An extreme values of the function <Emphasis Type=Italic>S</Emphasis>(<Emphasis Type=Italic>T</Emphasis>) in short intervals

We obtain new estimates for the maximum and minimum of the argument of the Riemann zetafunction on very short segments of the critical line. These results are based on the Riemann hypothesis.     

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.     

Sign change of the function <Emphasis Type=Italic>S</Emphasis>(<Emphasis Type=Italic>t</Emphasis>) on short intervals

A theorem for the sign variation of the argument of the Riemann zeta function S(t) in the interval (t − A, t + A) with A = 4.39 ln ln ln ln T for each t, T ≤ t ≤ T + H excluding values from the set E with the measure mes(E) = O(H(ln ln T)⁻¹(ln ln ln T)^−0,5) is proved.     

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.     

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.     

<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.     

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.     

A few properties of the third Jackson <Emphasis Type=Italic>q</Emphasis>-Bessel function

The Hahn–Exton (third Jackson) q-Bessel function attracts the attention of many researchers in mathematics. We add a few more properties of this important function, such as some identities and upper bounds involving this function, in relation with the coefficients of the corresponding basic Fourier–Bessel expansions.     

The finite <Emphasis Type=Italic>p</Emphasis>-groups with <Emphasis Type=Italic>p</Emphasis> conjugacy classes of non-normal subgroups

Let ν(G) be the number of conjugacy classes of non-normal subgroups of a finite group G. The finite groups for which ν(G) ≤ 2 were determined by Dedekind and by Schmidt in the early times of group theory. On the other hand, if G is a finite p-group, La Haye and Rhemtulla have proved that either ν(G) ≤ 1 or ν(G) ≥ p. In this note, we determine all finite p-groups satisfying ν(G) = p for p > 2.     

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.