## Large deviations of generalized renewal process

Published in Discrete Mathematics and Applications

Let (ξ(i), η(i)) ∈ ℝd+1, 1 ≤ i

Published in Discrete Mathematics and Applications

Let (ξ(i), η(i)) ∈ ℝd+1, 1 ≤ i

Published in Discrete Mathematics and Applications

We study subgroups of the direct product of two groups invariant under the action of permutations on factors. An invariance criterion for the subdirect product of two groups under the action of permutations on factors is put forward. Under certain additional constraints on permutations, we describe the subgroups of the direct product of a finite nu...

Published in Discrete Mathematics and Applications

A functional system of Boolean vector functions with a naturally defined superposition operation is considered. It is shown that each closed class of vector functions with α- or δ-functions as components has a finite basis.

Published in Discrete Mathematics and Applications

Orthomorphisms of Abelian groups with the minimum possible Cayley distance between them are studied. We describe the class of transformations mapping the given orthomorphism into the set of all orthomorphisms such that their Cayley distance from this orthomorphism takes the minimal possible value 2. Algorithms are suggested that construct all ortho...

Published in Discrete Mathematics and Applications

The complexity of the decision of polynomial (functional) completeness of a finite quasigroup is investigated. It is shown that the polynomial completeness of a finite quasigroup may be checked in time polynomially dependent on the order of the quasigroup.

Published in Discrete Mathematics and Applications

Integer random walk {Sn, n ≥ 0} with zero drift and finite variance σ2 stopped at the moment T of the first visit to the half axis (-∞, 0] is considered. For the random process which associates the variable u ≥ 0 with the number of visits the state ⌊uσ n $\begin{array}{} \displaystyle \sqrt{n} \end{array}$⌋ by this walk conditioned on T > n, the fu...

Published in Discrete Mathematics and Applications

The portfolio theory is used to formulate a multicriteria investment Boolean escaped gain minimization problem for searching all extreme portfolios. Stability aspects of this set against perturbed parameters of minimax Savage criteria are studied. We give lower and upper estimates for the stability radius for arbitrary Hölder norms on the three-dim...

Published in Discrete Mathematics and Applications

The previous paper was concerned with systems of equations over a certain family 𝓢 of quasigroups. In that work a method of elimination of an outermost variable from the system of equations was suggested and it was shown that further elimination of variables requires that the family 𝓢 of quasigroups satisfy the generalized distributive law (GDL). I...

Published in Discrete Mathematics and Applications

Predicates that are preserved by a semi-lattice function are considered. These predicates are called weak positive. A representation of these predicates are proposed in the form of generalized conjunctive normal forms (GCNFs). Properties of GCNFs of these predicates are obtained. Based on the properties obtained, more efficient polynomial-time algo...

Published in Discrete Mathematics and Applications

An efficient recursive method for synthesis of correlation-immune Boolean functions is proposed. At the first stage, this method uses minimal correlation-immune functions. A classification of 6-variable minimal correlation-immune functions under the Jevons group is put forward. New results on minimal correlation-immune functions are given.