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Plane waves and problems of steady vibrations in the theory of viscoelasticity for Kelvin-Voigt materials with double porosity

Svanadze M. M.

Archives of Mechanics

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2016

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Vol. 68, nr 6

441--458

EN

In the present paper the linear theory of viscoelasticity for Kelvin–Voigt materials with double porosity is considered. Some basic properties of plane harmonic waves are established and the boundary value problems (BVPs) of steady vibrations are investigated. Indeed on the basis of this theory three longitudinal and two transverse plane harmonic waves propagate through a Kelvin–Voigt material with double porosity and these waves are attenuated. The basic properties of the singular integral operators and potentials (surface and volume) are presented. The uniqueness and existence theorems for regular (classical) solutions of the BVPs of steady vibrations are proved by using the potential method (boundary integral equations method) and the theory of singular integral equations.

2

Probabilistic Constructions of Computable Objects and a Computable Version of Lovász Local Lemma

Rumyantsev A., Shen A.

Fundamenta Informaticae

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2014

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Vol. 132, nr 1

1--14

EN

A nonconstructive proof can be used to prove the existence of an object with some properties without providing an explicit example of such an object. A special case is a probabilistic proof where we show that an object with required properties appears with some positive probability in some random process. Can we use such arguments to prove the existence of a computable infinite object? Sometimes yes: following [8], we show how the notion of a layerwise computable mapping can be used to prove a computable version of Lovász local lemma.

3

Epichristoffel Words and Minimization of Moore Automata

Castiglione G., Sciortino M.

Fundamenta Informaticae

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2014

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Vol. 134, nr 3/4

319--333

EN

This paper is focused on the connection between the combinatorics of words and minimization of automata. The three main ingredients are the epichristoffel words, Moore automata and a variant of Hopcroft’s algorithm for their minimization. Epichristoffel words defined in [14] generalize some properties of circular sturmian words. Here we prove a factorization property and the existence of the reduction tree, that uniquely identifies the structure of the word. Furthermore, in the paper we investigate the problem of the minimization of Moore automata by defining a variant of Hopcroft’s minimization algorithm. The use of this variant makes simpler the computation of the running time and consequently the study of families of automata that represent the extremal cases of the minimization process. Indeed, such a variant allows to use the above mentioned factorization property of the epichristoffel words and their reduction trees in order to find an infinite family of Moore automata such that the execution of the algorithm is uniquely determined and tight.

4

A Domain View of Timed Behaviors

Dubtsov R., Oshevskaya E., Virbitskaite I.

Fundamenta Informaticae

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2014

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Vol. 133, nr 2/3

133--147

EN

The intention of this paper is to introduce a timed extension of transition systems with independence, and to study its categorical interrelations with other time-sensitive models. In particular, we show the existence of a chain of coreflections leading from a category of the model of timed transition systems with independence to a category of a specially defined model of marked Scott domains. As an intermediate semantics we use a timed extension of occurrence transition systems with independence, able to properly capture causality and independence relations which arise in the presence of time delays.

5

Some optimal control problems for partial differential inclusions

Kisielewicz M.

Opuscula Mathematica

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2008

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Vol. 28, no. 4

507-516

EN

Partial differential inclusions are considered. In particular, basing on diffusions properties of weak solutions to stochastic differential inclusions, some existence theorems and some properties of solutions to partial differential inclusions are given.

6

Macroscopic behaviour of locking materials with microstructure Part 1. Primal and dual elastic-locking potential. Relaxation

Telega J.J, Jemioło S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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1998

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Vol. 46, nr 3

265-276

EN

The series of three papers is concerned with macroscopic modelling of elastic perfectly locking materials with a microstructure. In Part I basic relations were formulated for such a body with an eY-periodic microstructure. Both displacement and stress approaches were discussed. The role of relaxation of the traction boundary condition was revealed. The locking limit analysis problem was also formulated.