On weighted generalized functions associated with quadratic forms

In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with Bessel operator.Comment: 16 page

On fractional powers of the Bessel operator on a semiaxis

In this paper we study fractional powers of the Bessel differential operator defined on a semiaxis. Some important properties of such fractional powers of the Bessel differential operator are proved. They include connections with Legendre functions for kernel representations, fractional integral operators of Liouville and Saigo, Mellin transform and index laws. Possible applications are indicated to differential equations with fractional powers of the Bessel differential operator.Comment: English version (pp. 1--8) and Russian version (pp. 9--18

Fourier-Bessels transform of a generalized function Vanishing outside a bounded surface

The Fourier-Bessel transform of any generalized function f € S'ev vanishing outside a bounded surface for any test function ψ(х) €Se

Polarization reversal and jump-like domain wall motion in stoichiometric LiTaO 3 produced by vapor transport equilibration

The polarization reversal and domain structure evolution has been studied in stoichiometric lithium tantalate prepared by vapor transport equilibration process. The first in situ visualization of domain kinetics has demonstrated the jump-like motion of few strictly oriented plane domain walls, which leads to short isolated current pulses in the switching current data. The proposed model of jump-like domain wall motion caused by interaction with pinning centers representing the areas with increased value of the threshold field is based on the effect of retardation of bulk screening. The derived formulas were applied successfully for analysis of the field dependence of the total switching time. The durations of wall jumps and wall stays (rest times) extracted from the switching current data are analyzed separately. The deceleration of the wall motion velocity during jump is controlled by the trail of residual depolarization field produced by bound charges and screening charges in the area behind the wall. The duration of the rest time is governed by the bulk screening of residual depolarization field. The value of Hurst exponent 0.75 obtained by fractal analysis of the switching current data has confirmed the essential influence of prehistory on the domain wall motion. The measurements of the coercive field by switching in bipolar triangular pulses in wide range of the field ramp rate have allowed us to extract the record low value of coercive field 60 V/mm for quasi-static polarization reversal. © 2012 American Institute of Physics

On the Question of the Concept and Content of Tactical-Forensic Support of Crime Investigation

The article deals with the most urgent for forensic questions about the concept and content of the tactical-forensic support of the investigation, in order to determine the place of this doctrinal category in the conceptual apparatus of science. Different approaches to the definition of the concept are analyzed, the Author's definition is formulated; considered the ratio of the concepts of tactical and forensic software, forensic software, tactics of investigative actions. The conclusion is formulated about the content of the security function of the concept under study, which consists in developing recommendations relevant to the practice of investigating the selection of the most optimal and effective means of tactical and forensic support in various situations

Measurement of young's modulus and hardness of Al-50 wt % Sn alloy phases using nanoindentation

The nanoindentation method was used to measure the Young's modulus and hardness of the phases of the alloy Al-50 wt % Sn: α-aluminum and eutectic. Samples are obtained in different ways, i.e., traditionally via the transition of the melt into a homogeneous structural state by heating to a certain temperature, followed by cooling using the cooling rate greater by the order than that of the traditional method and via the addition of 0.06 wt % Ti and 1 wt % Zr to the binary alloy. It has been found that the most significant effect of the Al-50 wt % Sn phases on the Young's modulus is the transition of the melt into a homogeneous structural state and the introduction of Zr into the melt. As part of the mathematical theory of elasticity, a numerical evaluation of the interfacial pressure that arises due to the difference between Young's modulus of α aluminum and eutectic has been performed. The calculation has showed that the extra pressure is nine times less for the alloy formed through the transition of the melt into a homogeneous structural state than for the alloy produced via a traditional way. © 2013 Pleiades Publishing, Ltd