The Green function of periodic boundary value problem with supplementary orthogonality conditions for bending of a string is obtained. The best constant of corresponding Sobolev inequality is found.

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In this paper we generalize multivalued contraction theorem due to S. B. Nadler [8]. As corollaries we obtain fixed point theorems for a multivalued operator in complete dislocated metric spaces and complete partial metric space.

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The concepts of semisimple, Archimedean, and semilocal pseudo MV-algebras are investigated and many interesting facts concerning them are given.

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Josep Maria Font and Ramon Jansana, inspired by previous work of Czelakowski, Blok and Pigozzi and of other members of the Barcelona algebraic logic group, studied the interaction between the algebraization of deductive systems in the sense of Tarski and the algebraization of Gentzen systems, connected with the deductive systems in various ways. Only recently, did the author extend the notion of a Gentzen system to the π-institution level and this extension provides the framework for the extension of some of the results of Font and Jansana to the categorical abstract algebraic logic level.

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In this paper we prove that Abelian groups and basic BCI-algebras are equivalent and by using it we have obtain more results.

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The aim of this paper is to study the properties of dual BCK-algebra and to prove that the MV -algebra is equvalent to the bounded commutative dual BCK-algebra.

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This paper introduces 2D lognormal diffusion random fields through their transition densities and studies the main analytical and statistical characteristics of these fields, based on the theoretical formulation for diffusion random fields given in [14]. Lognormal diffusions are characterized here in terms of stochastic partial differential equations, and Kolmogorov’s forward equation is obtained.

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We are concerned with a forest kinetic model equipped with the Dirichlet boundary conditions which has been presented by Kuzunetsov et al. [4]. We construct global solutions and construct a dynamical system determined from the Cauchy problem of the model equations. It is also shown that the dynamical system possesses a bounded absorbing set and every trajectory has a nonempty ω-limit set in a suitable weak topology. These results are then a modification of those obtained in our previous paper [1] from the Neumann condition case to the Dirichlet condition case.

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