On pp-index extremal groups

The question on connection between the structure of a finite group $G$ and the properties of the indices of elements of $G$ has been a popular research topic for many years. The $p$-index $|x^G|_p$ of an element $x$ of a group $G$ is the $p$-part of its index $|x^G|=|G:C_G(x)|$. The presented short note describes some new results and open problems in this direction, united by the concept of the $p$-index of a group element

On recognition of direct powers of finite simple linear groups by spectrum

The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the Kourovka Notebook proving that for every positive integer $k$, the $k$-th direct power of the simple linear group $L_{n}(2)$ is uniquely determined by its spectrum in the class of finite groups provided $n$ is a power of $2$ greater than or equal to $56k^2$.Comment: 17 page

O(1/N_f) Corrections to the Thirring Model in 2<d<4

The Thirring model, that is, a relativistic field theory of fermions with a contact interaction between vector currents, is studied for dimensionalities 2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species. The model is found to have no ultraviolet divergences at leading order provided a regularization respecting current conservation is used. Explicit O(1/N_f) corrections are computed, and the model shown to be renormalizable at this order in the massless limit; renormalizability appears to hold to all orders due to a special case of Weinberg's theorem. This implies there is a universal amplitude for four particle scattering in the asymptotic regime. Comparisons are made with both the Gross-Neveu model and QED.Comment: 22 pages in plain TeX, with 7 figs included using psfig.tex (Minor conceptual changes - algebra unaffected

Helioseismology, solar models and neutrino fluxes

We present our results concerning a systematical analysis of helioseismic implications on solar structure and neutrino production. We find Y$_{ph}=0.238-0.259$, $R_b/R_\odot=0.708-0.714$ and $\rho_b=(0.185-0.199)$ gr/cm$^3$. In the interval $0.2<R/R_\odot<0.65$, the quantity $U=P/\rho$ is determined with and accuracy of $\pm 5$\permille~or better. At the solar center still one has remarkable accuracy, $\Delta U/U <4$. We compare the predictions of recent solar models (standard and non-standard) with the helioseismic results. By constructing helioseismically constrained solar models, the central solar temperature is found to be $T=1.58 \times 10^7$K with a conservatively estimated accuracy of 1.4%, so that the major unceratainty on neutrino fluxes is due to nuclear cross section and not to solar inputs.Comment: 14 pages including 9 figures, LaTex file, espcrc2.sty is needed; to appear in Nucl. Phys. B Proc. Suppl., Proceedings of TAUP97 conference, Laboratori Nazionali del Gran Sasso, September 199

Gravitational Couplings of Intrinsic Spin

The gravitational couplings of intrinsic spin are briefly reviewed. A consequence of the Dirac equation in the exterior gravitational field of a rotating mass is considered in detail, namely, the difference in the energy of a spin-1/2 particle polarized vertically up and down near the surface of a rotating body is $\hbar\Omega\sin\theta$. Here $\theta$ is the latitude and $\Omega = 2GJ/(c^2 R^3)$, where $J$ and $R$ are, respectively, the angular momentum and radius of the body. It seems that this relativistic quantum gravitational effect could be measurable in the foreseeable future.Comment: LaTeX file, no figures, 16 page

High frequency ESR investigation on dynamical charge disproportionation and spin gap excitation in NaV_2O_5

A significant frequency dependence of the ESR line width is found in NaV_2O_5 between 34-100 K and the line width increases as the resonance frequency is increased from 95 GHz to 760 GHz. The observed frequency dependence is qualitatively explained in terms of the dynamical charge disproportionation. The present results show the essential role of the internal charge degree of freedom in a V-O-V bond. We have also proposed the existence of the Dzyaloshinsky-Moriya interaction in the low temperature charge ordered phase considering the breaking of the selection rule of ESR realized as the direct observation of the spin gap excitation.Comment: 9 figures submitted to J. Phys.Soc. Jp

Enhancement of the Thermal Conductivity in gapped Quantum Spin Chains

We study mechanism of magnetic energy transport, motivated by recent measurements of the thermal conductivity in low dimensional quantum magnets. We point out a possible mechanism of enhancement of the thermal conductivity in gapped magnetic system, where the magnetic energy transport plays a crucial role. This mechanism gives an interpretation for the recent experiment of CuGeO_3, where the thermal conductivity depends on the crystal direction.Comment: 4 pages, 2 figure

Providing energy decoupling of electric drive and electric grids for industrial electrical installations

Subjects of the research are industrial electric drives, witch maintain the operation of main actuating units of production machines and installations during the development of mineral resource deposits. The goal is to research the possibility to ensure the energy decoupling of industrial electric drives and electric grid by means of structural implementation of active rectifiers into frequency converters. The main purpose of energy decoupling is to eliminate the negative impact of low quality electric energy and changes in energy parameters on electric drive operation. In order to accomplish energy decoupling of electric drive with active rectifier, methods of mathematical and simulation modeling with mathematical application software package were used. The integrated simulation model with two electric drives, including active rectifier (energy decoupled electric drive) and diode rectifier (standard type electric drive), were created. Simulation model is provided with tools for oscillographic testing and analysis of the impact of power quality parameters on frequency converters and drive motors operation. The analysis of effectiveness of energy decoupling by means of active rectifier of frequency converter shows that drive motor completely retains the stability and controllability of rotation frequency and torque during the changes of power quality parameters in electric grid. The use of active rectifier allows to ensure the operation of electric drive in required mode in case of voltage decrease by 30 % with normative value of 5-10 %, i.e. energy decoupling provides high stability margin for voltage. Electric drive with active rectifier ensures energy decoupling in case of asymmetry of supply voltage. The control of mechanical variables of induction motor during offsets in amplitude and frequency in all phases of electric grid is ensured to be on required level