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.     

基于约束优化的联想记忆模型学习算法

本文提出了一种对称互连神经元网络的学习策略,利用全局约束优化方法确定连接权。优化过程采用了梯度下降技术。这种学习算法可以保证训练样本成为系统的稳定吸引子,并且具有优化意义上的最大吸引域。本文讨论了网络的存储容量,训练样本的渐近稳定性和吸引域大小。计算机实验结果说明了学习算法的优越性。     

Comparison of the methods for computing interference elastic wave fields in thin-layered media. 1

A nonstationary problem concerning the propagation of low-frequency waves for a model that consists of a packet of elastic layers lying on an elastic half-space is considered, and exact mathematical solutions in the form of repeated integrals are constructed in three basic forms. It is proved that these solutions satisfy initial conditions. The representation of solutions as a superposition of multiple waves is treated. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 332, 2006, pp. 220–239.     

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.     

Production and properties of metal-carbon composite coatings with a nanocrystalline structure

It is suggested to produce metal-carbon composite coatings by magnetron sputtering of mosaic cathodes, which are Group IV, V, and VI metals. The mosaic structure of the cathode elements are computer-optimized for each of the metals. Reflection electron diffraction studies show that the coatings have the amorphous or nanocrystalline structures, which are thermally stable. The coatings offer specific physical properties, in particular, low friction factor and high hardness.     

Two schemes for detecting CMOS analog faults

A design-for-testability scheme for detecting CMOS analog faults was reported by Favalli et al. (see ibid., vol.25, no.5, p.1239-46, 1990). The authors propose two alternative designs, one for small circuits and another for large circuits, which require significantly less area overhead (about 1/4 to 1/3) than that of Favalli's design. With the proposed modification in the first design, the untestable problem, which occurred in Favalli's design, can be alleviated. Furthermore, the proposed schemes are also fit to be implemented in VLSI circuits     

Discovery of a new long-lived isomeric state in 125Ce

A new long-lived isomeric state in the near proton dripline nucleus ¹²⁵Ce has been identified with Schottky mass spectrometry at GSI. The excitation energy E ^* = 103(12)keV and the decay time of 193(1)s have been obtained from a single stored fully ionized ^125m Ce⁵⁸⁺ ion. The data implies an E3 transition and a 1/2⁺ assignment for the spin of the isomer.