<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper an application of the well-known matrix method to an extension of the classical logic to many-valued logic is discussed: we consider an n-valued propositional logic as a propositional logic language with a logical matrix over n truth-values. The algebra of the logical matrix has operations expanding the operations of the classical propositional logic. Therefore we look over the Łukasiewicz, Post, Heyting and Rosser style expansions of the operations negation, conjunction, disjunction and with a special emphasis on implication.In the frame of consequence operation, some notions of semantic consequence are examined. Then we continue with the decision problem and the logical calculi. We show that the cause of difficulties with the notions of semantic consequence is the weakness of the reviewed expansions of negation and implication. Finally, we introduce an approach to finding implications that preserve both the modus ponens and the deduction theorem with respect to our definitions of consequence.</abstract>

Many-valued logics—implications and semantic consequences

<abstract xmlns="http://www.w3.org/1999/xhtml"> Compilers generate from the procedure or function call instruction a code that builds up an ”activation record” into the stack memory in run time. At execution of this code the formal parameters, local variables, data of visibility and the scope are pushed into the activation record, and in this record there are fields for the return address and the return value as well. In case of intensive recursive calls this is the reason of the frequent occurrences of the stack-overflow error messages. The classical technique for fixing such stack-overflows is to write programs in stackless programming style using tail recursive calls; the method is usually realised by Continuation Passing Style. This paper describes this style and gives an introduction to the new, special purpose stackless programming language Miller, which provides methods to avoid stack-overflow errors.</abstract>

Stackless programming in Miller

<abstract xmlns="http://www.w3.org/1999/xhtml"> The Yang-Mills fields have an important role in the non- Abelian gauge field theory which describes the properties of the quarkgluon plasma. The real time evolution of the classical fields is given by the equations of motion which are derived from the Hamiltonians to contain the term of the SU(2) gauge field tensor. The dynamics of the classical lattice Yang-Mills equations are studied on a 3 dimensional regular lattice. During the solution of this system we keep the total energy on constant values and it satisfies the Gauss law. The physical quantities are desired to be calculated in the thermodynamic limit. The broadly available computers can handle only a small amount of values, while the GPUs provide enough performance to reach out for higher volumes of lattice vertices which approximates the aforementioned limit.</abstract>

Yang-Mills lattice on CUDA

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we define the k-Fibonacci words in analogy with the definition of the k-Fibonacci numbers. We study their properties and we associate to this family of words a family of curves with interesting patterns.</abstract>

Instituto de Matemáticas y sus Aplicaciones Universidad Sergio Arboleda, Colombia

Departamento de Matemáticas Universidad Nációnál de Colombia, Colombia

On the k-Fibonacci words

<abstract xmlns="http://www.w3.org/1999/xhtml"> We consider in this paper the basis finite automaton and its some properties. We shall also consider some properties of special binary relation defined on the sets of states of canonical automata for the given language and for its mirror image. We shall also consider an algorithm of constructing the basis automaton defining the language which has a priory given variant of this relation.</abstract>

Russia, National Research Nuclear University “MEPhI”

Some more on the basis finite automaton

<abstract xmlns="http://www.w3.org/1999/xhtml"> In the paper we report on the parallel enumeration of the degree sequences (their number is denoted by G(n)) and zerofree degree sequences (their number is denoted by (Gz(n)) of simple graphs on n = 30 and n = 31 vertices. Among others we obtained that the number of zerofree degree sequences of graphs on n = 30 vertices is Gz(30) = 5 876 236 938 019 300 and on n = 31 vertices is Gz(31) = 22 974 847 474 172 374. Due to Corollary 21 in [52] these results give the number of degree sequences of simple graphs on 30 and 31 vertices.</abstract>

Parallel enumeration of degree sequences of simple graphs II

<abstract xmlns="http://www.w3.org/1999/xhtml"> We consider the problem of the computation of infp θp over the set of exponent pairs P ∋ p under linear constrains for a certain class of objective functions θ. An effective algorithm is presented. The output of the algorithm leads to the improvement and establishing new estimates in the various divisor problems in the analytical number theory.</abstract>

Linear programming over exponent pairs

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