A prime algebraic lattice can be characterised as isomorphic to the downwards-closed subsets, ordered by inclusion, of its complete primes. It is easily seen that the downwards-closed subsets of a partial order form a completely distributive algebraic lattice when ordered by inclusion. The converse also holds; any completely distributive algebraic lattice is isomorphic to such a set of downward...

We mean by a normal form a finite set of ordered pairs of subsets of a fixed set that fulfils two conditions: elements of it consist of disjoint sets and elements of it are incomparable w.r.t. inclusion. The underlying set corresponds to a set of propositional variables but is arbitrary. The correspodents to a normal form of a formula, e.g. a disjunctive normal form, is as follows. The normal f...

In this paper, we examine and compare De Morgan-, Kleene-, and Booleandisjunctive and conjunctive normal forms and consider their role in fuzzy settings. In particular, we describe normal forms and truth tables for classical fuzzy propositional logic and interval-valued fuzzy propositional logic that are completely analogous to those for Boolean propositional logic. Thus, determining logical eq...

This paper introduces an approach to the axiomatic theory of quadratic forms based on {tmem{presentable}} partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of {tmem{quadratically p...

This paper deals with the application of fourth kind Chebyshev wavelets (FKCW) in solving numerically a model of HIV infection of CD4+T cells involving Caputo fractional derivative. The present problem is a system of nonlinear fractional differential equations. The goal is to approximate the solution in the form of FKCW truncated series. To do this, an operational matrix of fractional integrati...

In this paper, stability for uncertain time variant linear systems with time delay is studied. A new sufficient condition for delay-dependent systems is given in matrix inequality form which depends on the range of delay. Then, we introduce a new direct computational method to solve delay systems. This method consists of reducing the delay problem to a set of algebraic equations by first expand...

In this paper, a new and efficient approach is applied for numerical approximation of the linear differential equations with variable coeffcients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coeffcients for the moments of derivatives of any differentiable function in terms of the original expansion coefficients of the f...

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

This paper is about the question whether a cycle in the l-adic cohomology of a smooth projective variety over Q, which is algebraic over almost all finite fields Fp, is also algebraic over Q. We use ultraproducts respectively nonstandard techniques in the sense of A. Robinson, which the authors applied systematically to algebraic geometry in [BS07] and [BS08]. We give a reformulation of the que...

This study concerns an analysis of what kinds of products are more suitable for distribution via the Internet than via traditional markets. The purpose of the analysis is to identify and fit marketing strategy to product in the virtual marketplace. The amount of product information needed by the consumer to reach a purchasing decision varies with the degree of consumer involvement with the purc...