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

100%

Telega J. J. , Jemioło S.

tom Vol. 46, nr 3

265-276

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.

Epichristoffel Words and Minimization of Moore Automata

75%

Castiglione G. , Sciortino M.

tom Vol. 134, nr 3/4

319--333

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.

The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian

75%

Liu B. , Yu J.

2000

tom 75

nr 3

271-280

We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: $-(ϕ_{p}(x'))' + d/dt grad F(x) + g(t,x(t),x(δ(t))$, x'(t), x'(τ(t))) = 0, t ∈ [0,1]; $x(t)=\underline{φ}(t),$ t ≤ 0; $x(t) = \overline{φ}(t)$, t ≥ 1. An existence result is obtained with the help of the Leray-Schauder degree theory, with no restriction on the damping forces d/dt grad F(x).