Production-frame Model of Representation of Data Domain

One of the most important problems of e-learning system is studied in given paper. This problem is building of data domain model. Data domain model is based on usage of correct organizing knowledge base. In this paper production-frame model is offered, which allows structuring data domain and building flexible and understandable inference system, residing in production system.

A Domain-Independent Otology-based Approach to Representation of Courseware Knowledge

This paper proposes an ontology-based approach to representation of courseware knowledge in different domains. The focus is on a three-level semantic graph, modeling respectively the course as a whole, its structure, and domain contents itself. The authors plan to use this representation for flexibie e- learning and generation of different study plans for the learners.

Limit Theorems for Regenerative Excursion Processes

This work is supported by Bulgarian NFSI, grant No. MM–704/97

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

Oscillation Theorems for Perturbed Second Order Nonlinear Differential Equations with Damping

Some oscillation criteria for solutions of a general perturbed second order ordinary differential equation with damping (r(t)x′ (t))′ + h(t)f (x)x′ (t) + ψ(t, x) = H(t, x(t), x′ (t)) with alternating coefficients are given. The results obtained improve and extend some existing results in the literature.

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

Oscillation Theorems for Second Order Sublinear Ordinary Differential Equations

Oscillation criteria are given for the second order sublinear non-autonomous differential equation. (r(t) (x)x′(t))′ + q(t)g(x(t)) = (t). These criteria extends and improves earlier oscillation criteria of Kamenev, Kura, Philos and Wong. Oscillation criteria are also given for second order sublinear damped non-autonomous differential equations.

Equisummability Theorems for Laguerre Series

Here we prove results about Riesz summability of classical Laguerre series, locally uniformly or on the Lebesgue set of the function f such that (∫(1 + x)^(mp) |f(x)|^p dx )^(1/p) < ∞, for some p and m satisfying 1 ≤ p ≤ ∞, −∞ < m < ∞.

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.

The Development of Parallel Resolution Algorithms Using the Graph Representation

The parallel resolution procedures based on graph structures method are presented. OR-, AND- and DCDP- parallel inference on connection graph representation is explored and modifications to these algorithms using heuristic estimation are proposed. The principles for designing these heuristic functions are thoroughly discussed. The colored clause graphs resolution principle is presented. The comparison of efficiency (on the Steamroller problem) is carried out and the results are presented. The parallel unification algorithm used in the parallel inference procedure is briefly outlined in the final part of the paper.

Approaches to Sequence Similarity Representation

We discuss several approaches to similarity preserving coding of symbol sequences and possible connections of their distributed versions to metric embeddings. Interpreting sequence representation methods with embeddings can help develop an approach to their analysis and may lead to discovering useful properties.

Ontological Approach to Domain Knowledge Representation for Information Retrieval in Multiagent Systems

An ontological representation of buyer interests’ knowledge in process of e-commerce is proposed to use. It makes it more efficient to make a search of the most appropriate sellers via multiagent systems. An algorithm of a comparison of buyer ontology with one of e-shops (the taxonomies) and an e-commerce multiagent system are realised using ontology of information retrieval in distributed environment.

Representation of Neural Networks by Dynamical Systems

Representation of neural networks by dynamical systems is considered. The method of training of neural networks with the help of the theory of optimal control is offered.

The Use of Situation Representation when Searching for Solutions in Computer Aided Design Systems

Projects solutions reuse methodology is offered for software development. The main idea consists in connection of the system objective with the situation using the entities which describe the condition of the system in the process of the objective statement. Every situation is associated with one or several design solutions, which can be used at the development. Based on this connection the situation representing language has been created, it lets to express a problem situation using a natural language describe. The similarity measure has been built to compare situations, it is based on the similarity coefficients with adding the absent part weight.

Normal ECG Recognition for Express-Diagnostics Based on Scale-Space Representation and Dynamic Matching

A novel approach of normal ECG recognition based on scale-space signal representation is proposed. The approach utilizes curvature scale-space signal representation used to match visual objects shapes previously and dynamic programming algorithm for matching CSS representations of ECG signals. Extraction and matching processes are fast and experimental results show that the approach is quite robust for preliminary normal ECG recognition.