Complex powers of classical SG-pseudodifferential operators

Abstract Under a suitable ellipticity condition, we show that classical SG-pseudodifferential operators of nonnegative order possess complex powers. We show that the powers are again classical and derive an explicit formula for all homogeneous components. Keywords: Complex power, Weighted symbols, Noncompact manifolds     

Numerical Prediction of the Strain State of Thermoset Matrix/Mineral Filler Composite Plates

The numerical prediction of the fields of inelastic strains (the linear invariant of the tensor of inelastic strains) in thermoset polyester/marble filler composite plates is discussed. A uniformly distributed load is applied to the plates, which lie on a steel base. The strain fields are predicted by means of the boundary element method by using creep test data for the composites and the polyester matrix itself. Identical creep tests were performed for two ages of the materials (1 month and 13 years), which allowed evaluating the aging effect. The study is carried out in two stages. At the first stage, the application of the generalized Maxwell-Gurevich equation to the thermoset matrix/mineral filler composite is demonstrated. The model parameters determined from the experimental creep data is used for the second stage, where the state of inelastic strains in the plates is predicted by applying the boundary element method. The influence of composite formulation (filler content) and physical aging of the polyester matrix on the state of inelastic strains in the plates is shown.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 145–156, March–April, 2005.     

Measured and calculated vertical structure of a sound field in the ocean

Results of measuring the monochromatic sound field with a dipping probe in the deep ocean are presented. The sound speed profile in the region of measurements had a minimum at a depth of 1600 m. The experiment was carried out in the Atlantic Ocean with the use of two vessels separated by a distance of approximately four ray cycles (～240 km). The experimental data are compared with the calculations based on a new concept of the Brillouin waves for describing the vertical structure of the sound field produced by rays. It is shown that a satisfactory agreement between experiment and calculation can be achieved by fitting the parameters of the experiment. Such a procedure allows one to refine or even to determine the experimental conditions, which not are always known. The proposed method of calculation offers an opportunity for solving inverse problems of ocean acoustics.     

Generation of angular momentum of fission fragments in a cluster model

Based on the dinuclear system concept, the role of bending vibrations in creation of the angular momentum of primary fission fragments is investigated. For ²⁵²Cf spontaneous fission, the angular momenta of the fragments are calculated as a function of the neutron multiplicity and compared with available experimental data. Different cluster compositions of the ²⁵²Cf fission modes at the scission point are considered.     

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.     

HPLC study of starch hydrolysis products obtained with α-amylase from bacillus amyloliquefaciens and bacillus licheniformis

Two bacterial α-amylases from new industrial strains were studied: α-amylase fromBacillus amyloliquefaciens CCM 3502 (Czechoslovak) and thermostable α-amylase fromBacillus licheniformis 44MB82 (Bulgarian). The thermostable enzyme hydrolyzed starch mainly to dextrins, and after 1 h, 30% of the products were oligosaccharides. TheB. amyloliquefaciens enzyme produced more maltooligosaccharides than the first enzyme (B. licheniformis). Within 1 h, up to 80% of the substrate were hydrolyzed, giving different spectrum of oligosaccharides in comparison with the thermostable one.     

Elastic and Thermophysical Properties of Poly(Vinyl Chloride) and Chlorinated Polyethylene Blends

The results of experimental and theoretical investigations of elastic and thermophysical properties of poly(vinyl chloride) (PVC) and chlorinated polyethylene (CPE) blends are presented. Eight types of specimens with different ratios of weight contents of PVC and CPE (PVC/CPE = 100/0, 90/10, 80/20, 60/40, 40/60, 20/80, 10/90, and 0/100) were tested. The effect of blend composition on the elastic constants (tensile and shear modulus) is discussed. The data on the thermal conductivity, thermal diffusivity, and heat capacity of the blends investigated are also presented.     

Approximate method of calculating stresses in a rectangular plate locally loaded by a harmonic force

From double trigonometric series for bending moments the slowly converging components are picked out. When the loading facets are small compared with the width of the plate, they are approximately summed by the analytical method. This simplifies substantially the calculation of bending moments and stresses in the zone of small loading facets compared with the usual expansion with respect to the natural vibration forms.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 84–88, 1989.