Supports of Measure Solutions for Spatially Homogeneous Boltzmann Equations

We prove that the support of the unique measure solution for the spatially homoge-neous Boltzmann equation in R3 is the whole space, if the initial distribution is not a Dirac measure and has 4-order moment. More precisely, we obtain the lower bound of exponential type for the probability of any small ball in ℝ³ relative to the measure solution.     

Diamond Structure BeO, Designable Super-Hard Materials and Semiconductor Be-Diamond

It is possible for Beryllium oxide （BeO） to have a cubic diamond structure although it normally has a hexagonal structure under ambient conditions. As the solution of cubic BN and diamond, the solid solution of cubic BeO- diamond or BeO-cBN-diamond can potentially be a kind of super-hard materials with designable hardness; and this solution has also been confirmed based on our preliminary first principles calculations. In addition, the nonstoichiometry of BeO could create a mobile carrier in the cubic BeO-C or BeO BN-C system and it might lead to a new type of semiconductor Be-diamond.     

Solutions of the Lévy type for the free vibration analysis of diagonally supported rectangular plates

A Lévy type solution is developed for the vibratory response of a simply supported rectangular plate subjected to a harmonic force distributed along the diagonal. The solution is then extended to determine the free vibration response of the same rectangular plate with inelastic lateral support on the diagonal. It is found that there is an excellent agreement between computed eigenvalues obtained here and those obtained by the author in an earlier paper in which a Navier type solution was utilized. The significant advantages inherent in the present Lévy type solution are discussed.     

Exact Solutions for Shear-free Motion of Spherically Symmetric Charged Perfect Fluid Distributions in General Relativity

An in-depth study of various methods, and their correlations, of obtaining exact solutions of Einstein-Maxwell field equations representing shear free motion of spherically symmetric charged perfect fluid distributions has been made. It is shown that one can employ isotropic coordinate systems without any loss of generality. However the investigations have been carried out in an arbitrary coordinate system. The exact solutions relating to simple situations viz. (i) homogeneous density distribution, ϱ=ϱ(t), (ii) conformally flat solutions and (iii) distributions obeying an equation of state, p=p(ϱ) are briefly discussed. The methods due to MCVITTIE (1967), introduced initially for neutral fluids, and MASHHON and PARTOVI (1979) where one assumes the metric in a convenient form form one group and the methods due to SHAH and VAIDYA (1968), CHAKRAVARTY and CHATTERJEE (1978), CHATTERJEE (1984) and SUSSMAN (1987) where one chooses suitably two arbitrary functions of integration form the other group. This splitting of various methods into two is based on the earlier analogous work for the neutral fluids due to SRIVASTAVA (1987). Using McVittie's procedure we obtain a solution which in its uncharged limit reduces to Friedmann-Robertson-Walker solution whereas for non-vanishing charge is equivalent to the solution due to SHAH and VAIDYA (1967). This solution is termed as generalised Shah-Vaidya solution or charged Friedmann-Robertson-Walker solution. A suitable generalisation of Mashhoon and Partovi's procedure has been found to contain MASHHOON-PARTOVI solution (1979) and SHAH-VAIDYA solution (1967) as members of a class. The method employed by CHATTERJEE (1978), which does not yield the general solution of the problem, has been shown to lead to the procedure adopted by SUSSMAN (1987) after it is generalised suitably. The McVittie type and Wyman type solutions introduced by Sussman has been found to be contained in McV class of metries discussed here. It is also found that solutions obtained by CHAKRAVARTY and CHATTERJEE (1978) represent a class of charged Kustaanheimo-Qvist solution which are expressible as elementary functions. Finally, all known solutions have been derived introducing an adhoc assumption in the form of a mathematical relation and searching for the solutions free from movable critical points.     

Isolators based on surface waves of Hno type in a rectangular waveguide containing a transversely magnetized ferrite

A solution is presented for propagation of H_no waves in a rectangular waveguide containing a transversely magnetized ferrite plate on one of the sides; the equation for the propagation constant has been solved numerically. Waves of surface type are found to accompany the waveguide type under certain conditions; the calculations define the conditions for these to occur and those for unidirectional propagation. This latter feature in the surface waves is used to design an isolator based on field bias.     

Some exact solutions of F(R) gravity with charged (a)dS black hole interpretation

In this paper we obtain topological static solutions of some kind of pure F(R) gravity. The present solutions are two kind: first type is uncharged solution which corresponds with the topological (a)dS Schwarzschild solution and second type has electric charge and is equivalent to the Einstein-Λ-conformally invariant Maxwell solution. In other word, starting from pure gravity leads to (charged) Einstein-Λ solutions which we interpreted them as (charged) (a)dS black hole solutions of pure F(R) gravity. Calculating the Ricci and Kreschmann scalars show that there is a curvature singularity at r = 0. We should note that the Kreschmann scalar of charged solutions goes to infinity as r → 0, but with a rate slower than that of uncharged solutions.     

