Sections, Selections and Prohorov's Theorem

The famous Prohorov theorem for Radon probability measures is generalized in terms of usco mappings. In the case of completely metrizable spaces this is achieved by applying a classical Michael result on the existence of usco selections for l.s.c. mappings. A similar approach works when sieve-complete spaces are considered

Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume

Baire spaces and Vietoris hyperspaces

We prove that if the Vietoris hyperspace CL(X) of all nonempty closed subsets of a space X is Baire, then all finite powers of X must be Baire spaces. In particular, there exists a metrizable Baire space whose Vietoris hyperspace CL(X) is not Baire. This settles an open problem of R. A. McCoy stated in 1975

Consonance and Cantor set-selectors

It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.peer-reviewe

DETERMINATION OF RATIONAL COMPOSITION AND CONCENTRATION OF SUPERFINE ALUMINIUM MODIFIER FOR MODIFYING OF THE ALLOY AK18 STRUCTURE

It is shown that for reaching of maximal effect of mo­ difying of alloy AK18 structure it is necessary to use super­ fine aluminium modifier AlSi12Sb15Ti5 in the quantity of 0,1% of melt mass or AlSb5Ti3 at the quantity of 0,5%

INFLUENCE OF SILUMIN DEOXIDIZER-MODIFIER ON THE STRUCTURE OF STEEL INGOTS

It is shown that introduction of structural-superfine silumin deoxidizer-modifier allows to decrease the quantity of input into liquid steel lump and tribe-hardware deoxidizers more than by 30%, to reduce the defects of ingots by liquating stripes half, to reduce the content of sulphur in steel by 11–26% and of phosphorus by 12–42% and also to grind the steel grade 2–8 times as much

MANUFACTURE AND USE OF SILUMIN WITH GLOBULAR SILICON

Methods of production of silumin with globular silicon are developed. The manufacturing of this new antifriction material are organized. The wear resistance and operational life of articles from silumin with globular silicon are on par with or surpass performance of similar articles of antifriction bronze, but the articles of silumin with globular silicon are lighter and three times cheaper than articles from antifriction bronze

COOLING METHOD OF SILUMINA CASTINGS AK15M3 AT VERTICAL CENTRIFUGAL CASTING

The way of cooling of castings from silumin AK15M3 is developed at the vertical centrifugal casting, enabling to receive bimetallic blanks with high-disperse eutectic and hypereutectic microstructures and minimal allowance for machining