Designs and Representation of the Symmetric Group

We study (generalized) designs supported by words of given composition. We characterize them in terms of orthogonality relations with Specht modules; we define some zonal functions for the symmetric group and we give a closed formula for them, indexed on ordered pair of semi-standard generalized tableaux: Hahn polynomials are a particular case. We derive an algorithm to test if a set is a design. We use it to search designs in some ternary self-dual codes.     

Formation of Metallophthalocyanine Trimers in Liquid Solutions

For solutions of the complexes of phthalocyanine (PhC) with magnesium (Mg-PhC) and of tetrachloromethyl-PhC with zinc (Zn-PhCCh) in mixtures of glycerin with dimethyl formamide (DMF) and for Zn-PhCCh in toluene and DMF it has been found that the electron absorption spectra substantially depend on the substance concentration. It is shown that these changes are attributable to the association of the molecules of pigments. The number of molecules in the associates and the equilibrium constants for this association are determined. The formation of the trimers of Mg-PhC in binary solutions and the dimers of Zn-PhCCh in toluene, DNF, and binary solutions has been established. It has been found that on association the Q absorption bands of the pigments shift to shorter wavelengths as compared to the bands of the monomers. For the Mg-PhC trimers, the shift is = 1410 cm^–1, while for the Zn-PhCCh dimers it is 990 cm^–1 in toluene, 930 cm^–1 in DMF, and 925 cm^–1 in the mixture of DMF with glycerin. It is concluded that the structure of the trimers and dimers is of the type of a stack in which molecules are arranged in parallel one above the other at a distance of 3.5 to 4.0 Å between the planes of the molecules. In association, the fluorescence intensity of the pigments decreases substantially (the decrease corresponds to the decrease in the concentration of the monomer molecules of phthalocyanines), with the fluorescence spectra remaining unchanged. Consequently, the associates of the pigments do not display pronounced fluorescence.     

Uniformly Packed Codes and More Distance Regular Graphs from Crooked Functions

Let V and W be n-dimensional vector spaces over GF(2). A function Q : V W is called crooked (a notion introduced by Bending and Fon-Der-Flaass) if it satisfies the following three properties:

Synthesis of amphiphilic polyacetal by polycondensation of aldehyde and polyethylene glycol as an acid‐labile polymer for controlled release of aldehyde

A new acid‐labile polymer having acetal moieties in the main chain was synthesized by polycondensation of poly (ethylene glycol) (PEG) and lilial, an aldehyde widely used in fragrance applications. The hydrophobicity of the resulting acetal moiety and the hydrophilicity of the PEG chain allowed the polyacetal to exhibit amphiphilicity. The polyacetal derived from PEG having weight average molecular weight (M_w) of 1000 (PEG1000) was soluble in water and self‐associated to form associates in water. The polyacetals were hydrolyzed in acidic aqueous solutions to release hydrophobic lilial from the systems. The release rate of aldehyde from the polyacetal derived from PEG1000 was higher than that from the polyacetal derived from PEG having M_w of 400 (PEG400). These results supported that the release rate of lilial can be controlled by the chain length of PEG, on which hydrophilicity of polyacetal depends. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Synthesis and properties of temperature-resistant and salt-tolerant tetra-acrylamide copolymer

Abstract

The acrylamide copolymer with acrylamide as its main monomer is a modified polyacrylamide. In addition, the acrylamide copolymer is generally to dissolve or swell in water and can be used as thickener, dispersant, flocculant and so on. Therefore, using Acrylamide AM, 2-acrylamide-2-methyl propanesulfonic acid AMPS, dimethyldodecyl (2-acrylamidoethyl) ammoniumbromide AQ₁₂ and vinyltriethoxysilane VTEO as raw materials so that a series of four-membered acrylamide copolymers are prepared in aqueous solution polymerization. The amphoteric structure in the polymer has a unique anti-polyelectrolyte behavior when it is electrically neutral, which can significantly improve the salt resistance of the aqueous polymer. In addition, the hydrolysis of the vinyltriethoxysilane containing silicon structure by hydrophobic association can improve the temperature resistance of the polymer. The optimal reaction conditions were determined by orthogonal experiment: the reaction temperature was 10?°C; the initiator concentration was 0.05?mol%; the monomer concentration was 25?wt% and the pH was 7. Properties of polymer solution indicated that the series of tetra-copolymer possessed salt-tolerant and heat-resisting performances. As an oil displacing agent, it can significantly improve the efficiency of oil displacement, and particularly highlights the effect of 4-member copolymer as an oil displacing agent.     

Conditional VaR estimation using Pearson’s type IV distribution

This paper presents a new value at risk (VaR) estimation model for equity returns time series and tests it extensively on Stock Indices of 14 countries. Two most important stylized facts of such series are volatility clustering, and non-normality as a result of fat tails of the return distribution. While volatility clustering has been extensively studied using the GARCH model and its various extensions, the phenomenon of non-normality has not been comprehensively explored, at least in the context of VaR estimation. A combination of extreme value theory (EVT) and GARCH has been explored to analyze financial data showing non-normal behavior. This paper proposes a combination of the Pearson’s Type IV distribution and the GARCH (1, 1) approach to furnish a new method with superior predictive abilities. The approach is back tested for the entire sample as well as for a holdout sample using rolling windows.     

The adiabatic approximation to exotic leptonic molecules: further analysis and a nonlinear equation for conditional amplitudes

Recent successful applications of a particular kind of adiabatic approximation to complexes of muons and positrons with atoms, motivated us to perform a new analysis of the molecular approximations on this perspective. We focus our attention mainly on the various levels of the adiabatic approximation and discuss if and how it can be stressed to yield exact results. In the course of this analysis a new nonlinear equation for conditional amplitudes was obtained.     

Improved convex upper bound via conditional comonotonicity

Comonotonicity provides a convenient convex upper bound for a sum of random variables with arbitrary dependence structure. Improved convex upper bound was introduced via conditioning by Kaas et al. [Kaas, R., Dhaene, J., Goovaerts, M., 2000. Upper and lower bounds for sums of random variables. Insurance: Math. Econ. 27, 151-168]. In this paper, we unify these results in a more general context using the concept of conditional comonotonicity. We also construct an approximating sequence of convex upper bounds with nice convergence properties.     

Contractive projections on Banach algebras

In this paper, we explore the properties of projections of norm one on general Banach algebras, in particular the relation with conditional expectations for algebras which arise in harmonic analysis.     

<Superscript>1</Superscript>H NMR spectroscopic study of the formation of molecular complexes of methanol with benzene and phenanthrene

Chemical shifts (c.s.) of ¹H nuclei in methanol are measured for methanol-benzene and methanol-phenanthrene systems. A method to determine the equilibrium constant of the molecular association reaction by NMR spectroscopy data is proposed for systems with low solubility of a compound when the dependence of c.s. on the composition is close to a straight line. The equilibrium constants for the formation of molecular complexes in methanol-benzene and methanol-phenanthrene systems are found.