Convex bodies and norms associated to convex measures

Isotropy-like properties are considered for finite measures with heavy tails. As a basic tool, we extend K. Ball’s relationship between convex bodies and finite logarithmically concave measures to a larger class of distributions, satisfying convexity conditions of the Brunn–Minkowski type.     

Reverse Brunn–Minkowski and reverse entropy power inequalities for convex measures

We develop a reverse entropy power inequality for convex measures, which may be seen as an affine-geometric inverse of the entropy power inequality of Shannon and Stam. The specialization of this inequality to log-concave measures may be seen as a version of Milman?s reverse Brunn–Minkowski inequality. The proof relies on a demonstration of new relationships between the entropy of high dimensional random vectors and the volume of convex bodies, and on a study of effective supports of convex measures, both of which are of independent interest, as well as on Milman?s deep technology of M-ellipsoids and on certain information-theoretic inequalities. As a by-product, we also give a continuous analogue of some Plünnecke–Ruzsa inequalities from additive combinatorics.     

Ion-implanted deuterium accumulation in a deposited tungsten coating

The effects of trapping of ion-implanted deuterium and its thermal desorption on the structure and stressed state of a tungsten coating deposited on a composite substrate is studied. The amount of accumulated deuterium, macrostresses of the coating, and the shape of thermal desorption spectra are shown to depend on the D⁺ ion fluence and the irradiation temperature. Possible mechanisms of these processes are proposed.     

Contribution of the triplet component of the supercurrent-carrying density of states to the Josephson current in a nonequilibrium superconductor/ferromagnet/superconductor junction

A weak link of two superconductors with s-type pairing through a ferromagnet has been theoretically investigated in the regime of a nonequilibrium spin-dependent distribution of electrons over energy levels in a ferromagnetic interlayer. It has been shown that, under the given conditions, the triplet component of the supercurrent-carrying density of states, which does not participate in the Josephson current transfer under equilibrium and spin-independent nonequilibrium conditions, is involved in the Josephson current transfer through the junction. In this case, the standard supercurrent transferred by the singlet component of the supercurrent-carrying density of states remains unchanged as compared to the case of the equilibrium distribution of electrons in the interlayer. An additional current transferred by the triplet component is controlled by a voltage that controls the specific shape and the degree of nonequilibrium of the electron distribution function in the interlayer. Depending on this controlling parameter, the additional current can substantially amplify or attenuate the standard supercurrent and also switch the junction between 0 and π states.     

, Vertex Isoperimetry and Concentration

. This approach refines results relating the spectral gap of a graph to the so-called magnification of a graph. A concentration result involving is also derived. Received July 22, 1998     

Isoperimetric problem on the real line

The isoperimetric problem on the real line for distributions with continuous positive densities is considered. Necessary and sufficient conditions under which the intervals (−∞, a) are extremal are suggested. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 5–9. Translated by V. Sudakov.     

Quantum-chemical models of KOH(KOBut)/DMSO superbasic systems and mechanisms of base-promoted acetylene reactions

The mechanisms of fundamental base-promoted acetylene reactions, namely, nucleophilic addition to the triple C ≡ C bond (vinylation) and nucleophilic addition of acetylenic carbanion to a carbonyl group (ethynylation), are addressed using three models of different complexity—pentasolvate, monosolvate, and anionic—which describe the catalytic superbasic systems MOH(OBu^t)/DMSO (suspensions of alkali hydroxides or tert-butoxides in dimethyl sulfoxide). The above acetylene reactions and sequential transformations of reagents arranged by the superbasic center are modeled within the framework of the most complete pentasolvate model, in which the superbase is represented by the KOH·5DMSO (KOBu^t·5DMSO) complexes. We have developed approaches to the construction of simplified models (monosolvate and anionic) to describe transformations in complex systems. The mechanisms of cascade assemblies of 6,8-dioxabicyclo[3.2.1]octanes, cyclopentenones, and furan cycles from ketones and acetylenes in the superbasic environment are investigated using a uniform B2PLYP/6-311+G**//B3LYP/6-31+G* approach, and the energy profiles of these different carbo- and heterocycles are analyzed.     

Concentration inequalities and limit theorems for randomized sums

Concentration properties and an asymptotic behaviour of distributions of normalized and self-normalized sums are studied in the randomized model where the observation times are selected from prescribed consecutive integer intervals. Research supported in part by NSF Gr. No. 0405587     

A method for solving the functional equation with variable delay

Mathematical simulation of physical conditions at a moving boundary in problems of wave reflection leads to a finite-difference equation with variable delay. If the reflector velocity is smaller than the wave-propagation velocity, the existence and uniqueness of the equation solution is proved using the principle of contraction maps and the method of successive approximations. It is shown that the solution can be expressed as a function of the composite argument that depends on one variable. The required accuracy of numerical calculations is ensured by partial sums when the argument is represented by an infinite converging series. N. I. Lobachevsky State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 900–905, September, 1999     

Effect of various components of slightly diluted tungsten-based alloys on the formation of defects in atomic displacement cascade regions: Field-ion microscopic analysis

New complex field-ion microscopic data for the formation of radiation-induced defects in VChV ultrapure tungsten, VA-3 commercial-grade tungsten, and four slightly diluted tungsten-based alloys (W-Hf-C, P39A; W-1.5% ThO₂, VT-15; W-5% Re, VR-5; and W-2% Fe, VZh-2) are reported. Samples were irradiated in an external unit by Ar⁺ and Ni⁺ ions of energy 35 keV. In the experiments, the ion current is kept at j=2.0 μA and the irradiation fluence equals Φt=5×10¹⁴ ions/cm². The clustering of single vacancies in samples irradiated is studied in relation to the impurity concentration and type. The distribution of vacancy clusters over the number of aggregated single vacancies is studied. These distributions are found to differ noticeably inside and outside the depletion zones. The mean lengths of focused substitutional atomic collision chains in samples with different impurity concentrations and types are measured indirectly. From these data, the efficiency of trapping intrinsic interstitials by various impurities in tungsten is estimated.