Study of Queuing Systems with a Generalized Departure Process

This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.

Application of the Heterogeneous System Prediction Method to Pattern Recognition Problem

* This work was financially supported by RFBR-04-01-00858.

Application of the Multivariate Prediction Method to Time Series

* This work was financially supported by RFBR-04-01-00858.

Intellect Sensing of Neural Network that Trained to Classify Complex Signals

An experimental comparison of information features used by neural network is performed. The sensing method was used. Suboptimal classifier agreeable to the gaussian model of the training data was used as a probe. Neural nets with architectures of perceptron and feedforward net with one hidden layer were used. The experiments were carried out with spatial ultrasonic data, which are used for car’s passenger safety system neural controller learning. In this paper we show that a neural network doesn’t fully make use of gaussian components, which are first two moment coefficients of probability distribution. On the contrary, the network can find more complicated regularities inside data vectors and thus shows better results than suboptimal classifier. The parallel connection of suboptimal classifier improves work of modular neural network whereas its connection to the network input improves the specialization effect during training.

Sequencing Jobs with Uncertain Processing Times and Minimizing the Weighted Total Flow Time

We consider an uncertain version of the scheduling problem to sequence set of jobs J on a single machine with minimizing the weighted total flow time, provided that processing time of a job can take on any real value from the given closed interval. It is assumed that job processing time is unknown random variable before the actual occurrence of this time, where probability distribution of such a variable between the given lower and upper bounds is unknown before scheduling. We develop the dominance relations on a set of jobs J. The necessary and sufficient conditions for a job domination may be tested in polynomial time of the number n = |J| of jobs. If there is no a domination within some subset of set J, heuristic procedure to minimize the weighted total flow time is used for sequencing the jobs from such a subset. The computational experiments for randomly generated single-machine scheduling problems with n ≤ 700 show that the developed dominance relations are quite helpful in minimizing the weighted total flow time of n jobs with uncertain processing times.

Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics

Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.

Branching Populations of Cells Bearing a Continuous Label

2000 Mathematics Subject Classification: 60J80.

A Stochastic Approach for Finding of Semantically Related Words

2000 Mathematics Subject Classification: 62P99, 68T50

An Adaptation of the Hoshen-Kopelman Cluster Counting Algorithm for Honeycomb Networks

We develop a simplified implementation of the Hoshen-Kopelman cluster counting algorithm adapted for honeycomb networks. In our implementation of the algorithm we assume that all nodes in the network are occupied and links between nodes can be intact or broken. The algorithm counts how many clusters there are in the network and determines which nodes belong to each cluster. The network information is stored into two sets of data. The first one is related to the connectivity of the nodes and the second one to the state of links. The algorithm finds all clusters in only one scan across the network and thereafter cluster relabeling operates on a vector whose size is much smaller than the size of the network. Counting the number of clusters of each size, the algorithm determines the cluster size probability distribution from which the mean cluster size parameter can be estimated. Although our implementation of the Hoshen-Kopelman algorithm works only for networks with a honeycomb (hexagonal) structure, it can be easily changed to be applied for networks with arbitrary connectivity between the nodes (triangular, square, etc.). The proposed adaptation of the Hoshen-Kopelman cluster counting algorithm is applied to studying the thermal degradation of a graphene-like honeycomb membrane by means of Molecular Dynamics simulation with a Langevin thermostat. ACM Computing Classification System (1998): F.2.2, I.5.3.

On the Coherence Between Probability and Possibility Measures

* This paper is supported by CICYT (Spain) under Project TIN 2005-08943-C02-01.

Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution

2000 Mathematics Subject Classification: 62F25, 62F03.

Mixed Negative Binomial Distribution by Weighted Gamma Mixing Distribution

Павел Т. Стойнов - В тази работа се разглежда отрицателно биномното разпределение, известно още като разпределение на Пойа. Предполагаме, че смесващото разпределение е претеглено гама разпределение. Изведени са вероятностите в някои частни случаи. Дадени са рекурентните формули на Панжер.

An Estimate of the Probability Pr(X

2000 Mathematics Subject Classification: 33C90, 62E99