Some Growth and Distortion Theorems for Close-to-Convex Harmonic Functions in the Unit Disc

MSC 2010: 30C45, 30C55

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Spectrum of Functions for the Dunkl Transform on R^d

Mathematics Subject Classification: 42B10

Problems and Theorems in the Theory of Multiplier Sequences

The purpose of this paper is (1) to highlight some recent and heretofore unpublished results in the theory of multiplier sequences and (2) to survey some open problems in this area of research. For the sake of clarity of exposition, we have grouped the problems in three subsections, although several of the problems are interrelated. For the reader’s convenience, we have included the pertinent definitions, cited references and related results, and in several instances, elucidated the problems by examples.

On the Quality of Decision Functions in Pattern Recognition

The problem of decision functions quality in pattern recognition is considered. An overview of the approaches to the solution of this problem is given. Within the Bayesian framework, we suggest an approach based on the Bayesian interval estimates of quality on a finite set of events.

HW Implementation of a Optimized Algorithm for the Application of Active Rules in a Transition P-system

P systems or Membrane Computing are a type of a distributed, massively parallel and non deterministic system based on biological membranes. They are inspired in the way cells process chemical compounds, energy and information. These systems perform a computation through transition between two consecutive configurations. As it is well known in membrane computing, a configuration consists in a m-tuple of multisets present at any moment in the existing m regions of the system at that moment time. Transitions between two configurations are performed by using evolution rules which are in each region of the system in a non-deterministic maximally parallel manner. This work is part of an exhaustive investigation line. The final objective is to implement a HW system that evolves as it makes a transition P-system. To achieve this objective, it has been carried out a division of this generic system in several stages, each of them with concrete matters. In this paper the stage is developed by obtaining the part of the system that is in charge of the application of the active rules. To count the number of times that the active rules is applied exist different algorithms. Here, it is presents an algorithm with improved aspects: the number of necessary iterations to reach the final values is smaller than the case of applying step to step each rule. Hence, the whole process requires a minor number of steps and, therefore, the end of the process will be reached in a shorter length of time.

On Maximal Function on the Laguerre Hypergroup

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20

Digital Collections in Regional Public Library “P. R. Slaveikov” – Veliko Tarnovo in the Context of the National Program for Preservation and Promotion of Literary Heritage

Nowadays the great public libraries in Bulgaria are gaining the appearance of digital centers which provide new informational resources and services in the digital space. The digital conversion as a way of preservation is one of the important priorities of Regional Public Library in Veliko Tarnovo. In the last few years we persistently search for possible ways of financing by national and foreign programs in this direction. In the beginning the strategy was oriented to digitalization of the funds with most urgent conversion – these of the local studies periodicals from 1878 till 1944 year. The digitalization of funds will create conditions of laying the basement of full text database of Bulgarian periodical publications. The technology that is offered gives opportunities for including other libraries in the Unified index, which can develop it into a National Unified index of periodical publications. The integrated informational environment that is created is an attractive, comfortable and useful place for work in home or at work for researchers, historians, art experts, bibliographers. The library readers use very actively all informational services of the library internet page and work competently with the on-line indexes provided there, they find the necessary title, which can be demanded later for usage in home or in the library, using electronic means again.

Exponential approximation in the norms and semi-norms

The deviations of some entire functions of exponential type from real-valued functions and their derivatives are estimated. As approximation metrics we use the Lp-norms and power variations on R. Theorems presented here correspond to the Ganelius and Popov results concerning the one-sided trigonometric approximation of periodic functions (see [4, 5 and 8]). Some related facts were announced in [2, 3, 6 and 7].