Hyperasymptotic expansions of confluent hypergeometric functions

Hyperasymptotic expansions were recently introduced by Berryand Howls, and yield refined information by expanding remaindersin asymptotic expansions. This paper gives a new method forobtaining hyperasymptotic expansions for integrals representingthe confluent hypergeometric U-function. At each level, theremainder is exponentially small compared with the previousremainders, and the number of new terms is increasing. Threenumerical illustrations confirm these exponential improvements.     

Certification of the sulphur content of three rapeseed reference materials

Summary The sulphur content of three rapeseed reference materials has been certified on the basis of measurements made by inductively coupled plasma-optical emission spectroscopy, isotope-dilution mass spectrometry and ion chromatography. Their suitability for the calibration of x-ray fluorescence spectrometers used for measuring sulphur in rapeseed samples was established.     

Weak antilocalization in a 2D electron gas with chiral splitting of the spectrum

Motivated by the recent observation of the metal-insulator transition in Si MOSFETs, a study is made of the quantum interference correction to the conductivity in the presence of the Bychkov-Rashba spin splitting. For a small splitting, a crossover from the localizing to antilocalizing regime is obtained. The antilocalization correction vanishes, however, in the limit of a large separation between the chiral branches. The relevance of the chiral splitting for the 2D electron gas in Si MOSFETs is discussed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 118–123 (25 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Estimation of the exchange constants in the Fe sublattice of the Y2Fe17 and Y2Fe17N3−δ compounds from the analysis of Mössbauer measurements

From the analysis of Mössbauer data for Y₂Fe₁₇ and Y₂Fe₁₇N_3−δ at various temperatures the hyperfine fields for 4f, 6g, 12j, 12k iron sites were estimated as a function of temperature. The reduced magnetizations calculated from the values of the hyperfine fields are fitted with a mean field model for four interacting sublattices using a computer program. The estimated exchange interaction from the fitting procedure between the 4f sites is found strongly negative (antiferromagnetic) in Y₂Fe₁₇ whereas in Y₂Fe₁₇N_3−δ it increases and becomes weak negative following a modified Slater-Néel curve. The rest of the exchange interactions are found positive or weak negative depending on the distances between the Fe atoms.     

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.