary and infinitary -- is dicussed, in general and in module categories, where they seem of particular importance. A list of algebraic examples is given, some old, some…

It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…

Invariant foliations are complicated random sets useful for describing and understanding the qualitative behaviors of nonlinear dynamical systems. We will consider invariant foliations for stochastic partial differential equation with…

We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an…

The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.

In this article, we deal with several notions in dynamical systems. Firstly, we prove that both closure function and orbital function are idempotent on set-valued dynamical systems. And we show that the compact limit set of a connected set…

We discuss analogies between the etale site of arithmetic schemes and the algebraic topology of dynamical systems. The emphasis is on Lefschetz numbers. We also discuss similarities between infinite primes in arithmetic and fixed points of…

We introduce the notion of accurate foundation sets and the accurate refinement property for right LCM semigroups. For right LCM semigroups with this property, we derive a more explicit presentation of the boundary quotient. In the context…

In the paper we define and characterize the asynchronous systems from the point of view of their autonomy, determinism, order, non-anticipation, time invariance, symmetry, stability and other important properties. The study is inspired by…