Generalized Artin–Hasse and Iwasawa Formulas for the Hilbert Symbol in a High-Dimensional Local Field

The generalized Hilbert symbol in a cyclotomic extension of an absolutely unramified higher local field of characteristic 0 with a perfect last residue field of characteristic p > 2 is considered. Generalized Artin–Hasse and Iwasawa formulas are derived from an explicit Kummer Type Vostokov formula. Bibliography: 13 titles.     

Decrease in the group velocity of a light pulse in the Bose-Einstein condensate of a dilute gas

A semiclassical theory of electromagnetically induced transparency in a Bose-Einstein condensate is considered. A nonlinear Schrödinger equation that describes the interaction of the Bose-Einstein condensate with an electromagnetic field is derived. An analysis of the obtained solutions to this equation demonstrates a decrease in the group velocity of the light pulse.     

Martensite Transformation in Nanoparticles and Nanomaterials

Journal of Nanoparticle Research - It was shown that the thermoelastic martensite transformation B2 ? B19 inside nanoparticles surrounded by amorphous matrix in Ni–Ti–Cu alloys as...     

Lubin–Tate Formal Groups over the Ring of Integers of a Multidimensional Local Field

Some isomorphism criteria for Lubin–Tate formal groups over the ring of integers of a multidimensional local field are given. Bibliography: 4 titles.     

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.     

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.     

Optical limiters and diffraction elements based on a COANP-fullerene system: Nonlinear optical properties and quantum-chemical simulation

The results of optical study and quantum-chemical simulation of a conjugated organic system, 2-cyclooctylamino-5-nitropyridine (COANP)-fullerene, performed to determine its potential for application as a limiter of visible and near-IR laser radiation and as a material for diffraction elements in systems for reversible recording of optical information, are presented. Complexation between a COANP molecule and fullerene is considered as one of the main mechanisms responsible for the corresponding properties of this system. For the first time, nonlinear optical characteristics of COANP-C₆₀ and COANP-C₇₀ systems are comparatively studied and the intermolecular interaction between a COANP molecule and fullerene is analyzed on the quantum-chemical level.     

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.