Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions

In this paper, the author considers the Cauchy problem for semilinear wave equations with critical exponent in n≥4 space dimensions. Under some positivity conditions on the initial data, it is proved that there can be no global solutions no matter how small the initial data are.     

Critical percolation exploration path and SLE 6: a proof of convergence

It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE ₆. We provide here a detailed proof, which relies on Smirnov’s theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy’s formula). The version of convergence to SLE ₆ that we prove suffices for the Smirnov–Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops. Research of Charles M.Newman was partially supported by the US NSF under grants DMS-01-04278 and DMS-06-06696.     

Electrochemical reduction of sodium metavanadate in an equimolar KCl-NaCl melt

Electrochemical reduction of sodium metavanadate in an equimolar KCl-NaCl melt and the effect of acid-base properties of environment on this process are studied by a voltammetry method on a stationary platinum electrode. It is established that the limiting current of the NaVO₃ electroreduction process has a kinetic nature. The process proceeds via an autoinhibition scheme and its rate is limited by an acid-base reaction conjugated with an irreversible charge transfer reaction. A substantial role of cationic composition of the melt is revealed experimentally. Following acidification of the KCl-NaCl-NaVO₃ melt by Mg²⁺ (from MgCl₂), the process passes from an irreversible kinetic regime into a reversible diffusion (quasi-diffusion) process. Values of stability constants for vanadates produced with the aid of acid-base titration of vanadium pentoxide by oxygen ions in experimental conditions are presented. These values are taken into account when calculating kinetic parameters of the NaVO₃ electroreduction.     

He-HCl体系各向异性势及分波散射截面的理论研究

首先用BFW势函数形式拟合了在CCSD(T)/aug-cc-pVQZ理论水平下计算的He-HCl相互作用能数据，获得了He原子与HCl分子相互作用的各向异性势；然后采用CC近似方法计算了He-HCl碰撞体系的微分散射截面和分波散射截面，并总结了分波散射截面的变化规律.结果表明，拟合势不但表达形式简洁，而且较好地描述了He-HCl系统相互作用的各向异性特征；利用碰撞体系分子间势的量子化学从头计算结果，可解决势能参数难以确定的问题.对进一步研究原子与分子碰撞机理有一定参考价值. 关键词： 各向异性势 势能参数 密耦近似 分波散射截面     

DESIGN OF A NOVEL 2-D UNIPLANAR CRLH-TL STRUCTURE

A novel uniplanar 2-D composite right/left-handed transmission line (CRLH-TL) structure is proposed based on a general transmission line theory and the way to increase the relative operating bandwidth in the left-handed (LH) region and lower the LH operating frequency is illustrated. In addition, a new method to extract parameters and calculate the Bloch impedance of the structure is presented. Numerical results of the dispersion as well as the extracted parameters are given, which are calculated based on full-wave simulation. The present 2-D uniplanar CRLH-TL structure is applicable to 2-D left-handed materials in lower and wider LH frequency range. Supported by the National Natural Science Foundation of China (No. 60371010) (No. 60471037) (No. 63531020)     

Nonlinear Schrödinger equations with symmetric multi-polar potentials

This paper deals with a class of nonlinear elliptic equations involving a critical power-nonlinearity as well as a potential featuring multiple inverse square singularities. When the poles form a symmetric structure, it is natural we wonder how the symmetry affects such mutual interaction. The present paper means to study this aspect from the point of view of the existence of solutions inheriting the same symmetry properties as the set of singularities. Mathematics Subject Classification (2000) 35J60, 35J20, 35B33     

书籍扫描图像畸变参数自动计算方法的研究

为实现书籍扫描图像的畸变自动校正,提出用多项式来描述各像素的理论灰度g(zi)与页面上对应点到扫描仪工作平面距离zi二者之间的关系。为确立该多项式,在畸变参数已知条件下扫描一幅图像,根据已知畸变参数求出zi,即可按最小二乘法原理由各像素灰度的实际值求出多项式的各个系数。实验证明,采用4阶多项式已能满足一般要求,并求出了各系数。对任意扫描图像,自动计算畸变参数的方法为:首先利用扫描图像上页边空白处各像素的灰度,对畸变参数进行估计,并求出zi的估计值;然后代入所确立的多项式,可求得g(zi);通过调整各畸变参数的估计值,直到g(zi)与gi最为接近,即得最佳畸变参数。用于图像校正实验,获得了较好的校正效果,最大误差由不校正时的41%下降到了6.9%。这使得无需用户测量并输入有关畸变参数即可进行自动校正。     

Precise lattice parameter measurements in CsCl-Br solid solutions between room temperature and 90°K by powder x-ray diffraction

Solid solutions of CsCl-Br in five different concentrations were prepared in sealed quartz tubes by heating the mixture to 1123°K for 6–8 hr and quenching to room temperature. X-ray diffractograms were taken at eight different temperatures between room temperature and 90°K for these solid solutions using the YPC50NM powder diffractometer and a continuous flow cryostat. The observed lattice parameters for each sample at each temperature obtained from the powder diffractograms were then extrapolated to give the true lattice parameters using the least square method with Nelson-Riley extrapolation scheme. The values of the true lattice parameters at each concentration and at each temperature were tabulated and the results discussed. It is shown that the lattice parameters vs temperature for some concentrations exhibit an anomalous behaviour. Contribution No. 691     

Adaptive Interpolation by Scaled Multiquadrics

We present an adaptive method to extract shape-preserving information from a univariate data sample. The behavior of the signal is obtained by interpolating at adaptively selected few data points by a linear combination of multiquadrics with variable scaling parameters. On the theoretical side, we give a sufficient condition for existence of the scaled multiquadric interpolant. On the practical side, we give various examples to show the applicability of the method.     

Critical currents in polycrystalline thin films of high-T c superconductors

Summary It is shown that the behaviour of the temperature dependence of the critical current in polycrystalline thin films of high-T _c superconductors depends crucially on the assumption made concerning the nature of the intergranular material. The usual assumption of a superconductor-insulator-superconductor (=SIS) ?sandwich? between each grain leads to a crossover fromI _c∼(1−T/T _c) toI _c∼(1−T/T _c)^3/2, for temperatures nearT _c (whereI _c is the critical current,T the absolute temperature, andT _c the superconducting transition temperature). Instead, for a superconductor-normal metal-superconductor (=SNS) sandwich the dependenceI _c∼(1−T/T _c)² is found for all temperatures. Consideration is given to the effect of self-magnetic field on the analysis. The comparison between expressions for continuous and granular systems is extended. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.