Berry–Esseen bounds in the entropic central limit theorem

Berry–Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.     

Phosphoramidite building blocks for efficient incorporation of 2′-O-aminoethoxy(and propoxy)methyl nucleosides into oligonucleotides

A simple and efficient method for the preparation of eight phosphoramidite building blocks for incorporation of 2′-O-(2-aminoethoxymethyl)ribonucleosides and 2′-O-(3-aminopropoxymethyl)ribonucleosides into synthetic oligonucleotides has been developed. The synthetic routes are maximally convergent and provide sufficient amounts of phosphoramidites for several solid-phase synthesis coupling reactions. Using acyclic derivatives 17a,b the overall yields of phosphoramidites 2 and 3 were increased up to 50% for pyrimidine nucleosides and up to 30% for purine derivatives with substantial decrease of total reaction steps. The 2′-O-substituent was found to be stable during oligonucleotide synthesis. The resulting oligonucleotides are of particular interest for post-synthetic functionalization and conjugation.     

Discrete isoperimetric and Poincaré-type inequalities

We study some discrete isoperimetric and Poincaré-type inequalities for product probability measures μ ⁿ on the discrete cube {0, 1} ⁿ and on the lattice Z ⁿ . In particular we prove sharp lower estimates for the product measures of boundaries of arbitrary sets in the discrete cube. More generally, we characterize those probability distributions μ on Z which satisfy these inequalities on Z ⁿ . The class of these distributions can be described by a certain class of monotone transforms of the two-sided exponential measure. A similar characterization of distributions on R which satisfy Poincaré inequalities on the class of convex functions is proved in terms of variances of suprema of linear processes. Received: 30 April 1997 / Revised version: 5 June 1998     

On the isoperimetric constants for product measures

Isoperimetric constants of product probability measures are known to have an almost dimension-free character. We propose a new proof based on certain Sobolev-type inequalities of additive type (introduced by the author in connection with the isoperimetric problem in Gauss space). Bibliography: 18 titles. Dedicated to Nina Nikolaevna Uraltseva Translated from Problemy Matematicheskogo Analiza, 40, May 2009, pp. 49–56.     

Deuterium-ion implantation into composite structures with tungsten coatings

The results of studying the accumulation and thermal desorption of ion-implanted deuterium from tungsten films deposited on various composite substrates are presented. The influence of the tungsten-film thickness and irradiation dose with D⁺ ions of intermediate energy on the amount of trapped deuterium and the shape of the spectra of the thermal desorption of deuterium in vacuum are studied. Possible mechanisms of these processes are discussed.     

S-N-D corner junctions in magnetic field

The dependence of the critical current of a highly transparent S-N-D corner junction on the applied magnetic field is determined for different orientations of a d-wave superconductor relative to the interface plane. It is shown that this dependence exhibits characteristic plateaus in a certain range of magnetic fields at low temperatures. These plateaus do not appear in the S-N-S corner junctions, indicating the presence of a superconductor with a sign-variable order parameter.     

On logarithmically concave measures and their applications to random processes linearly generated by independent values

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 194, pp. 28–29, 1992     

Substitution of bromine atom in 8-bromotheophylline by pyridine in the presence of o-phenylenephosphoric acid isocyanate

Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, p. 1000, July, 1988.     

Boundary value problems with a given particular solution

We modify a boundary value problem by specifying a particular solution of the original equation. This permits substantially extending the scope of mathematical problems to be considered.     

Calculation of the stability of β-cyclodextrin complexes of organic compounds using the QSPR approach

The QSPR model for predicting the Gibbs free energy of formation of complexes of different organic compounds with β-cyclodextrin has been constructed by the multiple linear regression method with the use of the double cross-validation procedure. The model has good predictive power.