Applying Stochastic Algorithms to a Locomotive Scheduling Problem

This paper addresses a problem common to all railway networks. Given a fixed train timetable and locomotives (or other forms of traction) of various types, each train must be allocated a locomotive. This paper examines the use of stochastic algorithms for such a problem. Two types of algorithm are used—a simple ‘local improvement’ method, performed successively from randomly chosen starting points, and a ‘simulated annealing’ approach. Both are found to give considerably better results than a deterministic method in current use, and the annealing approach is probably the better stochastic method.     

Rehabilitation of the Gauss-Jordan algorithm

Summary In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.     

An expedient route to diaza-spirocycles utilizing a sequential multicomponent α-aminoallylation/ring-closing metathesis strategy

A general method for the preparation of diaza-spirocycles is reported. This method used an olefin metathesis in order to construct the desired spirocyclic framework. Beginning with commercially available protected amino ketones, this strategy ultimately produced pharmacologically relevant diaza-scaffolds in an efficient and high-yielding process.     

Coverings of topological loops

In this paper, we show that in some cases, no proper covering of a locally compact group topologically generated by left translations of a topological loop can occur as the group topologically generated by left translations of a topological loop. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 22, Algebra and Geometry, 2004.     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

Effect of Alkali Metal Cation on Copolymerization of Acrylamide with Salts of 2-Acrylamido-2-methylpropanesulfonic Acid in Aqueous Solutions

The kinetics of radical copolymerization of acrylamide with lithium, sodium, and potassium 2-acrylamido-2-methylpropanesulfonates in concentrated aqueous solutions in the presence of potassium persulfate as initiating agent at pH 9 and 50°C was studied by dilatometry.     

Contact Interaction of Two Elastic Wedges

We consider the problem of contact of two elastic wedges and assume that only the vertices of the wedges touch before loading. After loading, the edges of both wedges come in contact near their common vertex. We reduce the constructed system of dual integral equations to a Fredholm integral equation of the second kind with difference kernel given on the semiaxis. We analytically solve the Fredholm equation by reducing it to the boundary-value Riemann problem for analytic functions. We obtain an analytic expression for contact stresses.     

The study and applications of photochemical-dynamical gravity wave model II

A nonlinear, compressible, non-isothermal gravity wave model that involves photochemistry is used to study the effects of gravity wave on atmospheric chemical species distributions in this paper. The changes in the distributions of oxygen compound and hydrogen compound density induced by gravity wave propagation are simulated. The results indicate that when a gravity wave propagates through a mesopause region, even if it does not break, it can influence the background distributions of chemical species. The effect of gravity wave on chemical species at night is larger than in daytime.     

Linear nonstationary optical dimensional resonances in atomic nanostructures

The existence of linear nonstationary optical resonances in a diatomic nanostructural object with a dipole-dipole atomic interaction has been proved. A new solution to the joint system of modified Bloch optical equations and nonlocal field equations is obtained for time intervals much shorter than the times of phase and energy relaxation. Formulas for effective polarizabilities of the object’s atoms, which have a set of dimensional resonances, are derived. The frequencies of these resonances significantly differ from the eigenfrequencies of the object’s atoms, and their properties depend on the interatomic distance, light-pulse duration, initial atomic inversions, and the orientation of the object’s axis relative to the direction of incidence of the external light wave.