Experimental and theoretical study of the line depolarizations and absolute intensities in the Raman spectra of multiatomic molecules IX. Acetyl bromide and acetyl bromide-d3

The absolute intensities of the lines in the Raman spectrum of the acetyl bromide spectrum were measured, and the system of electrooptical parameters was obtained. The electrooptical parameters of the acetyl chloride molecule can be used in the calculation for acetyl bromide.Translated from Izvestiya VUZ. Fizika, No. 4, pp. 56–61, April, 1970.     

Structures and orientational transitions in thin smectic films of tilted hexatic

We present detailed systematic studies of structural transformations in thin liquid crystal films with the transition from the smectic-C (SmC) to hexatic (HSmB) phase. For the first time, all possible structures reported in the literature are observed for one material (5O.6) with varying temperature and thickness. In unusual modulated structures, the equilibrium period of stripes is twice the domain size. We interpret these patterns in the framework of a phenomenological Landau-type theory, as equilibrium phenomena produced by a natural geometric frustration in a system having spontaneous splay distortion. The text was submitted by the authors in English.     

Base pair dynamic assisted charge transport in DNA

A one-dimensional model with time-dependent random hopping is proposed to describe charge transport in DNA. It permits the investigation of both diffusion of electrons and their tunneling between different sites in DNA. The tunneling appears to be strongly temperature-dependent. Observations of a strong (exponential) as well as a weak distance dependence of the charge transfer in DNA can be explained in the framework of our model.     

Photooxidation of alkylbenzenes and cyclohexane by atmospheric oxygen in acetonitrile sensitized by o-phenanthroline

Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, p. 2653, November, 1988.     

One-dimensional displacement of petroleum by aqueous solutions of sorption agents taking account of interlayer return flows

Experimental and theoretical investigations of the process of the displacement of petroleum by aqueous solutions of surface-active substances (surfactants), polymers, micelle solutions, and their combinations show that sorption phenomena can exert a considerable effect on the process of flooding [1, 2]. In some cases, they can lead to an appreciable lag of the front of the dissolved substance behind the carrier liquid and to the appearance of a second jump in the saturation of the displacing liquid [1, 3]. In [4] a mathematical model is proposed for the displacement of petroleum from a laminar stratum with isolated intercalculations of aqueous solutions of surfactants and polymers, taking account of sorption phenomena. In the present article, a study is made of the displacement of petroleum from a stratum by aqueous solutions of sorption agents, taking account of interlayer return flows of liquids.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 38–45, March–April, 1977.     

On the generation of solitons and breathers in the modified Korteweg-de Vries equation

We consider the evolution of an initial disturbance described by the modified Korteweg-de Vries equation with a positive coefficient of the cubic nonlinear term, so that it can support solitons. Our primary aim is to determine the circumstances which can lead to the formation of solitons and/or breathers. We use the associated scattering problem and determine the discrete spectrum, where real eigenvalues describe solitons and complex eigenvalues describe breathers. For analytical convenience we consider various piecewise-constant initial conditions. We show how complex eigenvalues may be generated by bifurcation from either the real axis, or the imaginary axis; in the former case the bifurcation occurs as the unfolding of a double real eigenvalue. A bifurcation from the real axis describes the transition of a soliton pair with opposite polarities into a breather, while the bifurcation from the imaginary axis describes the generation of a breather from the continuous spectrum. Within the class of initial conditions we consider, a disturbance of one polarity, either positive or negative, will only generate solitons, and the number of solitons depends on the total mass. On the other hand, an initial disturbance with both polarities and very small mass will favor the generation of breathers, and the number of breathers then depends on the total energy. Direct numerical simulations of the modified Korteweg-de Vries equation confirms the analytical results, and show in detail the formation of solitons, breathers, and quasistationary coupled soliton pairs. Being based on spectral theory, our analytical results apply to the entire hierarchy of evolution equations connected with the same eigenvalue problem. (c) 2000 American Institute of Physics.     

Some Generalizations of the Notion of Length

Two numerical characteristics of a nonrectifiable arc generalizing the notion of length are introduced. Geometrically, this notion can naturally be generalized as the least upper bound of the sums , where are the lengths of segments of a polygonal line inscribed in the curve and is a given function. On the other hand, the length of is the norm of the functional in the space ; its norms in other spaces can be considered as analytical generalizations of length. In this paper, we establish conditions under which the generalized geometric rectifiability of a curve implies its generalized analytic rectifiability.