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.     

Intuitionistic <Emphasis Type=Italic>I</Emphasis>-fuzzy topological spaces

The main purpose of this paper is to introduce the concept of intuitionistic I-fuzzy quasi-coincident neighborhood systems of intuitiostic fuzzy points. The relation between the category of intuitionistic I-fuzzy topological spaces and the category of intuitionistic I-fuzzy quasi-coincident neighborhood spaces are studied. By using fuzzifying topology, the notion of generated intuitionistic I-fuzzy topology is proposed, and the connections among generated intuitionistic I-fuzzy topological spaces, fuzzifying topological spaces and I-fuzzy topological spaces are discussed. Finally, the properties of the operators Iω, ι are obtained.     

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.     

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.     

Improved Full-Newton Step <Emphasis Type=Italic>O</Emphasis>(<Emphasis Type=Italic>nL</Emphasis>) Infeasible Interior-Point Method for Linear Optimization

We present several improvements of the full-Newton step infeasible interior-point method for linear optimization introduced by Roos (SIAM J. Optim. 16(4):1110–1136, 2006). Each main step of the method consists of a feasibility step and several centering steps. We use a more natural feasibility step, which targets the μ ⁺-center of the next pair of perturbed problems. As for the centering steps, we apply a sharper quadratic convergence result, which leads to a slightly wider neighborhood for the feasibility steps. Moreover, the analysis is much simplified and the iteration bound is slightly better.     

Three-webs <Emphasis Type=Italic>W</Emphasis>(1, <Emphasis Type=Italic>n</Emphasis>, 1) and associated systems of ordinary differential equations

We consider a three-web on a smooth manifold formed by two n-parameter families of curves and a one-parameter family of hypersurfaces. For such webs, we define a family of adapted frames, find the systemof structure equations, and study the differential-geometric objects that arise in differential neighborhoods up to the third order. We prove that each system of ordinary differential equations (SODE) uniquely defines a three-web. This allows us to describe properties of a SODE in terms of the corresponding three-web. In particular, we characterize autonomous SODE.     

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.     

Characterizations of some rings with <Emphasis Type=Italic>C</Emphasis>-projective, <Emphasis Type=Italic>C</Emphasis>-(FP)-injective and <Emphasis Type=Italic>C</Emphasis>-flat modules

Let R be a commutative ring and C a semidualizing R-module. We investigate the relations between C-flat modules and C-FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.     

A note on <Emphasis Type="Italic">f</Emphasis><Subscript><Emphasis Type="Italic">I</Emphasis></Subscript>-sets and <Emphasis Type="Italic">f</Emphasis><Subscript><Emphasis Type="Italic">I</Emphasis></Subscript> -continuous functions

Summary In [6] we introduced and investigated the notions of f_I -sets and f_I -continuous functions in ideal topological spaces. In this paper, we investigate their further important properties.