Partitions of a Polytope and Mappings of a Point Set to Facets

Three theorems of this paper generalize previous results of the author on conjectures of A. Bezdek and V.V. Proizvolov. They show the existence of mappings from a given point set to the set of facets of a given polytope that satistfy some special conditions. Developing the same technique, some results on convex polytope partitions are presented, two of them dealing with partitions with prescribed measures of parts. Then we prove a corollary on the existence of a possibly nonconvex polytope with a given set of vertices, containing given points in its interior. We also consider problems of the following type: find an assignment of vectors from a given set to the parts of a given convex partition of ℝⁿ so that the shifts of the parts by their corresponding vectors either do not intersect by interior points or cover ℝⁿ     

A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

Synthesis of Protein A Conjugates with Silver Nanoparticles

The single-stage synthesis of the conjugates of protein A with silver nanoparticles is performed. The dependence of the dispersity of the prepared sols on the composition of reaction mixture is investigated by optical spectroscopy and transmission electron microscopy. The relative stability of the obtained preparations with respect to the coagulation by NaCl is estimated.     

Effect of oxidizing environments on the diffusion-segregation boron distribution in the thermal silicon dioxide-silicon system

The diffusion-segregation boron distribution in the silicon dioxide-silicon system upon oxidation in different environments is studied by secondary-ion mass spectrometry and numerical simulation. The coefficient of boron segregation at the SiO₂/Si interface and the enhancement of boron diffusion in silicon as functions of the type of oxidizing environment (dry oxygen, wet oxygen, and the presence of hydrochloric acid vapor), the orientation of the silicon surface, and the temperature of oxidizing annealing are obtained. A qualitative model is proposed based on the assumption that the segregation mass transfer of boron through the SiO₂/Si interface is associated with the generation of nonequilibrium intrinsic interstitials.     

Efficiency of shear surface wave transformation by the motion of the confining domain wall

The transformation of a shear surface magnetoelastic wave by the motion of the 180° confining domain wall in a ferromagnet is considered. Changes in the wave spectrum due to the motion of the wall are correlated with the variations of the energies of the elastic and magnetic subsystems. The efficiency of surface wave transformation by the domain wall motion is estimated in terms of energy. The frequency dependences of the mean energy density of the wave are found. It is shown that the energy density grows with wall velocity.     

Quantum-Chemical Study of the Profiles of Reactions that Form Pyrrole Anion N-Adducts with CS<Subscript>2</Subscript> and CO<Subscript>2</Subscript>

The profiles of reactions leading to pyrrole anion N-adducts with CO₂ and CS₂ have been studied by the ab initio (RHF/6-31+G*, MP2/6-31+G*) and density functional (B3LYP/6-31+G*) methods. Addition of the pyrrole anion to the carbon disulfide molecule is accompanied by the appearance of a minimum corresponding to a pre-reaction complex. The transformation of the complex to the N-pyrrolyldithiocarboxylate anion occurs via a low activation barrier, which is due to repolarization of the C=S bonds. The profile of the reaction leading to the pyrrole anion N-adduct with CO₂ does not contain any intermediate stationary points throughout the whole route from reagents to products.Original Russian Text Copyright © 2004 by V. B. Kobychev, N. M. Vitkovskaya, I. L. Zaitseva, and B. A. Trofimov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 990–993, November–December, 2004.     

Using the new in–in method for the synthesis of polyisoprene/polystyrene heteroarm star polymers

The basis of the two‐step in–in method is as follows: star polymers with poly(divinyl benzene) cores, synthesized by the arm‐first method, include many unreacted double bonds in their core, and these double bonds can be attacked by the carbanions of some monomers such as styrene and dienes. In this work, linear polyisoprene chains were used to attack the double bonds existing in the poly(divinyl benzene) cores of polystyrene star polymers, so that a heteroarm star polymer with polystyrene and polyisoprene arms was synthesized. It was later well characterized with size exclusion chromatography, light scattering, viscometry, UV spectroscopy, dynamic mechanical thermal analysis, and ¹H NMR. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 135–142, 2003     

Annihilation of positrons in hydrogen-saturated titanium

The effect of atomic hydrogen on the electronic structure of α-titanium samples is studied using the electron-positron annihilation methods. It is shown that different states of hydrogen atoms are manifested in different ways in the positron lifetime distribution spectrum. The results of theoretical calculations of the first component of the positron lifetime are in accord with the obtained experimental data.