Interpolatory Hermite splines on rectangular domains

Based on Bittner and Urban’s construction of interpolatory multiwavelets [Kai Bittner, Karsten Urban, On interpolatory divergence-free wavelets, Math. Comput. 76 (258) (2007) 903-929], we use the truncation method to obtain interpolatory multiwavelets on rectangular domains in this paper. In addition, the characterization for the corresponding functional spaces is given.     

泛Clifford分析中无界域上的Cauchy积分公式和Cauchy-Pompeiu公式

本文研究了泛Clifford分析中的Cauchy积分公式和Cauchy-Pompeiu公式.通过引入修正的Cauchy核,得出了取值在泛Clifford代数上的两公式在无界域上的表达式.此两公式是有界域上的相应结果的推广,并为研究无界域上的边值问题打下了基础.     

Determination of the Molecular Arrangement in Liquid Crystals by Polarization of Fluorescence

Polarized luminescence intensity reading and the polarized absorbance spectra of 4-diethyl-amino-4′-nitrostilbene “impurity” in the n-butyl-p/p-hexyloxyphenyloxycarbonyl/-phenyl-carbonate liquid crystal were measured. Degrees of orientational order, S₁ and S₂, of the nematic liquid were calculated from relative values of the absorbance and luminescence intensity components. A function, which describes the angular molecular distribution with respect to a preferred direction in the liquid crystal, is plotted.     

PHYSICAL PROPERTIES OF SOME NOVEL NEMATIC BIMESOGENS FOR THE FLEXOELECTRIC EFFECT

Abstract

In a chiral nematic liquid crystal, the flexoelectric effect consists of a fast and linear coupling with an applied electric field. One difficulty to overcome is the unwinding of the helix that occurs at higher fields due to dielectric coupling. The use of bimesogens, which possess very low molecular dielectric anisotropy can improve flexoelectric characteristics. New bimesogen compounds have recently been synthesised that exhibit switching angles of 45° for applied fields of about 9 V.μm^?1. In this paper, results from dielectric, electro-optic and dynamic light scattering measurements are reported for the new bimesogenic mixture. The dielectric anisotropy Δε changes sign with temperature and its values range between -0.2 and 0.3 for the temperature range studied. For Δε weakly positive, no electric field Freedericksz transition could be induced but Williams domains are observed instead. The large decrease in the bend elastic constant to viscosity coefficient ratio is attributed to a large increase in the bend viscosity coefficient.     

A gap in the spectrum of the Neumann–Laplacian on a periodic waveguide

We study a spectral problem related to the Laplace operator in a singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder which contains a periodic arrangement of inclusions. On the boundary of the waveguide, we consider both Neumann and Dirichlet conditions. We prove that provided the diameter of the inclusion is small enough the spectrum of Laplace operator contains band gaps, i.e. there are frequencies that do not propagate through the waveguide. The existence of the band gaps is verified using the asymptotic analysis of elliptic operators.     

On Realizing Zero-Divisor Graphs

An algorithm is presented for constructing the zero-divisor graph of a direct product of integral domains. Moreover, graphs which are realizable as zero-divisor graphs of direct products of integral domains are classified, as well as those of Boolean rings. In particular, graphs which are realizable as zero-divisor graphs of finite reduced commutative rings are classified.     

Prüfer Conditions and the Total Quotient Ring

In this article, we consider two of the five well-studied extensions of the Prüfer domain notion to arbitrary commutative rings. In particular, we consider a class of rings that lies properly between Gaussian and Prüfer rings. We give a characterization of this property in terms of the total quotient ring and show that this property behaves nicely in conductor squares.     

On Semiprime Multiplication Modules over Pullback Rings

We classify all those indecomposable semiprime multiplication modules with finite-dimensional top over pullback of two Dedekind domains. We extend the definition and results given in [9 Ebrahimi Atani , S. , Farzalipour , F. ( 2009 ). Weak multiplication modules over a pullback of Dedekind domains . Colloquium Math. 114 : 99 – 112 .[Crossref] , [Google Scholar]] to a more general semiprime multiplication modules case.