Hopf equation in random force fields of arbitrary distribution

An equation is obtained in variational derivatives over the external fields for the space-time functional of the velocity field with an arbitrary distribution of the random fields. Equations are obtained for the moments and response functions. The exact operator solution of these equations is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 77–82, February, 1977.The author would like to express his thanks to L. Ya. Kobelev for helpful discussions.     

Reason for Different Solubility of Alkali Metal Chlorides in Cadmium Nitrate Solution

An idea that concentrated solutions of salts forming several crystal hydrates can be considered as systems of mixed solvents was developed within the framework of a phenomenological model of solution structure for the systems Cd(NO3)2-MCl-H2O (M = Li, Na, K, Cs). It was supposed that LiCl and CsCl preferentially interact with a solvent like Cd(NO₃)₂ nanohydrate, whereas NaCl and KCl, with a solvent like Cd(NO₃)₂ tetrahydrate.     

Nonself-Adjoint Operators with Almost Hermitian Spectrum: Weak Annihilators

We consider nonself-adjoint nondissipative trace class additive perturbations L=A+iV of a bounded self-adjoint operator A in a Hilbert space ,H. The main goal is to study the properties of the singular spectral subspace N _i ⁰ of L corresponding to part of the real singular spectrum and playing a special role in spectral theory of nonself-adjoint nondissipative operators.To some extent, the properties of N _i ⁰ resemble those of the singular spectral subspace of a self-adjoint operator. Namely, we prove that L and the adjoint operator ,L ^* are weakly annihilated by some scalar bounded outer analytic functions if and only if both of them satisfy the condition N _i ⁰ =H. This is a generalization of the well-known Cayley identity to nonself-adjoint operators of the above-mentioned class.     

Structural and electrophysical aspects of phenolphthalein coloration in plastic deformation under high pressure

The influence exerted on the process of phenolphthalein coloration by the electrophysical conditions under which its pressure treatment is carried out was studied.     

Algorithms for evaluating basic components of spectral functions of interference wave fields

Simple algorithms for finding a numerical solution on a complex plane of dispersion equations dependent on a real parameter are described. Algorithms for numerical integration along stationary contours on a complex plane in the case where the integrand possesses singularities of the pole and branch-point type are also presented. These algorithms are applied to compute the spectral functions of wave fields propagating in layered media. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 214, 1994, pp. 187–199. Translated by N. S. Zabavnikova.