A Recession Notion for a Class of Monotone Bivariate Functions

Using monotone bifunctions, we introduce a recession concept for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on variational problems. In the process we generalize some results by H. Brezis and H. Attouch relative to the convergence of the resolvents associated with maximal monotone operators.

On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is to show that well–known error estimates, established for the finite element approximation of elliptic EVPs with classical BCs, hold for the present types of EVPs too. Some attention is also paid to the computational aspects of the resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial numerical examples, the exact eigenpairs of which can be determined.

On the Mastering of Knowledge and Skills for Solving Mathematical Problems in the Context of the Relationship "Reflection–Synergy"

On the basis of topical investigations on the reflection in the mathematics education, in this article there are presented some contemporary ideas about refining the methodology of mastering knowledge and skills for solving mathematical problems. The thesis is developed that for the general logical and for some particular mathematical methods to become means of solving mathematical problems, first they need to be a purpose of the education.

Cataloguing the Slavonic Manuscript Collection of the Plovdiv Public Library – Problems and MARC 21* Solutions

MARC 21 (‘Machine-Readable Cataloguing’) is a US library standard established worldwide and recently translated also in Bulgarian (those parts used most by librarians in their everyday work). The Bulgarian translations are freely available on the NALIS website (http://www.nalis.bg/) under the Library Standards Section, where also an Online Multilingual Dictionary of MARC 21 Terms can be found. All these works are approved by the US Library of Congress and published on its MARC 21 website under Translations (http://www.loc.gov/marc/translations.html#bulgarian).

On some Extremal Problems of Landau

2000 Mathematics Subject Classification: Primary: 42A05. Secondary: 42A82, 11N05.