Thermodynamic functions of the mixing of methacrylic acid in organic solvents

The saturated vapor pressure over solutions of methacrylic acid is measured tensimetrically in acetonitrile, benzene, hexane, 1,2-dichloroethane, and acetic acid is measured tensimetrically at 290–350 K. The composition of equilibrium phases, the activity coefficients of the components, and the thermodynamic functions of the mixing (H ^E , G ^E , S ^E ) of the investigated solutions are calculated from the temperature dependence data.     

The propagation of nonlinear waves in a bidisperse fluidized bed

A study is made of the propagation of nonlinear kinematic waves of concentrations of solid particles in a fluidized bed of particles of two different sizes. A hyperbolic system of quasilinear equations is obtained which describes the propagation of the waves. A dependence of the characteristic velocities on the concentrations of the phases and the ratio of the sizes of the particles is found. The influence of an admixture of fine particles on the propagation of porosity waves in the fluidized bed is analyzed. The nature of the formation of jumps in the porosity depending on the concentration of the admixture is studied, as is the process of the transfer of the admixture of fine particles in the bed. The nature of the propagation of nonlinear waves in a fluidized bed of identical particles is clarified. A characteristic velocity is found and conditions are determined for the formation of discontinuities of concentration of the dispserse phase in rarefaction compression waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 49–58, January–February, 1985.     

On the complexity of linear boolean operators with thin matrices

Under consideration is the problem of constructing a square Booleanmatrix A of order n without “rectangles” (it is a matrix whose every submatrix of the elements that are in any two rows and two columns does not consist of 1s). A linear transformation modulo two defined by A has complexity o(ν(A) − n) in the base {⊕}, where ν(A) is the weight of A, i.e., the number of 1s (the matrices without rectangles are called thin). Two constructions for solving this problem are given. In the first construction, n = p ² where p is an odd prime. The corresponding matrix H _p has weight p ³ and generates the linear transformation of complexity O(p ² log p log log p). In the second construction, the matrix has weight nk where k is the cardinality of a Sidon set in ℤ _n . We may assume that

Analysis of branched oligophenylene by absorption and fluorescence spectra

A branched oligophenylene has been synthesized based on 1,3,5-tri(4′-bromophenyl)benzene. Absorption and fluorescence spectra were studied and fluorescence quantum yields and lifetimes were measured for the compound in solution. It is demonstrated that the absorption spectrum is a superposition of p-quaterphenyl, p-terphenyl, and biphenyl chromophore absorption bands in a 1:2:1 ratio. The oligomer fluorescence spectrum is found to depend on the excitation wavelength. It is shown that the oligomer fluorescence is determined by two fluorochromic groups, namely fragments with branched p-terphenyl and p-quaterphenyl units. The main fluorescence maxima for these fluorochromic groups coincide with each other and lie in the vicinity of λ = 360 nm. A very weak fluorescence band found in the region 380–440 nm is excited by light with a wavelength lying beyond the oligomer self-absorption region. The reasons for a decrease in fluorescence quantum yields of branched models and the studied oligophenylene as compared with those of linear p-polyphenylene chromophores are discussed.     

Fluorescent branched oligomers with polyphenyl and fluorenyl units

Absorption spectra and fluorescence parameters (spectra, quantum yields, and lifetimes) were obtained for a number of branched oligophenylenes (OPh) with long-wavelength chromophores such as p-quaterphenyl (OPh4-2), p-pentaphenyl (OPh5), and p-hexaphenyl (OPh6) and for oligofluorenylphenylenes (OFl) in solutions and films. It is demonstrated that the absorption spectrum of OPh4-2 is a superposition of p-quaterphenyl, p-terphenyl, and diphenyl absorption bands taken in a ∼3:2:2 ratio. The obtained OPh5 and OPh6 absorption and fluorescence spectra are shown to be determined mainly by the longest-wavelength chromophores, p-pentaphenyl and p-hexaphenyl, respectively. It is demonstrated that the obtained compounds contain traces of impurities with fluorescence at longer wavelengths than that of the base material. The branched oligomers exhibit high fluorescence quantum yields in solutions, those for OPh5 and OPh6 reaching 1. Transparent fluorescent films were produced from all of the synthesized oligomers.     

Turnability characteristics of solutions of differential systems

For each solution of a differential system, we define a set of turnability exponents of various ranks, which are obtained by minimization and time averaging of the number of zeros and various projections of the angular velocity of the solution onto subspaces of fixed dimensions. We obtain a number of properties of the introduced exponents and relations between them. We show that, in the case of an autonomous system, they are closely related to the absolute values of the imaginary parts of eigenvalues of the operator of the system.     

Auxiliary transfer matrices for three-dimensional integrable models

We formulate the local combinatorial method for constructing the complete set of operators that commute with the transfer matrix of the Zamolodchikov-Bazhanov-Baxter model in the vertex formulation. We find the compact functional equation satisfied by the generating functional of this complete set of operators. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 3, pp. 391–409, September, 2000.     

Complexity of computation in finite fields

We give a review of some works on the complexity of implementation of arithmetic operations in finite fields by Boolean circuits.     

A three-dimensional quantum integrable mapping

We derive a three-dimensional integrable mapping that gives the R-matrix of the Zamolodchikov model in the cyclic representation limit. We construct the discrete-time evolution generated by this mapping and derive a generating function for the integrals of motion. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 3, pp. 479–487, March, 1999.     

Coefficient Matrices of a Quantum Discrete Auxiliary Linear Problem

In the present paper, we describe general properties of quantum matrices that are coefficient matrices of an auxiliary problem for quantum discrete three-dimensional integrable models. Our goal is to prove a universal functional equation for the quantum determinant in the case of a finite-dimensional representation of a local Weyl algebra. Bibliography: 4 titles.