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.     

Carleman problem for two pairs of functions in a ring

We consider a particular case of the matrix Carleman problem for two pairs of functions in a ring and find a constructive solution of this problem. In addition, we propose an algorithm for the construction of solutions for two infinite systems of smooth transition and for a system of two singular equations of special type. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 662–671, May, 1997     

General-relativistic cosmology with expansion and rotation

A model of an expanding and rotating universe is constructed in the framework of general relativity. The parameters of the model are compared with the fundamental observables and shown to be in good agreement.Kaluzhsk Branch, N. É. Bauman Moscow State Technical University (MGTU). Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 71–77, June, 1993.     

Single-molecule single crystals

Various approaches to the preparation and verification of single-molecule single crystals are discussed for polyethylene and poly (oxyethylene). Analytic tools are electron microscopy, electron diffraction, and differential scanning calorimetry. The main difficulty in producing a single-molecule single crystal is to keep crystals from joining during growth.     

Influence of preparation methods on structure and properties of PA6/PA66 blends: A comparison of melt‐mixing and in situ blending

The blends composed of polyamide 6 (PA6) and polyamide 66 (PA66) were obtained using two different preparation methods, one of which was the melt‐mixing through a twin‐screw extruder and the subsequent injection molding; and the other, the in situ blending through anionic polymerization of ε‐caprolactam in the presence of PA66. For the former, there existed a remarkable improvement in toughness but a drastic drop in strength and modulus; however, for the latter, a reverse but less significant trend of mechanical properties change appeared. Various characterizations were conducted, including the analyses of crystalline morphology, crystallographic form, and crystallization and melting behaviors using polarized optical microscopy (POM), wide‐angle X‐ray diffraction (WAXD), and differential scanning calorimetry (DSC), respectively; observation of morphology of fractured surface with scanning electron microscope (SEM); measurement of glass transition through dynamic mechanical analysis (DMA); and the intermolecular interaction as well as the interchange reaction between the two components by Fourier transform infrared spectrometry (FT‐IR) and ¹³C solution NMR. The presence and absence of interchange reaction was verified for the in situ and melt‐mixed blends, respectively. It is believed that the transreaction resulted in a drop in glass transition temperature (T_g) for the in situ blends, contrary to an increase of T_g with increasing PA66 content for the melt‐mixed ones. And the two kinds of fabrication methods led to significant differences in the crystallographic form, spherulite size and crystalline content and perfection as well. Accordingly, it is attempted to explain the reasons for the opposite trends of changes in the mechanical properties for these two blends. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1176–1186, 2007