Application of Grid technology in computational chemistry

The key trends and prospects of development of computational chemistry that formed in the early 2010s are considered. The most advanced methods for solution of various types of challenges in the computational and quantum chemistry by calculations in the distributed environments (Grid) and on high-performance supercomputer installations and the application methods of parallel and distributed computations are demonstrated; the tailor-made technologies developed for these calculations are described.     

Algorithmically finite groups

We call a group Galgorithmically finite if no algorithm can produce an infinite set of pairwise distinct elements of G. We construct examples of recursively presented infinite algorithmically finite groups and study their properties. For instance, we show that the Equality Problem is decidable in our groups only on strongly (exponentially) negligible sets of inputs.     

Integrals containing products of Airy functions and planar photon propagation in a magnetic field

We derive a number of new results on integrals of products of Airy functions, using various integral transform techniques. As an application, we deduce a compact integral representation, suitable for numerical integration, of the one‐loop photon propagator in a magnetic field in 2 + 1 dimensional scalar quantum electrodynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Sufficient Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data

Suppose α is an orientation preserving diffeomorphism (shift) of \mathbbR₊=(0,￥){{\mathbb{R}}_+=(0,\infty)} onto itself with the only fixed points 0 and ∞. We establish sufficient conditions for the Fredholmness of the singular integral operator with shift

Knapsack problem with probability constraints

This paper is dedicated to a study of different extensions of the classical knapsack problem to the case when different elements of the problem formulation are subject to a degree of uncertainty described by random variables. This brings the knapsack problem into the realm of stochastic programming. Two different model formulations are proposed, based on the introduction of probability constraints. The first one is a static quadratic knapsack with a probability constraint on the capacity of the knapsack. The second one is a two-stage quadratic knapsack model, with recourse, where we introduce a probability constraint on the capacity of the knapsack in the second stage. As far as we know, this is the first time such a constraint has been used in a two-stage model. The solution techniques are based on the semidefinite relaxations. This allows for solving large instances, for which exact methods cannot be used. Numerical experiments on a set of randomly generated instances are discussed below.     

On orthogonal and selective activation of glycosyl thioimidates and thioglycosides: application to oligosaccharide assembly

Discrimination among S-thiazolinyl (STaz), S-benzoxazolyl (SBox), and S-ethyl anomeric leaving groups was achieved by fine-tuning activation conditions. Preferential glycosidation of a certain leaving group is determined neither by the strength of the activating reagent nor by the stability of the leaving group itself; instead, the type of activation plays the key role. The activation conditions established herein were applied to a sequential five-step synthesis of a hexasaccharide using six monosaccharide building blocks equipped with six different leaving groups.     

Microwave and UV excitation spectra of 4-fluorobenzyl alcohol at high resolution. S0 and S1 structures and tunneling motions along the low frequency -CH2OH torsional coordinate in both electronic states

Rotationally resolved electronic spectra of several low frequency vibrational bands that appear in the S(1) ← S(0) transition of 4-fluorobenzyl alcohol (4FBA) in the collision-free environment of a molecular beam have been observed and assigned. Each transition is split into two or more components by the tunneling motion of the attached -CH(2)OH group. A similar splitting is observed in the microwave spectrum of 4FBA. Analyses of these data show that 4FBA has a gauche structure in both electronic states, but that the ground state C(1)C(2)-C(7)O dihedral angle of ～60° changes by ～30° when the photon is absorbed. The barriers to the torsional motion of the attached -CH(2)OH group are also quite different in the two electronic states; V(2) ～ 300 cm(-1) high and ～60° wide in the S(0) state, and V(2) ～ 300 cm(-1) high and ～120° wide (or V(2) ～ 1200 cm(-1) high and ～60° wide) in the S(1) state. Possible reasons for these behaviors are discussed.     

Fast protonic conductivity in crystalline benzenehexasulfonic acid hydrates

We report on the crystal structures of two hydrates of benzenehexasulfonic acid, its water sorption isotherm, temperature- and humidity-dependent conductivity, along with ¹H NMR studies. At comparable humidities and temperatures, this crystalline material shows conductivity similar to Nafion, which conducts protons via liquid water channels. We believe that the presented discovery of fast protonic conductivity in benzenehexasulfonic acid at low humidities is encouraging for further efforts in developing highly sulfonated polymers as membranes for fuel cells.