Non-Linear Network-Flow Model of Lukasiewicz’s Multivalue Logic

The paper presents a new network-flow interpretation of Łukasiewicz’s logic based on models with an increased effectiveness. The obtained results show that the presented network-flow models principally may work for multivalue logics with more than three states of the variables i.e. with a finite set of states in the interval from 0 to 1. The described models give the opportunity to formulate various logical functions. If the results from a given model that are contained in the obtained values of the arc flow functions are used as input data for other models then it is possible in Łukasiewicz’s logic to interpret successfully other sophisticated logical structures. The obtained models allow a research of Łukasiewicz’s logic with specific effective methods of the network-flow programming. It is possible successfully to use the specific peculiarities and the results pertaining to the function ‘traffic capacity of the network arcs’. Based on the introduced network-flow approach it is possible to interpret other multivalue logics – of E.Post, of L.Brauer, of Kolmogorov, etc.

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

Data Flow Analysis and the Linear Programming Model

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

Primary and Secondary Empirical Values in Network Redimensioning

A model of an overall telecommunication network with virtual circuits switching, in stationary state, with Bernoulli-Poisson-Pascal (BPP) input flow, repeated calls, limited number of homogeneous terminals and 8 types of losses is considered. One of the main problems of network redimensioning is estimation of the traffic offered in the network because it reflects on finding of necessary number of equivalent switching lines on the basis of the consideration of detailed users behavior and target Quality of Service (QoS). The aim of this paper is to find a new solution of Network Redimensioning Task (NRDT) [4], taking into account the inconvenience of necessary measurements, not considered in the previous research [5]. The results are applicable for redimensioning of every (virtual) circuit switching telecommunication system, both for wireline and wireless systems (GSM, PSTN, ISDN and BISDN). For packet - switching networks proposed approach may be used as a comparison basis and when they work in circuit switching mode (e.g. VoIP).

Computer Networks Security Models - A New Approach for Denial-of-Services Attacks Mitigation

Computer networks are a critical factor for the performance of a modern company. Managing networks is as important as managing any other aspect of the company’s performance and security. There are many tools and appliances for monitoring the traffic and analyzing the network flow security. They use different approaches and rely on a variety of characteristics of the network flows. Network researchers are still working on a common approach for security baselining that might enable early watch alerts. This research focuses on the network security models, particularly the Denial-of-Services (DoS) attacks mitigation, based on a network flow analysis using the flows measurements and the theory of Markov models. The content of the paper comprises the essentials of the author’s doctoral thesis.

An Overview of Modelling Bulgarian Wildland Fire Behaviour by Application of a Mathematical Game Method and WRF-Fire Models

This paper presents the main achievements of the author’s PhD dissertation. The work is dedicated to mathematical and semi-empirical approaches applied to the case of Bulgarian wildland fires. After the introductory explanations, short information from every chapter is extracted to cover the main parts of the obtained results. The methods used are described in brief and main outcomes are listed. ACM Computing Classification System (1998): D.1.3, D.2.0, K.5.1.

A New Class of Processes for Formalizing and Generalizing Individual-Based Models: The Semi-Semi-Markov Processes

2000 Mathematics Subject Classification: 60K15, 60K20, 60G20,60J75, 60J80, 60J85, 60-08, 90B15.