Highly ordered hexatic phases with large spontaneous polarization

In this article the physical properties of hexatic phases of three substances MHPNBC, FOOPP and FNHPP have been studied by differential scanning calorimetry, texture observation and dielectric spectroscopy. Experimental results are discussed from the point of view of existing theories. It is interesting that two of the substances studied, the FOOPP and FNHPP, exhibit enhanced spontaneous polarization in the highly ordered SmI* phase and show a jump of the spontaneous polarization in the vicinity of the SmC*–SmI* transition. In the SmI* phase of FOOPP a very high value of spontaneous polarization of the order of 530?nC?cm^?2 was found. Based on the results obtained the macroscopic and microscopic properties of the hexatic phases are discussed.     

Triple solutions for a nonlocal functional boundary value problem by leggett–williams theorem

The existence of triple solutions for a second-order nonlocal functional boundary value problem is proved by using a fixed-point theorem on cones in Banach spaces due to Leggett and Williams. The obtained results are new even in the ordinary case for three-point boundary value problems discussed quite recently in [Xiaoming He and Weigao Ge (2002). Triple solutions for second-order three-point boundary value problems. J. Math. Anal. Appl., 268, 256–265].     

A note on Keldysh's perturbation formalism

The expansion theorem of quantum field theoy relating Heisenberg operators to asymptotic free-field operators is rewritten by means of the time-path technique, originally due to Schwinger, which to date has only found application in statistical mechanics. The theorem is combined with Bogoliubov's initial condition of vanishing correlations in the infinite past to rederive Keldysh's perturbation scheme for non-equilibrium statistical Green's functions.     

Ion equilibria in THF solutions of models of “living” methacrylonitrile oligomers with Li+ counterion

The electro-chemical characteristics of isobutyronitrile lithium (P₁Li) and 2-lithio-4-cyano-2,4-dimethylpentanenitrile (P₂Li) are studied. The dissociation constants K of P₁Li and P₂Li are of the order of 10^?11M and show that in THF mainly contact ion pairs exist. The lower value of K for P²Li is an indication for intramolecular complexation between the counterion and the cyano group, next to the active center. Both compounds tend to form ion triples. The results obtained show that in THF the nitrile group of the second monomer unit participates both in intra- and intermolecular interactions with the counterion.     

Feedback Grid Generation via Monotone Discretization for Two-point Boundary-Value Problems

We describe a uniformly enclosing discretization technique formildly nonlinear boundary-value problems. This method allowsus to derive a grid generation principle, using the distancebetween the lower and upper solutions to control the grid-generationprocedure. The convergence of the proposed feedback gridgenerationmethod is proved.     

Analyse multielementaire instrumentale des phosphates marocains par photoactivation nucleaire

Photonuclear activation and high resolution gamma-ray spectrometry have been used to determine non-destructively the concentrations of 25 trace elements in Maroccan phosphate rock. The activation was simultaneously performed for phosphate samples and multielement standards in the bremsstrahlung beam of a linear electron accelerator at 18 and 30 MeV maximum energies. Gamma-ray spectra were recorded with a 79 cm³ Ge(Li) detector and a programmable analyzer IN 96. A detailed study of interferences was carried out. Limits of detection between 0.5 and 125 μg·g^?1 were obtained.     

Growth morphology of zinc tris(thiourea) sulphate crystals

The growth morphology of crystals of zinc tris(thiourea) sulphate (ZTS) is investigated experimentally, and computed using the Hartman-Perdok approach. Attachment energies of the observed habit faces are calculated for determining their relative morphological importance. A computer code is developed for carrying out these calculations. A special procedure is adopted for computing the cohesive energy of a slice of the structure parallel to any rational crystallographic plane. For estimating the cohesive energies, formal charges on the experimentally determined atomic positions in the molecules of ZTS are calculated by ab initio molecular-orbital computations, with wave functions obtained by the Hartree-Fock procedure. Fairly good agreement with the observed crystal morphology is obtained for a model of growth mechanism in which ZTS is assumed to exist in solution sa szinc tris(thiourea) ions and sulphate ions.     

Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the First Kind

Fractional powers of linear multistep methods are suggestedfor the numerical solution of weakly singular Volterra integralequations of the first kind. The proposed methods are convergentof the order of the underlying multistep method. The stabilityproperties are directly related to those of the multistep method.     

The Grunsky Norm and Some Coefficient Estimates for Bounded Functions

We estimate the growth order in n of the Taylor coefficientsof bounded univalent functions in the unit disk. Our estimatedepends on the norm of the Grunsky operator. In particular,we improve the known results for coefficients of quasiconformallyextendible univalent functions. 1991 Mathematics Subject Classification30C50, 30C75, 30C55.