Embedding of Nonprimary Subgroups in the Symmetric Group S 9

The nonprimary subgroups of the symmetric group S ₉ are investigated. Embedding properties of these subgroups are listed in a table. Properties such as abnormality, pronormality, paranormality, weak normality, etc. were checked with the help of a computer. Algorithms and codes of the first author were used for this purpose. The research leans upon the technique of Burnside marks, as well as upon pertinent information on the table of marks of S ₉ from the computer algebra package GAP. The subgroups were investigated up to conjugacy; the total number of conjugacy classes of nonprimary subgroups of S ₉ is 432. Some subgroups were additionally checked by other programs based on the double coset method. Bibliography: 24 titles.     

Viscoelastic properties of nanostructured natural rubber/polystyrene interpenetrating polymer networks

The effects of the blend ratio and initiating system on the viscoelastic properties of nanostructured natural rubber/polystyrene‐based interpenetrating polymer networks (IPNs) were investigated in the temperature range of ?80 to 150 °C. The studies were carried out at different frequencies (100, 50, 10, 1, and 0.1 Hz), and their effects on the damping and storage and loss moduli were analyzed. In all cases, tan δ and the storage and loss moduli showed two distinct transitions corresponding to natural rubber and polystyrene phases, which indicated that the system was not miscible on the molecular level. However, a slight inward shift was observed in the IPNs, with respect to the glass‐transition temperatures (T_g's) of the virgin polymers, showing a certain degree of miscibility or intermixing between the two phases. When the frequency increased from 0.1 to 100 Hz, the T_g values showed a positive shift in all cases. In a comparison of the three initiating systems (dicumyl peroxide, benzoyl peroxide, and azobisisobutyronitrile), the dicumyl peroxide system showed the highest modulus. The morphology of the IPNs was analyzed with transmission electron microscopy. The micrographs indicated that the system was nanostructured. An attempt was made to relate the viscoelastic behavior to the morphology of the IPNs. Various models, such as the series, parallel, Halpin–Tsai, Kerner, Coran, Takayanagi, and Davies models, were used to model the viscoelastic data. The area under the linear loss modulus curve was larger than that obtained by group contribution analysis; this showed that the damping was influenced by the phase morphology, dual‐phase continuity, and crosslinking of the phases. Finally, the homogeneity of the system was further evaluated with Cole–Cole analysis. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1680–1696, 2003     

Thermal expansion and thermal conductivity of CuGa<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>In<Subscript>x</Subscript>Te<Subscript>2</Subscript> solid solutions

The thermal expansion coefficients and the thermal conductivity of Bridgman-grown crystals of CuGa_1−x In_xTe₂ solid solutions are investigated. It is found that the thermal expansion coefficient varies with x linearly, while the thermal conductivity is minimal when x=0.5. The Debye temperature and the rms dynamic atomic displacements are calculated from experimental data. It is shown that the Debye temperature decreases and the rms displacements in the crystal lattice sharply increase as the In content in the solid solutions grows.     

Norm Series in High-Dimensional Local Fields

In the present paper, the notion of norm series with respect to the norm residue symbol is generalized to high-dimensional local fields. Necessary and sufficient conditions for the existence of norm series are obtained. Bibliography: 12 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 60–83.     

Recording dynamic holograms in a semiconductor crystal CdF<Subscript>2</Subscript>:In

The kinetics of decay of a phase hologram in a semiconductor CdF₂ crystal with bistable In centers is studied. Kinetic constants of the hologram decay are found, and the potential relief of the bistable center is plotted. The resolving power of the crystal is evaluated and recording of a transparency is demonstrated.     

Approximation Properties AP s and p-Nuclear Operators (the Case 0 < s ≤ 1)

We investigate Banach spaces possessing (or not possessing) the approximation properties AP _s, 0 < s ≤ 1, in connection with the following known question in the geometric theory of operators: under which conditions on Banach spaces X and Y and on positive numbers r and p does the p-nuclearity of the second adjoint of a continuous operator T from X to Y imply the p-nuclearity of T? Actually, we give necessary and sufficient conditions under which this question is answered affirmatively. In addition, the corresponding counterexamples are obtained in the maximally strong form. For instance, it is shown (and this statement is a significant strengthening of the previous results of that sort) that there exists a pair of separable Banach spaces Z and W such that the spaces Z ^** and W have Schauder bases, while for every p, 1 ≤ p < 2, there is a non-p-nuclear operator from W to Z with a p-nuclear second adjoint. Earlier, in similar examples, the corresponding spaces did not possess even the Grothendieck approximation property. The technique developed in this paper does not allow us to treat the case p > 2. That case will be studied in a forthcoming paper of the author. Bibliography: 11 titles.     

Effect of maltodextrins on the surface activity of small-molecule surfactants

We report on the effect of commercially important polysaccharides (maltodextrins with variable dextrose equivalent (Paselli SA-2, MD-6 and MD-10) on the surface activity at the air–water interface of small-molecule surfactants (sms), possessing different hydrophobic–lipophilic balance ((SSL (Na⁺), the main component is a sodium salt of stearol–lactoyl lactic acid, and PGE (080), polyglycerol ester of C18 fatty acid), and widely used in food products. A marked change of the surface activity of sms was found in the presence of maltodextrins by tensiometry. The combined data of laser multiangle light scattering and mixing calorimetry have suggested that this result is governed by specific complex formation between maltodextrins and sms in aqueous medium. Measurements have been made of the molar mass, the second virial coefficient and the enthalpy of intermolecular interactions in aqueous solutions. The implication of a degree of polymerization of maltodextrins in this phenomenon was shown. The interrelation between the molecular parameters of the formed complexes and their surface activity at the air–water interface has been revealed and discussed.     

Justification of Averaging Method for Multifrequency Impulsive Systems

We prove new theorems on the justification of the averaging method for multifrequency oscillation systems with pulse influence at fixed times.     

On Necessary and Sufficient Conditions for the Asymptotic Stability of Impulsive Systems

We prove that the sufficient conditions for the asymptotic stability of impulsive systems obtained by Gurgula and Perestyuk are also necessary conditions.