The generalized characteristic polynomial, corresponding resolvent and their application

We introduced previously the generalized characteristic polynomial defined by $P_C(\lambda)={\rm det}\,C(\lambda),$ where $C(\lambda)=C+{\rm diag}\big(\lambda_1,\dots,\lambda_n\big)$ for $C\in {\rm Mat}(n,\mathbb C)$ and $\lambda=(\lambda_k)_{k=1}^n\in \mathbb C^n$ and gave the explicit formula for $P_C(\lambda)$. In this article we define an analogue of the resolvent $C(\lambda)^{-1}$, calculate it and the expression $(C(\lambda)^{-1}a,a)$ for $a\in \mathbb C^n$ explicitly. The obtained formulas and their variants were applied to the proof of the irreducibility of unitary representations of some infinite-dimensional groups.Comment: 24

Temperature dependent conductivity of polycrystalline Cu 2ZnSnS 4 thin films

pre-printThe temperature-dependent conductivity of Cu2ZnSnS4 (CZTS) thin films prepared by sulfurization of different sputtered ZnS/Cu/Sn stacks and also of the same stack annealed for different times was investigated from 30-300 K. Fitting of the through-thickness conductivity requires a model including Mott variable-range hopping (M-VRH), nearest-neighbor hopping (NNH), and thermionic emission over grain boundary (GB) barriers. The GB barrier height varies sensitively from 50-150 (65) meV with annealing and especially with [Cu]/([Zn]þ[Sn]) ratio but is independent of [Zn]/[Sn] ratio. These results are critical for understanding the behavior of solar cells based on polycrystalline CZTS absorber layers

Effect of Substrate Temperature on the Structural Properties of CdxZn1-xTe Films Grown by Close-Spaced Sublimation Method

In this work by energy dispersive analysis of X-rays, scanning electron microscopy and X-ray diffraction methods films of CdxZn1-xTe solid solution, obtained by a close-spaced vacuum sublimation technique under different temperatures of glass substrate, has been studied. Films were deposited by the co sublimation of Cadmium Telluride (CdTe) and Zinc Telluride (ZnTe) chunks, mixed in the ratio of 2:1. The effect of substrate temperature on the surface morphology, elemental and phase composition, lattice parameter, scattering domain sizes has been studied. The results of these studies can be used for obtaining absorber layers of tandem solar cells, basic layers of X-ray and gamma detectors

Effect of Substrate Temperature on the Structural Properties of CdxZn1-xTe Films Grown by Close-Spaced Sublimation Method

In this work by energy dispersive analysis of X-rays, scanning electron microscopy and X-ray diffraction methods films of CdxZn1-xTe solid solution, obtained by a close-spaced vacuum sublimation technique under different temperatures of glass substrate, has been studied. Films were deposited by the co sublimation of Cadmium Telluride (CdTe) and Zinc Telluride (ZnTe) chunks, mixed in the ratio of 2:1. The effect of substrate temperature on the surface morphology, elemental and phase composition, lattice parameter, scattering domain sizes has been studied. The results of these studies can be used for obtaining absorber layers of tandem solar cells, basic layers of X-ray and gamma detectors

Декодер квадратурних інтерференційних сигналів

The analysis and research of interference signals of the interferometric system for measuring ultra-small linear movements has been accomplished. The features of devices performing reverse counting the numbers of interference fringes are considered. The realization of the device reversely counting the in-crement intervals for the signal’s phase has been suggested. Fig.: 7. Refs: 13 titles.Проведен анализ и исследование интерференционных сигналов интерферометрической системы по измерению сверхмалых линейных перемещений. Рассмотрены особенности построения устройств реверсивного счета числа интерференционных полос. Предложена реализация устройства реверсивного счета числа интервалов прироста фазы сигнала. Ил.: 7. Библиогр.: 13 наим.Проведено аналіз і дослідження інтерференційних сигналів інтерферометричної системи по виміру надмалих лінійних переміщень. Розглянуто особливості побудови пристроївреверсивногорахування числа інтерференційних смуг. Запропоновано реалізацію пристрою реверсив ного рахування числа інтервалів приросту фази сигналу

Прецизійна система термостабілізації підвищеної потужності

An analysis of principles construction of temperature stabilization and an experimental research on temperature stabilization system have been carried out. The features of design and construction of systems for automatic temperature control have been considered. A realization of highly efficient temperature controller is proposed. The principles of construction of temperature stabilization systems using Peltier thermoelectric modules are investigated. A highly effective thermal stabilization system for Peltier modules with output power >50 W without the use of expensive controllers has been developed. It is shown that the created thermostabilization system ensures stability of temperature maintenance 0,01 °С. The highly effective system of thermal stabilization optimally combines the basic specifications: high temperature stability, high energy efficiency, low current ripple TEM and low cost. The urgency of the development is due to the fact that the known temperature controllers, which provide high accuracy of the maintenance of the set temperature level in the established modes and good quality of transient processes, have a complicated technical implementation with the use of either programmable controllers or computer control. Their disadvantage is a high cost and low accuracy of temperature stabilization in the range of 0,01–0,1 С. Regulators with a simple technical implementation and low price support the accuracy of stabilizing the temperature of 0,1 С in the established modes with significant error and do not provide stability of the stabilization system in conditions of change in wide limits of the temperature of the surrounding environment. The highly stable temperature regulator proposed in the article with a relatively simple technical implementation solves this contradiction. The controller uses a one-circuit automatic temperature control system. The control loop contains a proportional-integral-differential (PID) regulator, which, in conditions of disturbing effects on the stability of maintaining the desired temperature of the object, provides the necessary change in the control signal at the input of the control circuit.Проведен анализ принципов построения систем температурной стабилизации и экспериментальные исследования по разработке системы термостабилизации. Рассмотрены особенности разработки и построения систем автоматического регулирования температуры. Предложена реализация высокоэффективного регулятора температуры.Проведено аналіз принципів побудови систем температурної стабілізації та експериментальні дослідження з розробки системи термостабілізації. Розглянуто особливості розробки та побудови систем автоматичного регулювання температури. Запропоновано реалізацію високоефективного регулятора температури