Regular and Other Kinds of Extensions of Topological Spaces

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

* The author was supported by NSF Grant No. DMS 9706883.

Integral Representations of Generalized Mathieu Series Via Mittag-Leffler Type Functions

Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30

Representations of Inverse Functions by the Integral Transform with the Sign Kernel

Mathematics Subject Classification: Primary 30C40

Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function

AMS Subj. Classification: MSC2010: 11F72, 11M36, 58J37

Motzkin Decomposable Sets

Theodore Motzkin proved, in 1936, that any polyhedral convex set can be expressed as the (Minkowski) sum of a polytope and a polyhedral convex cone. We have provided several characterizations of the larger class of closed convex sets, Motzkin decomposable, in finite dimensional Euclidean spaces which are the sum of a compact convex set with a closed convex cone. These characterizations involve different types of representations of closed convex sets as the support functions, dual cones and linear systems whose relationships are also analyzed. The obtaining of information about a given closed convex set F and the parametric linear optimization problem with feasible set F from each of its different representations, including the Motzkin decomposition, is also discussed. Another result establishes that a closed convex set is Motzkin decomposable if and only if the set of extreme points of its intersection with the linear subspace orthogonal to its lineality is bounded. We characterize the class of the extended functions whose epigraphs are Motzkin decomposable sets showing, in particular, that these functions attain their global minima when they are bounded from below. Calculus of Motzkin decomposable sets and functions is provided.

Characterizations of the Solution Sets of Generalized Convex Minimization Problems

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.

On some Finite-Dimensional Representations of Artin Braid Group

Валентин В. Илиев - Авторът изучава някои хомоморфни образи G на групата на Артин на плитките върху n нишки в крайни симетрични групи. Получените пермутационни групи G са разширения на симетричната група върху n букви чрез подходяща абелева група. Разширенията G зависят от един целочислен параметър q ≥ 1 и се разцепват тогава и само тогава, когато 4 не дели q. В случая на нечетно q са намерени всички крайномерни неприводими представяния на G, а те от своя страна генерират безкрайна редица от неприводими представяния на групата на плитките.

Integral Representations of Functional Series with Members Containing Jacobi Polynomials

MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10

INFRAWEBS BPEL-Based Editor for Creating the Semantic Web Services Description

INFRAWEBS project [INFRAWEBS] considers usage of semantics for the complete lifecycle of Semantic Web processes, which represent complex interactions between Semantic Web Services. One of the main initiatives in the Semantic Web is WSMO framework, aiming at describing the various aspects related to Semantic Web Services in order to enable the automation of Web Service discovery, composition, interoperation and invocation. In the paper the conceptual architecture for BPEL-based INFRAWEBS editor is proposed that is intended to construct a part of WSMO descriptions of the Semantic Web Services. The semantic description of Web Services has to cover Data, Functional, Execution and QoS semantics. The representation of Functional semantics can be achieved by adding the service functionality to the process description. The architecture relies on a functional (operational) semantics of the Business Process Execution Language for Web Services (BPEL4WS) and uses abstract state machine (ASM) paradigm. This allows describing the dynamic properties of the process descriptions in terms of partially ordered transition rules and transforming them to WSMO framework.

Computing and Visualizing Solution Sets of Interval Linear Systems

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Groups with Decomposable Set of Quasinormal Subgroups

A subgroup H of a group G is said to be quasinormal if HX = XH for all subgroups X of G. In this article groups are characterized for which the partially ordered set of quasinormal subgroups is decomposable.

Spline Subdivision Schemes for Compact Sets. A Survey

Dedicated to the memory of our colleague Vasil Popov January 14, 1942 – May 31, 1990 * Partially supported by ISF-Center of Excellence, and by The Hermann Minkowski Center for Geometry at Tel Aviv University, Israel

Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

* This work was supported by the CNR while the author was visiting the University of Milan.