Some Para-Hermitian Related Complex Structures and Non-existence of Semi-Riemannian Metric on Some Spheres

It is shown that the spheres S^(2n) (resp: S^k with k ≡ 1 mod 4) can be given neither an indefinite metric of any signature (resp: of signature (r, k − r) with 2 ≤ r ≤ k − 2) nor an almost paracomplex structure. Further for every given Riemannian metric on an almost para-Hermitian manifold with the associated 2-form φ one can construct an almost Hermitian structure (under certain conditions, two different almost Hermitian structures) whose associated 2-form(s) is φ.

Application of Lyapunov's Direct Method to the Existence of Integral Manifolds of Impulsive Differential Equations

The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations. By means of piecewise continuous functions which are generalizations of the classical Lyapunov’s functions, sufficient conditions for the existence of integral manifolds of such equations are found.

Existence of Global Solutions to Supercritical Semilinear Wave Equations

∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.

A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications

ACM Computing Classification System (1998): E.4.

Construction of Optimal Linear Codes by Geometric Puncturing

Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4.

Existence of Solutions for a Class of Quasi-Linear Singular Integro-Differential Equations

2000 Mathematics Subject Classification: 45F15, 45G10, 46B38.

Strong-weak Stackelberg Problems in Finite Dimensional Spaces

We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present some approximation results when the parameter ǫ goes to zero. Finally, as an example, we consider an optimization problem associated to a best bound given in [2] for a system of nondifferentiable convex inequalities.

The Nonexistence of some Griesmer Arcs in PG(4, 5)

In this paper, we prove the nonexistence of arcs with parameters (232, 48) and (233, 48) in PG(4,5). This rules out the existence of linear codes with parameters [232,5,184] and [233,5,185] over the field with five elements and improves two instances in the recent tables by Maruta, Shinohara and Kikui of optimal codes of dimension 5 over F5.

Parallel Class Intersection Matrices of Orthogonal Resolutions

This work was partially supported by the Bulgarian National Science Fund under Contract No MM 1405. Part of the results were announced at the Fifth International Workshop on Optimal Codes and Related Topics (OCRT), White Lagoon, June 2007, Bulgaria

Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

Generalized Scalarizing Problems GENS and GENSLex of Multicriteria Optimization

* This paper is partially supported by the National Science Fund of Bulgarian Ministry of Education and Science under contract № I–1401\2004 "Interactive Algorithms and Software Systems Supporting Multicriteria Decision Making".

Methods of Regularities Searching Based on Optimal Partitioning

The purpose of discussed optimal valid partitioning (OVP) methods is uncovering of ordinal or continuous explanatory variables effect on outcome variables of different types. The OVP approach is based on searching partitions of explanatory variables space that in the best way separate observations with different levels of outcomes. Partitions of single variables ranges or two-dimensional admissible areas for pairs of variables are searched inside corresponding families. Statistical validity associated with revealed regularities is estimated with the help of permutation test repeating search of optimal partition for each permuted dataset. Method for output regularities selection is discussed that is based on validity evaluating with the help of two types of permutation tests.

Optimal Control of Heterogeneous Systems

Цветомир Цачев - В настоящия доклад се прави преглед на някои резултати от областта на оптималното управление на непрекъснатите хетерогенни системи, публикувани в периодичната научна литература в последните години. Една динамична система се нарича хетерогенна, ако всеки от нейните елементи има собствена динамиката. Тук разглеждаме оптимално управление на системи, чиято хетерогенност се описва с едномерен или двумерен параметър – на всяка стойност на параметъра отговаря съответен елемент на системата. Хетерогенните динамични системи се използват за моделиране на процеси в икономиката, епидемиологията, биологията, опазване на обществената сигурност (ограничаване на използването на наркотици) и др. Тук разглеждаме модел на оптимално инвестиране в образование на макроикономическо ниво [11], на ограничаване на последствията от разпространението на СПИН [9], на пазар на права за въглеродни емисии [3, 4] и на оптимален макроикономически растеж при повишаване на нивото на върховите технологии [1]. Ключови думи: оптимално управление, непрекъснати хетерогенни динамични системи, приложения в икономиката и епидемиолегията

Characterization of Schrödinger Processes with Unbounded Potentials

2000 Mathematics Subject Classification: 49L20, 60J60, 93E20