Cauchy problem and averaging in Fock space

We investigate a Cauchy problem in the Fock space for a system consisting of a two-level atom, a quantum field, and a classical field. A solution estimate is obtained for the Cauchy problem with initial data from a special class. This class is invariant with respect to the dynamic semigroup of the system. We propose an averaging method for solving the Cauchy problem in the case where the Hamiltonian parameters differ greatly in the order of magnitude. An estimate of the averaging error is obtained. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 1, pp. 92–106, October, 1998.     

Synthesis of ω-amino- and ω-carboxyalkylamides of N-acetylmuramoyl-L-alanyl-D-isoglutamine

The synthesis has been effected of derivatives of MDP having a spacer with an amino or carboxy group. The final stage of the synthesis was the condensation of Boc-L-Ala-D-iGln with 6-aminohexanol (followed by the two-stage replacement of the hydroxy by an azido group) or with benzyl 6-aminohexanoate.Simferopol' State University. Translated from Khimiya Prirodnykh Soedinenii, No. 1, pp. 122–125, January–February, 1993.     

一种锰铜压阻测量新方法

 简单分析了几种常用的恒流供电锰铜压阻测量方法，并对这些测试方法的特点和不足进行了讨论。最后介绍一种利用数字示波器进行高保真高精度测量的方法，利用此法不仅提高了压力测量的精度，并且把小阻值锰铜压力计的测量范围向低端扩展到0.17 GPa。     

Thermal activation of complexation reaction on aerosil surface

The influence of temperature in the 20–100°C range on processes of bimolecular interaction in the aerosil-phenanthrene-trinitrobenzene system has been studied. Temperature-stimulated CTC accumulation on the surface is found. Activation energies of complex formation are estimated. Quenching of phenanthrene fluorescence by acceptor has a mixed static and dynamic character.     

小视角对颜色差别阀的影响

在均匀颜色空间的颜色差别计箅中,亮度和色彩的作用是相关且不同的,尤其是在目标尺度对人眼张角(亦称视角)小于30角度分的条件下观察,由于亮度差和色彩差受视角变化的影响程度不同步,使得人眼颜色差别分辨阈亦不确定。本文通过一定的试验和计算,探讨了在不同的亮度差和色彩差的情况下,颜色差别阈受视角影响的变化规律。     

Noncoercive Boundary Value Problems for Elliptic Partial Differential and Differential-Operator Equations

In this paper we find conditions guarantee that irregular boundary value problems for elliptic differential-operator equations of the second order in an interval are fredholm. We apply this result to find some algebraic conditions guarantee that irregular boundary value problems for elliptic partial differential equations of the second order in cylindrical domains are fredholm. Apparently this is the first paper where the regularity of an elliptic boundary value problem is not satisfied on a manifold of the dimension equal to dimension of the boundary. Nevertheless the problem is fredholm and the resolvent is compact. It is interesting to note that the considered boundary value problems for elliptic equations in a cylinder being with separating variables are noncoercive.     

Subthreshold ϕ-meson production and medium effects in proton-nucleus reactions

Within the spectral function approach, we study the direct production and decay via the dikaon (dimuon) channel of ϕ mesons in the interactions of 2.4-and 2.7-GeV protons with light and medium target nuclei. It is shown that the K ⁺ K ⁻ (μ⁺ μ⁻) invariant-mass distribution consists of the two components, which correspond to the ϕ decay “outside” and “inside” the target nucleus. The first (narrow) component has the free ϕ width, while the second (broad) component is distorted by the nuclear matter owing to resonance-nucleon scattering and a possible in-medium modification of the kaons and ρ meson at finite baryon density. The relative strength of the “inside” and “outside” components is analyzed in different scenarios for the ϕ width and momentum cut. It is demonstrated that the width of the resulting dimuon invariant-mass distribution on medium nuclei is larger than the free ϕ width by a factor of about 2 if the total ϕ in-medium width is used and the respective cutoff for the ϕ three-momentum is applied, whereas the resulting dikaon invariant-mass distribution has an insignificant sensitivity to the ϕ in-medium properties owing to the strong absorption of the K ⁻ in the surrounding nuclear matter. On the other hand, because of the distortion of the K ⁺ and K ⁻ on their way out of the target nucleus mainly due to the hadronic kaon potentials, the latter distribution is broadened and shifted to higher invariant masses, which means that the measurement of such broadening would give additional evidence for the modification of the kaon and antikaon properties in the nuclear medium. The text was submitted by the author in English.     

Monotonicity criteria for difference schemes designed for hyperbolic equations

Previously formulated monotonicity criteria for explicit two-level difference schemes designed for hyperbolic equations (S.K. Godunov’s, A. Harten’s (TVD schemes), characteristic criteria) are extended to multileveled, including implicit, stencils. The characteristic monotonicity criterion is used to develop a universal algorithm for constructing high-order accurate nonlinear monotone schemes (for an arbitrary form of the desired solution) based on their analysis in the space of grid functions. Several new fourth-to-third-order accurate monotone difference schemes on a compact three-level stencil and nonexpanding (three-point) stencils are proposed for an extended system, which ensures their monotonicity for both the desired function and its derivatives. The difference schemes are tested using the characteristic monotonicity criterion and are extended to systems of hyperbolic equations.