Diffusion approximation of normalized integrals of weakly dependent processes and its applications

We obtain exact estimates for the rate of convergence of normalized integrals of weakly dependent stationary processes to the standard Wiener process in the uniform metric in probability. These estimates are then applied to the investigation of the behavior of stochastic systems with curvilinear boundaries subjected to the action of weakly dependent random perturbations.Translated from Ukrainskii Matematicheskii Zhumal, Vol.46, No. 11, pp. 1449–1466, November, 1994.The present work was performed as a part of Project No. 8 of the Ministry of Education of the Ukraine. The manager of the project is Prof. N. A. Perestyuk.     

Derivation of quantum kinetic equation from the Liouville-von Neumann equation

A quantum Markov kinetic equation is derived from the Liouville—von Neumann equation in the framework of second-order kinetic perturbation theory. The proposed method can be used to obtain an equation that describes the quantum diffusion of a particle in a crystal.Moscow Aviation Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No.1, pp. 33–43, July, 1994.     

Special characteristics of the propagation of three-dimensional viscous jets

Numerical investigations were made of the propagation, in a supersonic wake, of uncalculated jets, flowing out of nozzles of square and rectangular cross section, and of lumped jets, made up of from two to nine individual jets; the special characteristics of their flow were investigated in the initial, transitional, and main sections. Specifically, for lumped jets, the possibility of replacing them by a single axisymmetric jet, equivalent in mass-flow rate, is discussed. To calculate a three-dimensional unexpanded supersonic jet, flowing out into a wake, in [1] it was proposed to use a numerical method for solving a simplified system of Navier-Stokes equations for steady-state flow, and numerical investigations were made of the three-dimensional interaction of four jets in a supersonic wake, at small distances from the outlet cross section of the nozzle, i.e., mainly in the initial sections of the jets, where the mixing layers along the boundaries of the jets are still not closed. Here the method of [1] is used to study the special characteristics of three-dimensional viscous jets at large distances from the outlet cross section of the nozzle in the region of the main section, where the mixing layers have come together and a single three-dimensional jet has been formed. The system of equations, the boundary conditions, the numerical method, the system of coordinates, and the nomenclature used are the same as in [1].     

Nonclassical critical indices in the statistical theory of liquids and equations of state with regular and scaling components

Nonclassical critical indices γ = 9/8 and β = 3/8 obtained in works using the statistical theory of liquids are used to approximate data on the isothermal compressibility of ⁴He and SF₆ on critical isochores and binodals, and on the shape of a binodal. The ratio of asymptotic compressibility coefficients Γ ₀ ⁺ /Γ ₀ ^? on critical isochores and binodals is determined from experiments using statistical theory and it is shown that Γ ₀ ⁺ /Γ ₀ ^? coincides with the magnitude of this ratio for linear scaling model with γ = 9/8 and β = 3/8 indices. Highly accurate P-ρ-T data on ⁴He and SF₆ are approximated at these values of the indices using new combined equations of state that include regular and scaling components. The advantage of describing of P-ρ-T data in this manner, compared to describing them with the same equations of state using the critical indices of the three-dimensional Ising model, is demonstrated.     

Estimates for the Rate of Convergence in Ordinary Differential Equations under the Action of Random Processes with Fast Time

We study the procedure of averaging in the Cauchy problem for an ordinary differential equation perturbed by a certain Markov ergodic process. We establish several estimates for the rate of convergence of solutions of the original problem to solutions of the averaged one. __________ Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 435–457, April, 2005.     

Photophysics ofβ-carotene and related compounds (review)

A review of data on the photophysics of carotenoids is presented. Results of investigations of spectroscopic, temporal, and energy parameters of excited S₁ and S₂ singlet states of β-carotene and related compounds are critically examined. These states give rise to extremely high probabilities (10¹¹–10¹³ sec⁻¹) of radiationless deactivation of the electronic excitation energy in carotenoids. Results of investigations of photophysical properties of triplet states of carotenoids are considered mainly from the standpoint of quenching of singlet oxygen and triplet states of organic molecules by carotenoids. Institute of Molecular and Atomic Physics, Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 5–19, January–February, 1997.     

New fluorene‐based copolymers containing oxadiazole pendant groups: Synthesis,characterization, and polymer stability

A series of fluorene‐based copolymers containing hole blocking/electron transporting diphenyloxadiazole units were synthesized by means of Suzuki‐Miyaura coupling of selected aromatic dibromo‐ and diboronato‐ derivatives catalyzed with a Pd(PPh₃)₄ catalyst. All of the copolymers with various composition of main‐chain units were characterized by SEC chromatography, NMR, UV–vis, fluorescence and IR spectroscopy, and DSC. The emission stability of fluorene copolymers was improved by the replacement of alkyl groups on the C‐9 carbon of fluorene with aryl groups or by the incorporation of anthracene units into the copolymer main chain. A comparison of luminescence properties of pristine and annealed thin layers of studied copolymers was performed. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4532–4546, 2009