Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials

Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.     

Micromechanics of ferroelectric polymer-based electrostrictive composites

Electrostriction refers to the strain induced in a dielectric by electric polarization, which is usually very small for practical application. In this paper, we present a micromechanical analysis on the effective electrostriction of a ferroelectric polyvinylidene fluoride trifluoroethylene [P(VDF-TrFE)] polymer-based composite, where the exact connections between the effective electrostrictive coefficients and effective elastic moduli are established, and numerical algorithm for the prediction of the effective electrostrictive coefficients of the composite in terms of its microstructural information is developed. From our calculations, enhanced electrostriction in the composite has been demonstrated, and optimal microstructure for electrostriction enhancement has been identified. Our analysis provides a mechanism for the electrostriction enhancement, where the electrostrictive strain several times higher than that of polymer matrix can be obtained, if the microstructure of the composites can be carefully tailored.     

Mapping properties of wave and scattering operators for two-body Schrödinger operators

The modified wave and scattering operators are shown to be bounded between weighted L ²-spaces for two-body Schrödinger operators with long range potentials.     

锡(Ⅳ)-偶氮邻苯二酚苯基荧光酮-吐温-80体系分光光度法测定岩石中微量锡

pH值在7.0-8.5的范围内，锡与偶氮邻苯二酚苯基荧光酮、吐温－80形成络合物，其最大吸收峰556nm，摩尔吸光系数2.9×10^5L·mol^-1·cm^-1，锡的含量在0－6μg/25mL范围内遵守比耳定律，本方法对干扰离子的影响和消除进行了研究，本方法已被用于岩石样中锡的测定，结果满意。     

Microlocal study of topological Radon transforms and real projective duality

Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces.     

Proof of semialgebraic covering mapping cylinder conjecture with semialgebraic covering homotopy theorem

In this paper we prove the semialgebraic version of Palais' covering homotopy theorem, and use this to prove Bredon's covering mapping cylinder conjecture positively in the semialgebraic category. Bredon's conjecture was originally stated in the topological category, and a topological version of our semialgebraic proof of the conjecture answers the original topological conjecture for topological G-spaces over “simplicial” mapping cylinders.     

Asymptotic robustness of standard errors in multilevel structural equation models

Data in social and behavioral sciences are often hierarchically organized. Multilevel statistical methodology was developed to analyze such data. Most of the procedures for analyzing multilevel data are derived from maximum likelihood based on the normal distribution assumption. Standard errors for parameter estimates in these procedures are obtained from the corresponding information matrix. Because practical data typically contain heterogeneous marginal skewnesses and kurtoses, this paper studies how nonnormally distributed data affect the standard errors of parameter estimates in a two-level structural equation model. Specifically, we study how skewness and kurtosis in one level affect standard errors of parameter estimates within its level and outside its level. We also show that, parallel to asymptotic robustness theory in conventional factor analysis, conditions exist for asymptotic robustness of standard errors in a multilevel factor analysis model.     

1,3-diallyl-5-[ω-(diphenylphosphino)alkyl] isocyanurates in reactions of complex formation with palladium(ii) dichloride

The reactions of phosphine derivatives of diallyl isocyanurates with palladium(ii) dichloride lead to the formation of complexes, whose structure, composition, and stability depend on the length of the methylene chain between the isocyanurate and diphenylphosphine fragments in the ligand. 1,3-Diallyl-5-[5′-(diphenylphosphino)pentyl and 10′-(diphenyl-phosphino)decyl] isocyanurates with PdCl₂ form monomeric L₂PdCl₂ trans-complexes in which P atoms of the ligands participate in coordination with the metal. 1,3-Diallyl-5-[2′-(diphenylphosphino)ethyl] isocyanurate with PdCl₂ forms a dimeric (LPdCl₂)₂ complex, which decomposes in a solution to the monomer including solvent molecule into the coordination sphere of the metal. The reactions of 1,3-diallyl-5-[4′-(diphenylphosphino)butyl] isocyanurate and 1,3-diallyl-5-[6′-(diphenylphosphino)hexyl] isocyanurate with PdCl₂ give monomeric chelate LPdCl₂ complexes in which one of the allyl groups of the isocyanurate cycle participates in coordination with the central ion along with the phosphorus atom. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1859–1865, September, 1998.