Structural trends of 77Se?1H spin–spin coupling constants and conformational behavior of 2‐substituted selenophenes

Experimental measurements and second‐order polarization propagator approach (SOPPA) calculations of ⁷⁷Se? ¹H spin–spin coupling constants together with theoretical energy‐based conformational analysis in the series of 2‐substituted selenophenes have been carried out. A new basis set optimized for the calculation of ⁷⁷Se? ¹H spin–spin coupling constants has been introduced by extending the aug‐cc‐pVTZ‐J basis for selenium. Most of the spin–spin coupling constants under study, especially vicinal ⁷⁷Se? ¹H couplings, demonstrated a remarkable stereochemical behavior with respect to the internal rotation of the substituent in the 2‐position of the selenophene ring, which is of major importance in the stereochemical studies of the related organoselenium compounds. Copyright © 2009 John Wiley & Sons, Ltd.     

Stability and accuracy functions for a multicriteria Boolean linear programming problem with parameterized principle of optimality “from Condorcet to Pareto”

A multicriteria Boolean programming problem with linear cost functions in which initial coefficients of the cost functions are subject to perturbations is considered. For any optimal alternative, with respect to parameterized principle of optimality “from Condorcet to Pareto”, appropriate measures of the quality are introduced. These measures correspond to the so-called stability and accuracy functions defined earlier for optimal solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an optimal alternative preserves its optimality are calculated. To illustrate the way how the stability and accuracy functions can be used as efficient tools for post-optimal analysis, an application from the voting theory is considered.     

Weak variations of Lipschitz graphs and stability of phase boundaries

In the case of Lipschitz extremals of vectorial variational problems, an important class of strong variations originates from smooth deformations of the corresponding non-smooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produce directions of differentiability of the functional and lead to singularity-centered necessary conditions on strong local minima: an equality, arising from stationarity, and an inequality, implying configurational stability of the singularity set. To illustrate the underlying coupling between inner and outer variations, we study in detail the case of smooth surfaces of gradient discontinuity representing, for instance, martensitic phase boundaries in non-linear elasticity.     

The synthesis of Leishmania major phosphoglycan fragments

The triglycosyl monophosphate 1, heptaglycosyl triphosphates 2 and 3, and octaglycosyl triphosphate 4, which are fragments of the phosphoglycan part of Leishmania major lipo- and proteo-phosphoglycans have been prepared using di- and tri-saccharide H-phosphonates for construction of the phosphodiester bridges.     

The morphology,electron structure,and optical properties of self-assembled silicon nanostructures on the surface of highly oriented pyrolytic graphite

The results of studies of the morphology, electronic structure, and optical properties of self-assembled silicon nanostructures on the surface of highly oriented pyrolytic graphite are reported. The structures are fabricated by electron-beam-assisted evaporation in high-vacuum conditions. It is found that, at thicknesses of about one monolayer, the atomic structure of the layer is similar to that of graphene with the interatomic spacing ～2.4 Å. At film thicknesses larger than one monolayer, clusters about 5 nm in dimensions are formed on the substrate surface.     

Decomposable symmetric designs

The first infinite families of symmetric designs were obtained from finite projective geometries, Hadamard matrices, and difference sets. In this paper we describe two general methods of constructing symmetric designs that give rise to the parameters of all other known infinite families of symmetric designs. The method of global decomposition produces an incidence matrix of a symmetric design as a block matrix with each block being a zero matrix or an incidence matrix of a smaller symmetric design. The method of local decomposition represents incidence matrices of a residual and a derived design of a symmetric design as block matrices with each block being a zero matrix or an incidence matrix of a smaller residual or derived design, respectively.     

Simulated annealing algorithm for the robust spanning tree problem

This paper addresses the robust spanning tree problem with interval data, i.e. the case of classical minimum spanning tree problem when edge weights are not fixed but take their values from some intervals associated with edges. The problem consists of finding a spanning tree that minimizes so-called robust deviation, i.e. deviation from an optimal solution under the worst case realization of interval weights. As it was proven in Kouvelis and Yu (Robust Discrete Optimization and Its Applications, Kluwer Academic, Norwell, 1997), the problem is NP-hard, therefore it is of great interest to tackle it with some metaheuristic approach, namely simulated annealing, in order to calculate an approximate solution for large scale instances efficiently. We describe theoretical aspects and present the results of computational experiments. To the best of our knowledge, this is the first attempt to develop a metaheuristic approach for solving the robust spanning tree problem.     

Groups whose lattice of centralizers is a sublattice of the subgroup lattice

An earlier conjecture suggests that the lattice of centralizers is modular in the title groups. We prove it to hold for two classes of groups whose lattice of centralizers has finite length — groups with the normalizer condition and locally finite groups.Translated fromAlgebra i Logika, Vol. 33, No. 5, pp. 475–513, September–October, 1994.     

Renormalization group in the theory of developed turbulence. The problem of justifying the Kolmogorov hypotheses for composite operators

In this paper, the stochastic theory of developed turbulence is considered within the framework of the quantum field renormalization group and operator expansions. The problem of justifying the Kolmogorov-Obukhov theorem in application to the correlation functions of composite operators is discussed. An explicit expression is found for the critical dimension of a general-type composite operator. For an arbitrary UV-finite composite operator, the second Kolmogorov hypothesis (the viscosity-independence of the correlator) is proved and the dependence of various correlators on the external turbulence scale is determined. It is shown that the problem involves an infinite number of Galilean-invariant scalar operators with negative critical dimensions. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 122–136, January, 1997.