WANDs of the black ring

Necessary conditions for various algebraic types of the Weyl tensor in higher dimensions are determined. These conditions are then used to find Weyl aligned null directions for the black ring solution. It is shown that the black ring solution is algebraically special, of type I_i, while locally on the horizon the type is II. One exceptional subclass – the Myers-Perry solution – is of type D.     

On the Steklov-Type Biharmonic Problem in Unbounded Domains

We study the unique solvability of the Steklov–type biharmonic problem in unbounded domains under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight |x| ^a . Depending on the value of the parameter a, we prove uniqueness theorems or present exact formulas for the dimension of the solution space of the Steklov–type biharmonic problem in the exterior of a compact set and in a half-space.     

Spherically Symmetric Solutions of Light Galileon

We have been studied the model of light Galileon with translational shift symmetry ? → ? + c. The matter Lagrangian is presented in the form \(\mathcal {L}_{\phi }= -\eta (\partial \phi )^{2}+\beta G^{\mu \nu }\partial _{\mu }\phi \partial _{\nu }\phi \). We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of \(f(R,R^{\mu \nu }T_{\mu \nu }^{m})\). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon’s field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ? = t, which it is remembered by us dilaton field.     

Long-range order in a polycrystalline Pd-30 at % Au solid solution

Using x-ray analysis, at % the existence of regions with a long-range order of the Cu₃Au type has been established in a polycrystalline Pd-30 at % Au solid solution.     

STEADY SOLUTIONS OF THE OPTICAL SOLITON EQUATION WITH A NONLINEAR RESPONSE DELAY TERM

The exact solution of the optical soliton equation with a nonlinear response delay term has been obtained by using the method of separating variables. The new type of optical solitary wave solution, which is quite different from the bright and dark soliton solutions, has been found for a special case.     

Gravitational field of a radiating rotating body

A nonstationary solution of the Einstein field equations, corresponding to the field of a radiating rotating body, is presented. The solution is algebraically special of Petrov type II with a twisting, shear-free, null congruence identical to that of the Kerr metric. The new metric bears the same relation to the Kerr metric as does Vaidya's metric to the Schwarzschild metric, in the sense that in both cases the radiating solution is generated from the nonradiating one by replacing the mass parameter by an arbitrary function of a retarded time coordinate. The energy-momentum tensor in the present case, however, has two terms, a Vaidya type radiative one and an additional nonradiative residual term. Due to the presence of the nonradiative term in this case, however, the energy-momentum tensor becomes Vaidya-like asymptotically only, thus allowing for a geometrical optics interpretation. Asymptotically, part of the radiation field is purely electromagnetic with a Maxwell tensor which admits only one principal null direction corresponding to the undirectional flow of radiation.     

Effect of the ultrasonic emitter on the distortion performance of the parametric array loudspeaker

The parametric array loudspeaker (PAL) is a type of directional loudspeaker that utilizes the nonlinear acoustic effect to create the audible sound in an ultrasonic beam. Due to this unusual sound principle, it is inevitable that nonlinear distortion is incurred in the sound transmission of the PAL. Numerous modulation methods aiming to reduce the nonlinear distortion have been developed on the basis of the Berktay’s far-field solution, but they often perform in an unexpected manner. The degraded practical performance has been credited to the inaccuracy of the Berktay’s far-field solution. In this paper, we demonstrate the effect of the ultrasonic emitter on the distortion performance of the PAL and suggest that the Berktay’s far-field solution remains to be a good model equation.     

A Solution of Weyl-Lanczos Equations for Arbitrary Petrov Type D Vacuum Spacetimes

A Lanczos potential for an arbitrary Petrov type D vacuum spacetimes, using the compacted spin coefficient formalism (or GHP-formalism), has been obtained; which in turn leads to a solution of Weyl-Lanczos equations.     

ANALYTICAL SOLUTION OF THE 2n-DIMENSIONAL FOKKER-PLANCK EQUATION WITH HARMONIC OSCILLATOR POTENTIAL

An analytical solution is obtained for the 2n-dimensiona Fokker-Planck equation (F-P equation for short) with the harmonic oscillator potential. A few steps are involved in the derivation. First,the Lagrangian subsidiary equation is solved; then with its integral constants as new variables of the F-P equation, the diffusion equation is obtained and solved; at last, expressed in the original phase space, the solution of the F-P equation .is finally obtained. The analysis for the solution is made. The solution is a Gaussian type function and a δ-function of time. If a particle moves in a well in ali directions, then as t→∞, the distribution function can reach a stationary nonzero distribution-Maxuwell-Boltzmann type distribution (M-B distribution for short).As an example, the 2-dimensional F-P equation is solved and discussed in detail.     

