The Deformed Trigonometric Functions of two Variables

MSC 2010: 33B10, 33E20

Fractional Integration of the Product of Bessel Functions of the First Kind

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09

Numerical Issues in Using MATLAB

Михаил Константинов, Весела Пашева, Петко Петков - Разгледани са някои числени проблеми при използването на компютърната система MATLAB в учебната дейност: пресмятане на тригонометрични функции, повдигане на матрица на степен, спектрален анализ на целочислени матрици от нисък ред и пресмятане на корените на алгебрични уравнения. Причините за възникналите числени трудности могат да се обяснят с особеностите на използваната двоичната аритметика с плаваща точка.

Inequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions

MSC 2010: 33E12, 30A10, 30D15, 30E15

On Sandwich Theorem of Analytic Functions Involving Integral Operator

2000 Mathematics Subject Classification: 30C45

A solution of the trigonometric moment problem via Tagamlitzki's "Theorem of the Cones"

In 1952 Y. Tagamlitzki gave an elegant proof of the classical Bochner’s theorem on the positively definite functions. Unfortunately, he never published his proof. In this paper we consider a related but simpler problem, the trigonometric moment problem, by using Tagamlitzki’s approach.

Fractional Trigonometric Korovkin Theory in Statistical Sense

2000 Mathematics Subject Classification: 41A25, 41A36.

Exploring Linear Functions – Representational Relationship

Experiences from a German-Ukrainian project for the joint development of dynamic learning environments are reported. General methodological and technological aspects are discussed as well as special items arising from the cross-cultural collaboration.

Algebraic Computations with Hausdorff Continuous Functions

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.

Essential Arity Gap of Boolean Functions

In this paper we investigate the Boolean functions with maximum essential arity gap. Additionally we propose a simpler proof of an important theorem proved by M. Couceiro and E. Lehtonen in [3]. They use Zhegalkin’s polynomials as normal forms for Boolean functions and describe the functions with essential arity gap equals 2. We use to instead Full Conjunctive Normal Forms of these polynomials which allows us to simplify the proofs and to obtain several combinatorial results concerning the Boolean functions with a given arity gap. The Full Conjunctive Normal Forms are also sum of conjunctions, in which all variables occur.

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.

On Averaging Null Sequences of Real-Valued Functions

If ξ is a countable ordinal and (fk) a sequence of real-valued functions we define the repeated averages of order ξ of (fk). By using a partition theorem of Nash-Williams for families of finite subsets of positive integers it is proved that if ξ is a countable ordinal then every sequence (fk) of real-valued functions has a subsequence (f'k) such that either every sequence of repeated averages of order ξ of (f'k) converges uniformly to zero or no sequence of repeated averages of order ξ of (f'k) converges uniformly to zero. By the aid of this result we obtain some results stronger than Mazur’s theorem.

A Recession Notion for a Class of Monotone Bivariate Functions

Using monotone bifunctions, we introduce a recession concept for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on variational problems. In the process we generalize some results by H. Brezis and H. Attouch relative to the convergence of the resolvents associated with maximal monotone operators.

Complete Systems of Hermite Associated Functions

It is proved that if the increasing sequence {kn} n=0..∞ n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply connected subregion of C\R then the system of Hermite associated functions Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.

Asplund Functions and Projectional Resolutions of the Identity

*Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by the Grant of the Faculty of Civil Engineering of the Czech Technical University No. 2003.