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.     

Resonance effects in a phased antenna array constructed from rectangular waveguides

Translated from Matematicheskie Modeli i Optimizatsiya Vychislitel'nykh Algoritmov, pp. 131–143, 1993.     

Single-molecule single crystals

Various approaches to the preparation and verification of single-molecule single crystals are discussed for polyethylene and poly (oxyethylene). Analytic tools are electron microscopy, electron diffraction, and differential scanning calorimetry. The main difficulty in producing a single-molecule single crystal is to keep crystals from joining during growth.     

Synthesis of 1-(3-alkyl-2,3-dideoxy-D-pentofuranosyl)uracils with potential anti-HIV activity.

1-(3-Alkyl-2,3-dideoxy-alpha,beta-D-erythro-pentofuranosyl)uracils and 1-(3-alkyl-2,3-dideoxy-alpha,beta-D-threo-pentofuranosyl)uracils have been prepared from (E)-4,5-di-O-acetyl-2,3-dideoxy-aldehydo-D-glycero-pent-2-enose by a Michael addition reaction of the appropriate organocopper reagent followed in subsequent order by glycosidation of the resulting 3-alkyl-4,5-diacetoxypentanal with methanolic hydrogen chloride, protection with p-methoxybenzoyl chloride, and trimethylsilyl triflate catalyzed coupling with 2,4-di-O-(trimethylsilyl)uracil. The nucleosides were deprotected by treatment with 33% methylamine in absolute ethanol and separated by reversed-phase HPLC.     

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     

A symmetry-adapted force-constant lattice-dynamical model for single-walled carbon nanotubes

We develop a lattice-dynamical model based on the screw symmetry of single-walled carbon nanotubes that allows for reducing the size of the dynamical matrix to six, for all tube chiralities. The model uses force constants derived from fitting to the phonon dispersion of 2D graphite. We present the calculation procedure in a clear and transparent way, making the model easier to follow. We calculate the phonon dispersions of a number of nanotubes of different chiralities. The splitting of two highest Raman active modes and the radial breathing mode frequency are studied by changing the tube diameter and chirality.     

Eulerian limit for 2D Navier-Stokes equation and damped/driven KdV equation as its model

We discuss the inviscid limits for the randomly forced 2D Navier-Stokes equation (NSE) and the damped/driven KdV equation. The former describes the space-periodic 2D turbulence in terms of a special class of solutions for the free Euler equation, and we view the latter as its model. We review and revise recent results on the inviscid limit for the perturbed KdV and use them to suggest a setup which could be used to make a next step in the study of the inviscid limit of 2D NSE. The proposed approach is based on an ergodic hypothesis for the flow of the 2D Euler equation on iso-integral surfaces. It invokes a Whitham equation for the 2D Navier-Stokes equation, written in terms of the ergodic measures. Dedicated to Vladimir Igorevich Arnold on his 70th birthday     

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.     

Synthesis and thermal behaviour of salicylaldimine-based liquid crystalline symmetrical dimers

A series of symmetrical dimers consisting of salicylaldimine moieties connected by flexible alkylene central spacer via ether linkages has been synthesized. In order to validate the empirical rule suggested by Date et al. to account for the smectic behaviour of such dimers, the chain length of the terminal alkoxy chain has been kept constant (C₈) while the number of methylene units in the central spacer was varied from C₃ to C₁₁. Another aim of the present investigation was to understand structure-property relationship in these dimers in which the salicylaldimine mesogenic segment has been used for the first time in dimers. The mesomorphic behaviour of these dimers was evaluated using optical microscopy and differential scanning calorimetry and the structure of some of the mesophases has been further investigated with the help of X-ray diffraction. Our studies reveal that the dimers consisting of 3 to 8 methylene units in the flexible spacer show only smectic (smectic C and smectic A) phases. For the dimers containing 4, 6 and 8 methylene units in the central spacer, a unique filament growth pattern has been observed in the smectic A phase while cooling from the isotropic phase. The dimers containing of C₉ to C₁₁ methylene groups exhibit the nematic phase in addition to smectic modifications. This observation indicates that when the terminal chains are shorter than the spacer, the tendency to form smectic phases is not fully extinguished but is perhaps reduced.