Complex Adaptive On-line Learning System “Theory of Automatic Control"

The controlled from distance teaching (DT) in the system of technical education has a row of features: complication of informative content, necessity of development of simulation models and trainers for conducting of practical and laboratory employments, conducting of knowledge diagnostics on the basis of mathematical-based algorithms, organization of execution collective projects of the applied setting. For development of the process of teaching bases of fundamental discipline control system Theory of automatic control (TAC) the combined approach of optimum combination of existent programmatic instruments of support was chosen DT and own developments. The system DT TAC included: controlled from distance course (DC) of TAC, site of virtual laboratory practical works in LAB.TAC and students knowledge remote diagnostic system d-tester.

Fuzzy Set Theory Approach as the Basis of Analysis of Financial Flows in the Economical Security System

The problems of formalization of the process of matching different management subjects’ functioning characteristics obtained on the financial flows analysis basis is considered. Formal generalizations for gaining economical security system knowledge bases elements are presented. One of feedback directions establishment between knowledge base of the system of economical security and financial flows database analysis is substantiated.

The Approach to Development the Human Resources Intellectual Management System. Management Procedures

The Article suggests an approach to designing the Human Resources Intellectual Management System in order to increase Human Resources reliability, using the management methods known from the Theory of Management.. The Article examines the realization of the Subsystem of implementing management methods by the number of management procedures, executing the corresponding management method.

Self-organization of Functioning Process of Expert System with the Use of Subject Domain Ontology

Optimization of design, creation, functioning and accompaniment processes of expert system is the important problem of artificial intelligence theory and decisions making methods techniques. In this paper the approach to its solving with the use of technology, being based on methodology of systems analysis, ontology of subject domain, principles and methods of self-organisation, is offered. The aspects of such approach realization, being based on construction of accordance between the ontology hierarchical structure and sequence of questions in automated systems for examination, are expounded.

Bivirtual Organization as a Queuing System

The main features of virtual organizations are outlined. The mathematical models of functioning of virtual organization are offered on the basis of theory of queuing systems. Characteristics of efficiency are examined.

The Model of Unreliable Elements (Human Resources) Intellectual Management System on the Basis of Their Psychological and Personal Characteristics

The Article suggests a possible approach to creation of the Intellectual Management System for human resources and personnel (during their professional tasks solving), and that could consider personal characteristics and psychological condition of the human resources as an “unreliable” element. The Article describes some elements of the Intellectual Management System: professional activity model and “unreliable” element (human resources) model.

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.

A Cauchy Integral Related to a Robot-safety Device System

We introduce a robot-safety device system attended by two different repairmen. The twin system is characterized by the natural feature of cold standby and by an admissible “risky” state. In order to analyse the random behaviour of the entire system (robot, safety device, repair facility) we employ a stochastic process endowed with probability measures satisfying general Hokstad-type differential equations. The solution procedure is based on the theory of sectionally holomorphic functions, characterized by a Cauchy-type integral defined as a Cauchy principal value in double sense. An application of the Sokhotski-Plemelj formulae determines the long-run availability of the robot-safety device. Finally, we consider the particular but important case of deterministic repair.

On the KAM - Theory Conditions for the Kirchhoff Top

* Partially supported by Grant MM523/95 with Ministry of Science and Technologies.

Self-Learning Fuzzy Spiking Neural Network as a Nonlinear Pulse-Position Threshold Detection Dynamic System Based on Second-Order Critically Damped Response Units

Architecture and learning algorithm of self-learning spiking neural network in fuzzy clustering task are outlined. Fuzzy receptive neurons for pulse-position transformation of input data are considered. It is proposed to treat a spiking neural network in terms of classical automatic control theory apparatus based on the Laplace transform. It is shown that synapse functioning can be easily modeled by a second order damped response unit. Spiking neuron soma is presented as a threshold detection unit. Thus, the proposed fuzzy spiking neural network is an analog-digital nonlinear pulse-position dynamic system. It is demonstrated how fuzzy probabilistic and possibilistic clustering approaches can be implemented on the base of the presented spiking neural network.

An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

Queue Length Simulations in a Finite Single-line Queueing System with Repeated Calls

2000 Mathematics Subject Classification: 60K25.

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.