About Learning Discrete Mathematics at Bulgarian School

The present work is dedicated to the learning discrete mathematics at Bulgarian school. A review of syllabuses and standards has been made. A project of learning discrete mathematics elements from first to twelve class is proposed.

An eMathTeacher Tool for Active Learning Fleury’s Algorithm

An eMathTeacher [Sánchez-Torrubia 2007a] is an eLearning on line self assessment tool that help students to active learning math algorithms by themselves, correcting their mistakes and providing them with clues to find the right solution. The tool presented in this paper is an example of this new concept on Computer Aided Instruction (CAI) resources and has been implemented as a Java applet and designed as an auxiliary instrument for both classroom teaching and individual practicing of Fleury’s algorithm. This tool, included within a set of eMathTeacher tools, has been designed as educational complement of Graph Algorithm active learning for first course students. Its characteristics of visualization, simplicity and interactivity, make this tutorial a great value pedagogical instrument.

Description Reduction for Restricted Sets of (0,1) Matrices

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Гиперплоскости в «Множествах и Расстояниях Соответствия»: Кластеризация

Рассматриваются общие проблемы кластеризации. Предложена концепция «множеств» и «расстояний соответствия» в построении кластеров, рассмотрены модели кластеризации, в которых «множествами соответствия» являются гиперплоскости, а «расстояниями соответствия» – различные варианты расстояний в связи с соответствующими гиперплоскостями. Развит аппарат псевдообращения по Муру – Пенроузу: приведены рекуррентные формулы возмущения для ортогональных проекторов и R-операторов, связанных с псевдообращением. Рекуррентные формулы возмущения использованы для построения алгебраического варианта Jack Knife’а. Приведена сборка важных для приложений результатов, касающихся псевдообращения.

Использование Алгоритма Ускоренного Вероятностного Моделирования в Схеме Табу-Поиска

Рассматривается метаэвристический метод комбинаторной оптимизации, основанный на использовании алгоритмов табу-поиска и ускоренного вероятностного моделирования. Излагается общая вычислительная схема предложенного метода, названного алгоритмом GS-tabu. Приведены результаты серии вычислительных экспериментов по решению известных задач коммивояжера и квадратичных задач о назначении.

Об Одной Задаче Распознавания Последовательности, Включающей Повторяющийся Вектор

* Работа поддержана грантами РФФИ 09-01-00032, 07-07-00022 и грантом АВЦП Рособразования 2.1.1/3235

Generating More Boundary Elements of Subset Projections

Composition problem is considered for partition constrained vertex subsets of n dimensional unit cube E^n . Generating numerical characteristics of E^n subsets partitions is considered by means of the same characteristics in 1 − n dimensional unit cube, and construction of corresponding subsets is given for a special particular case. Using pairs of lower layer characteristic vectors for E^(1-n) more characteristic vectors for E^n are composed which are boundary from one side, and which take part in practical recognition of validness of a given candidate vector of partitions.

On some Generalizations of a Class of Discrete Functions

In this paper we examine discrete functions that depend on their variables in a particular way, namely the H-functions. The results obtained in this work make the “construction” of these functions possible. H-functions are generalized, as well as their matrix representation by Latin hypercubes.

Models of Alternating Renewal Process at Discrete Time

We study a class of models used with success in the modelling of climatological sequences. These models are based on the notion of renewal. At first, we examine the probabilistic aspects of these models to afterwards study the estimation of their parameters and their asymptotical properties, in particular the consistence and the normality. We will discuss for applications, two particular classes of alternating renewal processes at discrete time. The first class is defined by laws of sojourn time that are translated negative binomial laws and the second class, suggested by Green is deduced from alternating renewal process in continuous time with sojourn time laws which are exponential laws with parameters α^0 and α^1 respectively.

Optimization of Discrete-Time, Stochastic Systems

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

Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Notes on the Solution of Dynamic Optimization Problems with Explicit Controls in Discrete-Time Economic Models

Йордан Йорданов, Андрей Василев - В работата се изследват методи за решаването на задачи на оптималното управление в дискретно време с безкраен хоризонт и явни управления. Дадена е обосновка на една процедура за решаване на такива задачи, базирана на множители на Лагранж, коята често се употребява в икономическата литература. Извеждени са необходимите условия за оптималност на базата на уравнения на Белман и са приведени достатъчни условия за оптималност при допускания, които често се използват в икономиката.

Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80