<Emphasis Type=Italic>A</Emphasis>-deformations of a surface with stationary lengths of <Emphasis Type=Italic>LGT</Emphasis>-lines

We investigate infinitesimal areal deformations (A-deformations) of the first order under which the lengths of LGT-lines of a surface are preserved in the E ₃ -space. We prove that any regular surface of the class C ⁴ of nonzero Gaussian curvature without umbilical points admits nontrivial A-deformations with stationary lengths of LGT-lines.     

Nilpotency in type <Emphasis Type=Italic>A</Emphasis> cyclotomic quotients

We prove a conjecture made by Brundan and Kleshchev on the nilpotency degree of cyclotomic quotients of rings that categorify one-half of quantum sl(k).     

About the computation of the signature of surface singularities <Emphasis Type=Italic>z</Emphasis><Superscript><Emphasis Type=Italic>N</Emphasis></Superscript> + <Emphasis Type=Italic>g</Emphasis>(<Emphasis Type=Italic>x,y</Emphasis>) = 0

In this article we describe our experiences with a parallel Singular implementation of the signature of a surface singularity defined by z ^N + g(x; y) = 0.     

About <Emphasis Type=Italic>I</Emphasis>(<Emphasis Type=Italic>J</Emphasis>)-approximately continuous functions

A generalization of density point with respect to category and I(J)-density topology has been presented in [5]. This papers deals with some basic properties of the corresponding I(J)-approximately continuous functions and gives answer when these functions are of the first Baire class and when they are Darboux functions.     

<Emphasis Type=Italic>N</Emphasis>-homogeneous <Emphasis Type=Italic>C</Emphasis>*-algebras generated by idempotents

In this paper we consider n-homogeneous C*-algebras generated by idempotents. We prove that a finitely generated unital n-homogeneous (when n is greater than or equals 2) C*-algebra A can be generated by a finite set of idempotents if and only if the algebra A contains at least one nontrivial idempotent.     

Radicals of <Emphasis Type=Italic>l</Emphasis>-rings and one-sided <Emphasis Type=Italic>l</Emphasis>-ideals

We consider the plane deformation of an infinite body with a cylindrical inclusion whose mechanical and thermophysical characteristics differ from those of the material of the body for a heat flow and tensile forces given far from the inclusion. Stress intensity factors in the vicinity of a crack located on the continuation of the diameter of the inclusion are determined by the solution of a singular integral equation using the method of mechanical quadratures. We investigate the ratio of the length of the crack to the distance between it and the inclusion at which the regular kernel of the integral equation can be neglected in calculations. In this case, analytic formulas for the determination of the stress intensity factors are obtained.     

Ideals which generalize (<Emphasis Type=Italic>v</Emphasis><Superscript>0</Superscript>)

Countable products of finite discrete spaces with more than one point and ideals generated by Marczewski-Burstin bases (assigned to trimmed trees) are examined, using machinery of base tree in the sense of B. Balcar and P. Simon. Applying Kulpa-Szymanski Theorem, we prove that the covering number equals to the additivity or the additivity plus for each of the ideals considered.     

Every weakly initially <Emphasis Type=Italic>m</Emphasis>-compact topological space is <Emphasis Type=Italic>m</Emphasis>PCAP

The statement in the title solves a problem raised by T. Retta. We also present a variation of the result in terms of [μ, κ]-compactness.     

<Emphasis Type=Italic>O</Emphasis>-Stable Theories

A well-developed technique created to study stable theories (M. Morley, S. Shelah) is applied in dealing with a class of theories with definable linear order. We introduce the notion of an o-stable theory, which generalizes the concepts of o-minimality, of weak o-minimality, and of quasi-o-minimality. It is proved that o-stable theories are dependent, but they do not exhaust the class of dependent theories with definable linear order, and that every linear order is o-superstable.     

New results in <Emphasis Type=Italic>G</Emphasis>-best approximation in <Emphasis Type=Italic>G</Emphasis>-metric spaces

The purpose of this paper is to introduce and discuss the concepts of G-best approximation and a ₀ -orthogonality in the theory of G-metric spaces. We consider the relationship between these concepts and the dual X and obtain some results on subsets of G-metric spaces similar to normed spaces.