On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

Fractional Calculus of the Generalized Wright Function

Mathematics Subject Classification: 26A33, 33C20.

Generalized Nets Model of an E-Learning System Software Architecture

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshko ff and Lubomir Tschakaloff , Sofi a, July, 2006.

Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5

∗ Research partially supported by INTAS grant 97-1644

Evaluation of Pareto/D/1/k Queue by Simulation

The finding that Pareto distributions are adequate to model Internet packet interarrival times has motivated the proposal of methods to evaluate steady-state performance measures of Pareto/D/1/k queues. Some limited analytical derivation for queue models has been proposed in the literature, but their solutions are often of a great mathematical challenge. To overcome such limitations, simulation tools that can deal with general queueing system must be developed. Despite certain limitations, simulation algorithms provide a mechanism to obtain insight and good numerical approximation to parameters of queues. In this work, we give an overview of some of these methods and compare them with our simulation approach, which are suited to solve queues with Generalized-Pareto interarrival time distributions. The paper discusses the properties and use of the Pareto distribution. We propose a real time trace simulation model for estimating the steady-state probability showing the tail-raising effect, loss probability, delay of the Pareto/D/1/k queue and make a comparison with M/D/1/k. The background on Internet traffic will help to do the evaluation correctly. This model can be used to study the long- tailed queueing systems. We close the paper with some general comments and offer thoughts about future work.

Krätzel Function as a Function of Hypergeometric Type

2000 Mathematics Subject Classification: 33C60, 33C20, 44A15

Generalized Discernibility Function Based Attribute Reduction in Incomplete Decision Systems

A rough set approach for attribute reduction is an important research subject in data mining and machine learning. However, most attribute reduction methods are performed on a complete decision system table. In this paper, we propose methods for attribute reduction in static incomplete decision systems and dynamic incomplete decision systems with dynamically-increasing and decreasing conditional attributes. Our methods use generalized discernibility matrix and function in tolerance-based rough sets.