Light propagation in a weak gravitational field of a stochastic system of pointlike sources

Trajectories of light rays in a gravitational field created by a homogeneous distribution of pointlike masses are considered in the framework of General Relativity. A method of approximate computation of statistical characteristics of such trajectories is suggested, with the accuracy up to first order in the gravitational constant. The estimates of the shift in the direction of a light ray and of the change in the angular coordinates of the light source are obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 79–83, December, 1986.     

Analogs of purine nucleosides. 4. 7-Alkylated 9-(2-hydeoxymethyl)guanine

7,9-Disubstituted guaninium hydrohalides were synthesized by the reaction of 9- and 7-(2-hydroxymethyl)guanines with alkyl halides. The effect of the structure of the alkylating agent on the direction and yield of the alkylation reaction was established. The possibility of the conversion of the salts obtained to the free bases in a weakly alkaline medium was investigated. The synthesized compounds were characterized by the UV and ¹H and ¹³C NMR spectra. The ability of the synthesized compounds to inhibit replication of the herpes virus (VPG-1) was demonstrated.See [1] for Communication 3.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 641–646, May, 1989.     

Thermal radio emission of a homogeneous half-space with a rough boundary

Khar'kov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 8, pp. 927–932, August, 1989.     

On approximating periodic functions by singular integrals with positive kernels

In the two-dimensional case, new approximation characteristics for functions belonging to saturation classes of continuity modules for the spaces L_p of periodic functions are obtained. The problem of approximating a function by an analog of Fejér’s integral in the space of periodic functions square integrable on the period is considered. Bibliography: 5 titles. Dedicated to the 100th anniversary of G. M. Goluzin’s birthday __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 51–72.     

Modeling the thermomechanical behavior of physically nonlinear materials under monoharmonic loading

We analyze approximate approaches to the modeling of the thermomechanical behavior of physically nonlinear materials under harmonic loading. The approaches are based on various harmonic-linearization schemes and the concept of complex moduli. Mechanical and mathematical features of various schemes are considered. Some modifications of the model are proposed to account for various aspects of material behavior under harmonic loading. The problems of vibration and dissipative heating of physically nonlinear bodies are formulated. The main thermomechanical characteristics are analyzed for some classes of problems.The study was partially sponsored by the State Fund for Basic Research of the Ministry of Education and Science of Ukraine (Grant No. 01.07/00050).Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 3–34, September 2004.     

A four stages numerical pair with optimal phase and stability properties

In this paper we obtain, for the first time in the literature a new numerical pair. The properties of the new pair are:

1. 1.
   symmetric two-step algorithm,
    
2. 2.
   four-stages scheme,
    
3. 3.
   scheme of tenth-algebraic order,
    
4. 4.
   the approximations of the layers are taken place as follows: first and second layer on the point \(x_{n-1}\), third layer on the point \(x_{n}\), fourth layer on the point \(x_{n+1}\),
    
5. 5.
   the method has eliminated the phase-lag and its first derivative,
    
6. 6.
   excellent stability and interval of periodicity properties (i.e. interval of periodicity equal to \(\left( 0, \infty \right) \).
    

For this new numerical pair we present a detailed theoretical analysis. Finally, we prove the efficiency of the new scheme by applying it to the solution of systems of coupled Schrödinger equations.

     

Casimir effect at nonzero temperatures in a closed Friedmann Universe

For massive and massless scalar fields with an arbitrary coupling to gravity, we investigate finite-size (Casimir) effects on the free energy at nonzero temperatures in a slowly evolving closed Friedmann universe. The renormalized expressions for the free energy and the resulting energy density and pressure are found and their physical properties are discussed. The equation of state turns out to have the form P=/3 for radiation with arbitrary coupling.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 2, pp. 307–320, November, 1996.     

On -mappings between algebraic Cauchy-Riemann manifolds and separate algebraicity for holomorphic functions

We prove the algebraicity of smooth -mappings between algebraic Cauchy-Riemann manifolds. A generalization of separate algebraicity principle is established.