On a Conjecture Concerning a Theorem of Cramér and Wold

A conjecture concerning the Cramér–Wold device is answered in the negative by giving a Fourier-free, probabilistic proof using only elementary techniques. It is also shown how a geometric idea allows one to interpret the Cramér–Wold device as a special case of a more general concept.     

Unusual electro-optical response of an oblique columnar phase formed by a bent-core mesogen

Mesophases formed by bent-core mesogens have attracted special attention because they can organise into fluid phases with polar order and supramolecular chirality. In this paper, a new five-ring bent-core mesogen is presented which forms a columnar mesophase. The structure is built up by layer fragments and possesses an oblique two-dimensional lattice with a layer group of the type p112/a. The columnar phase can be transformed into a ferroelectric SmCP phase (SmCP_F) by application of a sufficiently high electric field (25 V µm^-1). This field-induced transition was found to be reversible. The mechanism of the polar switching depends on the frequency of the applied electric field. The switching takes place in the usual way by a collective rotation of the molecules around the tilt cone. At very low frequencies (0.1 Hz and lower), the polar switching is based on a collective rotation of the molecules around their long axes. In the latter case, the switching is accompanied by an inversion of the layer chirality.     

Calculation of Chlorin IR Spectrum by Density Functional Theory

The structure, frequencies of normal vibrations, and absolute intensities of bands in the IR spectra of chlorin and four of its symmetric isotopomers were calculated using DFT/B3LYP with the 6-31G(d) basis set. The force field was scaled by the Pulay method in independent and dependent natural coordinates. A method for obtaining effective force fields without using experimental data for the frequencies of fundamental vibrations was proposed. It has been demonstrated that most vibrations of the porphyrin macrocycle have characteristic frequencies upon hydrogenation of the pyrrolenine ring and only 12 vibrations differed significantly. The IR spectra of chlorin and its isotopomers were modelled. Frequencies were assigned and normal vibrations were interpreted for the examined molecules.     

正交曲线坐标系中加速度的拉氏方程求法

采用拉格朗日方程给出一种求解正交曲线坐标系中加速度的简捷方法。     

凸多边形上的Bezier曲面片

本文建立了正多边形上的重心坐标，并构造了多边形上的Ｂｅｚｉｅｒ曲面片、     

Polar Interface Optical Phonon Modes and Fr(o*)hlich Electron-Phonon Interaction Hamiltonians in an Arbitrary Layer-Number Quantum Well System

By using determinant method as in our recent work, the IO phonon modes, the orthogonal relation forpolarization vector, electron-IO phonon Frohlich interaction Hamiltonian, the dispersion relation, and the electron-phonon coupling function in an arbitrary layer-number quantum well system have been derived and investigated withinthe framework of dielectric continuum approximation. Numerical calculation on seven-layer Alx Ga1-x As/GaAs systemshave been performed. Via the numerical results in this work and previous works, the general characters of the IO phononmodes in an n-layer coupling quantum well system were concluded and summarized. This work can be regarded as ageneralization of previous works on IO phonon modes in some fixed layer-number quantum well systems, and it providesa uniform method to investigate the effects of IO phonons on the multi-layer coupling quantum well systems.     

联苯乙烯类蓝色发光材料DPVBi的合成及发光性质研究

合成了联苯乙烯类蓝色有机发光材料DPVBi[4，4′-二(2，2-二苯乙烯基)-1，l′-联苯]，用^1H-NMR，IR，元素分析等方法对其结构进行了表征。以DPVBi作发光层制备了电致发光器件，其结构为：ITO／CuPc／NPB／DPVBi/Alq3／LiF／Al，研究了器件的电致发光性质。器件最高亮度达4 373cd/cm^2，最大流明效率为1．24 lm／w，在20mA／cm^2电流密度驱动下的亮度为434cd／cm^2，CIE色坐标为x=0．15，y=0．16，器件的蓝色发光具有较好的色纯度。重点对器件发光色度的稳定性进行了研究，结果表明，随电流密度(4～4 000mA／cm^2)的变化，器件色度具有很好的稳定性。     

Generalized projections, decompositions, and the Pythagorean-type theorem in Banach spaces

In this paper, we investigate new properties of the generalized projection operators on convex closed cones in uniformly convex and uniformly smooth Banach spaces; establish decompositions theorems for arbitrary elements both in primary and dual spaces; and prove the Banach space analogue of the Pythagorean-type theorem. Earlier, all these results were known only in Hilbert spaces.     

Estimates for the low‐frequency electromagnetic fields scattered by two adjacent metal spheres in a lossless medium

Inductive electromagnetic means, currently employed in real physical applications and dealing with voluminous bodies embedded in lossless media, often call for analytically demanding tools of field calculation at modeling stage and later on at numerical stage. Here, one is considering two closely adjacent perfect conductors, possibly almost touching one another, for which the 3D bispherical geometry provides a good approximation. The particular scattering problem is modeled with respect to the two solid impenetrable metallic spheres, which are excited by a time‐harmonic magnetic dipole, arbitrarily orientated in the 3D space. The incident, the scattered, and the total non‐axisymmetric electromagnetic fields yield rigorous low‐frequency expansions in terms of positive integral powers of the real‐valued wave number in the exterior medium. We keep the most significant terms of the low‐frequency regime, that is, the static Rayleigh approximation and the first three dynamic terms, while the additional terms are small contributors and they are neglected. The typical Maxwell‐type problem is transformed into intertwined either Laplace's or Poisson's potential‐type boundary value problem with impenetrable boundary conditions. In particular, the fields are represented via 3D infinite series expansions in terms of bispherical eigenfunctions, obtaining analytical closed‐form solutions in a compact fashion. This procedure leads to infinite linear systems, which can be solved approximately within any order of accuracy through a cutoff technique.