We study data nets, a generalisation of Petri nets in which tokens carry data from linearlyordered infinite domains and in which whole-place operations such as resets and transfers are possible. Data nets subsume several known classes of infinite-state systems, including multiset rewriting systems and polymorphic systems with arrays. We show that coverability and termination are decidable for a...

A class F of partial recursive functions is called recursively enumerable if there exists an r.e. set J ⊆ N such that F = {φi | i ∈ J}. We prove that every r.e. class F of partial recursive functions with infinite domains must have a recursive witness array, i.e. there is a computable array of finite sets X = [Xn]n∈ω such that (i) for every f ∈ F one has f(n) ∈ Xn for infinitely many n and (ii)...

We introduce the geometric structure underlying port-Hamiltonian models for distributed parameter systems exhibiting moving material domains. The first part of paper aims at introducing differential tools needed to represent infinite-dimensional on time–varying spatial domains in a port–based framework. A throughout description way we extend presented seminal work [25], where only fixed were co...

The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses recently introduced infinite and infinitesimal numbers being in accordance with the principle ‘The part is less than the whole’ observed in the physical worl...

We prove gradient boundary blow up rates for ergodic functions in bounded domains related to fully nonlinear degenerate/singular elliptic operators. As a consequence, we deduce the uniqueness, constants, of functions. The results are obtained by means Liouville type classification theorem half-spaces infinite value problems nonlinear, uniformly

According to Weyl, “‘inexhaustibility’ is essential the infinite”. However, he distinguishes two kinds of inexhaustible, or merely potential, domains: those that are “extensionally determinate” and not. This article clarifies Weyl's distinction explains its enduring logical philosophical significance. The sheds lights on contemporary debate about potentialism, which in turn affords a deeper und...

The Hardy space on the unit ball in C provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for modules over domains in C and for finitely-connected domains only for Hardy-like spaces, the bundle shifts. M...

In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and total measure is finite. sense, associated operators on these display similarities to elliptic bounded domains in continuum. Specifically, prove lower bounds show by examples upper cannot be established.

We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary point z0 of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported away from z0 cannot vanish to infinite order at z0 unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the...

Absorbing boundary conditions have been developed for various types of problems to truncate infinite domains in order to perform computations. But absorbing boundary conditions have a second, recent and important application: parallel computing. We show that absorbing boundary conditions are essential for a good performance of the Schwarz waveform relaxation algorithm applied to the wave equati...