离子液体中聚氧化乙烯(PEO)相变过程中的氢键效应

我们把Flory-Huggins模型推广应用到聚合物/离子液体体系,研究聚氧化乙烯(PEO)在离子液体[EMIM][BF_4]中相变过程中的氢键效应,理论模型考虑了三种类型氢键(Ⅰ型:PEO-[EMIM]~+氢键,Ⅱ型:PEO-[BF_4]~-氢键和Ⅲ型:[EMIM]~+-[BF_4]~-氢键)的形成,分析了三种类型的氢键分数随温度、 PEO体积分数的变化.研究发现,三种类型的氢键分数随温度的升高而减少.在较小PEO体积分数条件下,增加PEO体积分数,Ⅰ型、Ⅱ型氢键分数轻微地减小;在较大PEO体积分数条件下,增加PEO体积分数,Ⅰ型、Ⅱ型氢键分数急剧减少.Ⅲ型氢键分数随着PEO体积分数的增加而急剧降低.由于三种氢键效应,第二维里系数A_2随温度的增加而减小.通过计算分析不同分子量的PEO在[EMIM][BF_4]中的相图发现,在PEO体积分数较低的条件下,Ⅰ型、Ⅱ型和Ⅲ型氢键是PEO相变的主要驱动力;在PEO体积分数较高的条件下,Ⅰ型和Ⅱ型氢键在PEO相变过程中起到主导作用.     

Zu Abrikosovs Theorie der periodischen Lösungen der GL-Gleichungen für Supraleiter 2. Art

Abrikosov's method to get periodic solutions of the GL-equations for superconductors of type II is reformulated in order to make higher approximations possible. It is shown that instead of the external magnetic field, the average field in the superconductor must be used as fixed quantity in the approximations; then the method can be extended to a general iteration procedure with a fixed period-parallelogram for the solution. In the first approximation every periodic solution is given by a simple product of ?-functions; among those solutions which possess one flux quantum per period-parallelogram only, the hexagonal modification has the lowest free energy as already proposed byKleiner et al.     

Subdiffusion and stable laws

This paper examines particle diffusion in N-dimensional Euclidean space with traps of the return type. Under the assumption that the random continuous-diffusion time has a finite mean value, it is established that subdiffusion (which is characterized by an increase in the width of the diffusion packet with time according to the t ^α -law, where α<1; for normal diffusion α=1) emerges if and only if the distribution density of the random time a particle spends in a trap has a tail of the power-law type ∝t ^α−1. In these conditions the asymptotic expression for the distribution density of a diffusing particle is found in terms of the density of a one-sided stable law with a characteristic exponent α. It is shown that the density is a solution of subdiffusion equations in fractional derivatives. The physical meaning of the solution is discussed, and so are the properties of the solution and its relation to the results of other researchers in the field of anomalous-diffusion theory. Finally, the results of numerical calculations are discussed. Zh. éksp. Teor. Fiz. 115, 2113–2132 (June 1999)     

Computational (MP2 and DFT) modeling of the substrate/inhibitor interaction with the LDH active pocket in the gas phase and aqueous solution: bimolecular charged (pyruvate/oxamate–guanidinium cation) and neutral adducts (pyruvic/oxamic acids–guanidine)

Two types of bimolecular adducts were studied for the substrate and inhibitor of lactate dehydrogenase (LDH), one type of adducts between ionic species, α‐keto‐carboxylates (pyruvate and oxamate) and the guanidinium cation, and the other type of adducts between neutral species, α‐ketocarboxylic (pyruvic and oxamic) acids and guanidine. Calculations were performed in the gas phase and aqueous solution using the MP2 and PCM methods and the 6‐31++G** basis set. Application of the DFT(B3LYP) and PCM methods led to similar results. A change of the adducts' preference was observed when proceeding from the gas phase to aqueous solution. This change is in good agreement with the acidity–basicity scales in both phases. Formation constant (K_HB) for adduct between neutral species is greater for pyruvic than for oxamic acid in the gas phase, whereas a reverse situation takes place in aqueous solution, where the K_HB value for adduct between ionic species is smaller for pyruvate than for oxamate. The water molecules favor interactions of more polar oxamate with the guanidinium cation. Stronger interaction with this cation, a model of the arginine fragment of the LDH pocket, suggests that oxamate (inhibitor of LDH) has stronger binding properties in aqueous solution than pyruvate (substrate of LDH). Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical method for problems of diffraction on semi-infinite structures

We propose a method which transforms homogeneous integral equations into inhomogeneous ones for problems of diffraction by semi-infinite structures. New integral equations and the corresponding stationary functionals dependent on the desired scattering parameters are obtained. The consideration is performed for the open-end diffraction problem of a parallel-plate waveguide which has a rigorous solution, but the method has sufficient generality to use it for two-dimensional surface integral equations describing planar and nonplanar structures as well as for an arbitrary structure of waveguide transformer type, the solution for which can be sought in the finite domain. The method is based on field representation at the infinity as incident and scattered waves. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 3, pp. 235–245, March 2006.