Analytic calculation of scaling dimensions: Tricritical hard squares and critical hard hexagons

The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance.     

On Brennan's Conjecture for a Special Class of Functions

In this paper, we prove Brennan's conjecture for conformal mappings f of the disk {z : | z| < 1} assuming that the Taylor coefficients of the function log(zf′(z)/f(z)) at zero are nonnegative. We also obtain inequalities for the integral means over the circle |z| = r of the squared modulus of the function zf′(z)/f(z).     

Calculation of Normal Vibrations of Chlorin by the Method of Density Functionals

Using the DFT/B3LYP method with a 6-31G(d) basis set, the structure, normal vibration frequencies, and the absolute band intensities in the IR spectra of the chlorin molecule and its four symmetric isotopomers have been calculated. Scaling of the force field by the Pulay method in independent and natural coordinates has been carried out. A method for obtaining effective force fields without using experimental data on the fundamental vibration frequencies is proposed. By comparing the vibration modes and constructing special matrices, complete assignment of the fundamental frequencies of porphin and chlorin has been carried out. It has been shown that the majority of porphin macroring vibrations upon pyrrolenine ring hydrogenation are frequency-characteristic and only 12 vibrations change considerably. A frequency correlation with regard for the mode transition between chlorin and all its isotopomers under consideration has been established. Comparative analysis of the force fields of porphin and chlorin in dependent natural coordinates has revealed the unique nonlocal character of the change in force constants of the macroring upon hydrogenation of one pyrrolenine ring. Modeling of the IR spectra of chlorin and its isotopomers has been performed. Assignment and interpretation of the normal vibrations of the molecules under consideration have been carried out.     

Autour du théorème de Ferrand–Obata (Concerning the Theorem of Ferrand–Obata)

The aim of this article is to give a new dynamical proof of the Ferrand–Obata theorem when the manifold is compact. This will give us a generalisation of this theorem to transversally conformal foliations ofcodimension greater than three and constant basic functions.     

Cardy's formula for some dependent percolation models

We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice  (with alternating updates of two sublattices) [7]; it may also be realized on the triangular lattice 𝕋 with flips when a site disagrees with six, five and sometimes four of its six neighbors. Received: 24 December 2001     

一种新型有机电致微腔结构的双模发射

采用结构Glass／DBR／ITO／NPB／NPB：Alq／Alq／Al制作了有机微腔电致发光器件。将空穴传输材料与发光材料以一定比例混合作为发光层，为了便于对比，在不改变有机层的膜厚的情况下同时制作了传统的异质结微腔器件，发现两种器件的发光光谱有很大不同，器件的复合效率与传统的异质结器件相比也得到了很大提高，这是因为将两种有机材料混合能消除界面势垒，提高器件的复合效率，从而提高了器件的发光性能，实现了微腔双模发射，且两个模式的半峰全宽分别为8nm和12nm。通过进一步优化器件结构可以实现微腔白光发射。     

Three-pencil lattices on triangulations

In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S ₃ on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.      

High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

Let _l be the critical exponent associated with the probability thatl independentN-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ₂=0.6240±0.0005±0.0011 and ₃=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ₂=5/8 and ₃=35/24.     

Chromium and yttrium-doped magnesium aluminum oxides prepared from layered double hydroxides

Layered double hydroxides with the hydrotalcite-like structures, containing Mg²⁺ and Al³⁺, doped with Cr³⁺ and Y³⁺, have been prepared by precipitation at constant pH. The weight percentages of Cr³⁺ and Y³⁺ were 1, 2, or 3%, and 0.5 or 1%, respectively. Single phases were obtained in all cases, whose crystallinity decreased as the content in Cr and Y was increased. The solids have been characterised by element chemical analysis, powder X-ray diffraction, thermal analyses (differential, thermogravimetric and programmed reduction), FT-IR and UV–vis spectroscopies; the specific surface areas have been determined from nitrogen adsorption isotherms at −196 °C. Upon calcination at 1200 °C for 5 h in air all solids display a mixed structure (spinel and rock salt for MgO); these solids have also been characterised by these techniques and their chromatic coordinates (CIE – L^*a^*b^*) have been determined. Their pink colour makes these solids suitable for being used as ceramic pigments.