An Automatic Procedure for Updating the Block Size in the Block Conjugate Gradient Method for Solving Linear Systems

The paper considers the problem of constructing an efficient automatic procedure for reducing the block size in the block conjugate gradient method insuring that the resulting rate of convergence is comparable with that of the block conjugate gradient method with constant block size. The numerical results provided show that, independently of the type of distribution of the smallest eigenvalues of the preconditioned matrix, the procedure suggested always leads to a decrease of the arithmetic costs with respect to those of the block method with constant block size. Bibliography: 8 titles.     

Formation of coherent spatial structures in the reaction-diffusion atmospheric system under the action of a planetary wave

On the example of the effect of an atmospheric wave with given amplitude on the density oscillations of minor gas constituents near the mesopause (at heights 80–90 km, we consider the influence of the quasi-resonant periodic spatial transport on a distributed system responding subharmonically to a periodic external action (diurnal sunlight variations). Numerical modeling revealed the formation of a coherent horizontal distribution of the dynamical variables (i.e., the concentrations of small constituents). Application of this effect to the mesopause conditions is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 47, No. 9, pp. 739–752, September, 2004.     

Practical OR for Undergraduates in the Swinburne Course

Much of the debate over OR education over the last ten years has been confined to the relevance of the content and style of programmes at the postgraduate level. This paper focuses on the undergraduate level and discusses the way in which practical elements have been successfully incorporated at this level in Australia. These elements include the use of case study material from the literature, case problem solving groups, industrial projects and 12 months paid employment through a co-operative education programme. The use of each of the above and the context with which they fit into the programme is covered as are the benefits and problems associated with the programme.     

Diffraction of normal shock wave by yawed wedges

The diffraction of normal shock with yawed wedges of small angles have been considered in this paper. Vorticity distribution of the fluid particle over the diffracted shock has been determined for several Mach numbers of the shock wave. The Mach reflection effects have also been investigated when the bend is concave to the flow.     

Two-limit problems for almost semicontinuous processes defined on a Markov chain

We consider almost upper-semicontinuous processes defined on a finite Markov chain. The distributions of functionals associated with the exit of these processes from a finite interval are studied. We also consider some modifications of these processes. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 555–565, April, 2007.     

Variations on the theme of solvability by radicals

We discuss the problem of representability and nonrepresentability of algebraic functions by radicals. We show that the Riemann surfaces of functions that are the inverses of Chebyshev polynomials are determined by their local behavior near branch points. We find lower bounds on the degrees of equations to which sufficiently general algebraic functions can be reduced by radicals. We also begin to classify rational functions of prime degree whose inverses are representable by radicals.     

Representations of bornological algebras

Bounded representations of bornological algebras are considered. The left and right bornological radicals in bornological algebras are introduced. It is shown that the left (right) bornological radical of a bornological algebra A is equal to the intersection of all bornologically closed maximal regular left (respectively, right) ideals of A, and both these radicals of A and the Jacobson radical of A coincide if A is an advertive and simplicial bornological algebra (in particular, a bornological Q-algebra). Bibliography: 16 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 9–22.     

An exponentially fitted special second-order finite difference method for solving singular perturbation problems

An exponentially fitted special second-order finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. A fitting factor is introduced in a tri-diagonal finite difference scheme and is obtained from the theory of singular perturbations. Thomas Algorithm is used to solve the system and its stability is investigated. To demonstrate the applicability of the method, we have solved several linear and non-linear problems. From the results, it is observed that the present method approximates the exact solution very well.     

Topological K-groups of two-dimensional local fields

A complete two-dimensional local field K of mixed characteristic with finite second residue field is considered. The existence of a completely ramified extension L of K such that L is a standard field is assumed. It is proved that the rank of the quotient U(1)K ₂ ^top K/T_K, where T_K is the closure of the torsion subgroup, is equal to the degree of the constant subfield of K over ℚ_p. I. B. Zhukov constructed a set of generators of this quotient in the case where K is a standard field. In this paper, two natural generalizations of this set are considered, and it is proved that one of them generates the entire group and the other generates its subgroup of finite index. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 343, 2007, pp. 206–221.