Spontaneous photorefractive effect in Sr1−x CaxTiO3 (x=0.014)

The temperature dependence of the principal values of the refractive index in Sr_1−x Ca_xTiO₃ (x=0.014) has been measured in the 17–275 K range under various conditions of sample illumination with 1.96 eV photons. The spontaneous photorefractive contribution δn ^ph to the temperature-induced variation of the refractive index of Sr_1−x Ca_xTiO₃, which appears after illumination of the sample in the ferrophase (transition temperature T _c=32 K) and persists in the paraphase under heating up to 150 K, has been separated. The photoinduced polarization has been estimated. Fiz. Tverd. Tela (St. Petersburg) 39, 711–713 (April 1997)     

Kinetic features of ethylene polymerization over supported catalysts [2,6‐bis(imino)pyridyl iron dichloride/magnesium dichloride] with AlR3 as an activator

The effects of polymerization temperature, polymerization time, ethylene and hydrogen concentration, and effect of comonomers (hexene‐1, propylene) on the activity of supported catalyst of composition LFeCl₂/MgCl₂‐Al(i‐Bu)₃ (L = 2,6‐bis[1‐(2,6‐dimethylphenylimino)ethyl] pyridyl) and polymer characteristics (molecular weight (MW), molecular‐weight distribution (MWD), molecular structure) have been studied. Effective activation energy of ethylene polymerization over LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a value typical of supported Ziegler–Natta catalysts (11.9 kcal/mol). The polymerization reaction is of the first order with respect to monomer at the ethylene concentration >0.2 mol/L. Addition of small amounts of hydrogen (9–17%) significantly increases the activity; however, further increase in hydrogen concentration decreases the activity. The IRS and DSC analysis of PE indicates that catalyst LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a very low copolymerizing ability toward propylene and hexene‐1. MW and MWD of PE produced over these catalysts depend on the polymerization time, ethylene and hexene‐1 concentration. The activation effect of hydrogen and other kinetic features of ethylene polymerization over supported catalysts based on the Fe (II) complexes are discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5057–5066, 2007     

Improved scales of spaces and elliptic boundary-value problems. III

We study elliptic boundary-value problems in improved scales of functional Hilbert spaces on smooth manifolds with boundary. The isotropic Hörmander-Volevich-Paneyakh spaces are elements of these scales. The local smoothness of a solution of an elliptic problem in an improved scale is investigated. We establish a sufficient condition under which this solution is classical. Elliptic boundary-value problems with parameter are also studied.     

Some results of the local theory of smooth functions

We present results of the investigation of the local behavior of smooth functions in neighborhoods of their regular and critical points and prove theorems on the mean values of the functions considered similar to the Lagrange finite-increments theorem. We also study the symmetry of the derivative of an analytic function in the neighborhood of its multiple zero, prove new statements of the Weierstrass preparation theorem related to the critical point of a smooth function with finite smoothness, determine a nongradient vector field of a function in the neighborhood of its critical point, and consider one critical case of stability of an equilibrium position of a nonlinear system. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 2, pp. 231–267, February, 2007.     

On the weakened Siegel’s conjecture

In the paper, we prove that two definitions of E-functions present in mathematics are equivalent if E-functions satisfy second-order linear differential equations. For this set of functions, a weakened variant of the well-known Siegel conjecture about representability of any E-function by a polynomial of hypergeometric functions is also proved. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 33–39, 2005.     

Moving and oscillating transversely one-dimensional laser solitons

Transversely one-dimensional moving and oscillating solitons in a wide-aperture laser with saturable absorber with fast (inertialess) nonlinearity are found by numerical simulation. The regions of existence of such solitons and of their complexes are presented.     

Regularities of the interaction of hydrogen jets during combustion in a supersonic high-temperature flow

The efficiency of combustion in a supersonic high-temperature flow at spread and local hydrogen feed is considered. Similarities and distinctions of combustion in open and confined space were examined with consideration given to the effect of gasdynamic structures typical of supersonic air jets.     

Photothermal techniques applied to the determination of the water vapor diffusion coefficient and thermal diffusivity of edible films.

Water vapor diffusion coefficient (WVDC) and thermal diffusivity (alpha) were determined in gelatin-starch films through photothermal techniques. The effect of different variables in the elaboration of these films, such as starch and glycerol concentrations and pH, were evaluated through the response surface methodology. The results indicated that an increase in the glycerol concentration and pH favored the WVDC of the films. On the other hand, alpha was influenced principally by the starch content and pH of the film-forming solution. The minimum alpha value was 4.5 x 10(-4) cm2/s, which is compared with alpha values reported for commercial synthetic polymers.     

Entanglement of qutrits

For two types of qutrits specified by the dynamical symmetry SU(3) and SU(2), we consider the difference in entanglement caused by the lack of quantum observables in the latter case. In particular, we show that the SU(2) qutrits can have specific separable entanglement caused by quantum correlations of intrinsic degrees of freedom in a single party without interparty correlations.     

Areal objects and the problem of the λ term in the theory of gravitation

The following areal objects are considered: an ether thread contracting two material points and a multidimensional ether fibre in the pseudo-Euclidean world of events. An ether space-time model with an arbitrarily determined Riemannian metric is constructed and the problem of the λ term in Einstein equations is discussed in this regard.