Greedy Approximation with Regard to Bases and General Minimal Systems

*This research was supported by the National Science Foundation Grant DMS 0200187 and by ONR Grant N00014-96-1-1003

Projectively Solid Sets and an N-dimensional Piccard's Theorem

We discuss functions f : X × Y → Z such that sets of the form f (A × B) have non-empty interiors provided that A and B are non-empty sets of second category and have the Baire property.

Dense Continuity and Selections of Set-Valued Mappings

∗ The first and third author were partially supported by National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under grant MM-701/97.

P-Sequential Spaces and Cleavability

∗ Supported by the Serbian Scientific Foundation, grant No 04M01

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.

Pseudoradial Spaces: Finite Products and an Example From CH

∗ The first named author’s research was partially supported by GAUK grant no. 350, partially by the Italian CNR. Both supports are gratefully acknowledged. The second author was supported by funds of Italian Ministery of University and by funds of the University of Trieste (40% and 60%).

Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations

Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.

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.

The Point of Continuity Property: Descriptive Complexity and Ordinal Index

∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

∗ Partially supported by Grant MM-428/94 of MESC.

Abstract Subdifferential Calculus and Semi-Convex Functions

∗ The work is partially supported by NSFR Grant No MM 409/94.

Conference on Geometry and Mathematical Physics, Bulgaria, Zlatograd, 28.08-01.09.2005

List of Participants

Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators of rank and order two.

Toward Clemens' Conjecture in Degrees between 10 and 24

1 Supported in part by the Norwegian Research Council for Science and the Humanities. It is a pleasure for this author to thank the Department of Mathematics of the University of Sofia for organizing the remarkable conference in Zlatograd during the period August 28-September 2, 1995. It is also a pleasure to thank the M.I.T. Department of Mathematics for its hospitality from January 1 to July 31, 1993, when this work was started. 2Supported in part by NSF grant 9400918-DMS.

When does a Bounded Domain Cover a Projective Manifold? (Survey)

* The research has been partially supported by Bulgarian Funding Organizations, sponsoring the Algebra Section of the Mathematics Institute, Bulgarian Academy of Sciences, a Contract between the Humboldt Univestit¨at and the University of Sofia, and Grant MM 412 / 94 from the Bulgarian Board of Education and Technology