Related papers: Modeling the Dialectic
Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called "iterated…
A parallel method for computing Boolean expressions based on the properties of finite free Boolean algebras is presented. We also show how various finite combinatorial objects can be codded in the formalism of Boolean algebras and counted…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
One of the very first results about designs over finite fields, by S. Thomas, is the existence of a cyclic 2-$(n,3,7)$ design over $\mathbb{F}_{2}$ for every integer $n$ coprime with 6. Here, by means of difference methods, we reprove and…
We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and…
In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal…
The finite spectrum of a first-order sentence is the set of positive integers that are the sizes of its models. The class of finite spectra is known to be the same as the complexity class NE. We consider the spectra obtained by limiting…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
We review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixed-hybrid schemes, we…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
We show that for finite n at least 3, every first-order axiomatisation of the varieties of representable n-dimensional cylindric algebras, diagonal-free cylindric algebras, polyadic algebras, and polyadic equality algebras contains an…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
In this review article the construction of first order coordinate differential calculi on finitely generated and finitely related associative algebras are considered and explicit construction of the bimodule of one form over such algebras…
We construct the first examples of an algorithmically complex finitely presented residually finite groups and first examples of finitely presented residually finite groups with arbitrarily large (recursive) Dehn function and depth function.…
This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first order theory of finite groups. The focus is on concepts from stability theory…
In this paper, we study arbitrary (not necessarily associative) 3-dimensional algebras. Such an algebra A is determined by a basis and the corresponding multiplication table, which is specified by 27 structure constants. We describe all…
It is presently our aim to undertake the discussion, of the Parts I and II, on the infinitesimal level and outline as well the transition from infinitesimal to finite, the main reason for this being, of course, the well known fact that…