Why the Afshar experiment does not refute complementarity

A modified version of Young's experiment by Shahriar Afshar demonstrates that, prior to what appears to be a “which-way” measurement, an interference pattern exists. Afshar has claimed that this result constitutes a violation of the Principle of Complementarity. This paper discusses the implications of this experiment and considers how Cramer's Transactional Interpretation easily accommodates the result. It is also shown that the Afshar experiment is analogous in key respects to a spin one-half particle prepared as “spin up along x”, subjected to a nondestructive confirmation of that preparation, and post-selected in a specific state of spin along z. The terminology “which-way” or “which-slit” is critiqued; it is argued that this usage by both Afshar and his critics is misleading and has contributed to confusion surrounding the interpretation of the experiment. Nevertheless, it is concluded that Bohr would have had no more problem accounting for the Afshar result than he would in accounting for the aforementioned pre- and post-selection spin experiment, in which the particle's preparation state is confirmed by a nondestructive measurement prior to post-selection. In addition, some new inferences about the interpretation of delayed choice experiments are drawn from the analysis.     

The realization and structure of complete Lie algebras whose nilpotent radicals are Heisenberg algebras

The realization and siructure of complete Lie algebras whose nilpotent radicals are Heisenberg algebras over the complex field C are given.     

On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution

Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested. An erratum to this article is available at .     

具有公共对称面的两个二次回转面的相贯线

本文论述了常见的两个二次回转面轴线相交和平等时,其相贯线在公共对称面（投影面）的投影分别为双曲线和抛物线,只有在特殊情况下是直线,椭圆和圆,并举例说明在计算机上绘图的方法。     

Formula for Analyzing Hopf Bifurcation

CesariandHaleshowedthat[1],usingLiapunov-Schmidtreduction,theHopfbifurcationcanbetreatedasbifurcationofzerosofacertainreducedmapping.Consideranautonomoussystemofordinarydifferentialequation(ODE)definedneartheoriginoftheformdudt A(λ)u F(u,λ)=0,　u∈Rn,λ∈Rm(1)whereλisthebifurcationparameter,A(λ)isann×nmatrix,A(0)satisfiestheHopfhypothesis:ithassimpleeigenvalues±iandhasnoothereigenvalueslyingontheimaginaryaxis,F(u,λ)arethehigher-ordertermsofuandbothofAandFareC∞functionsofλ.Fixed…     

悬挂系统阻尼非对称性对车身振动的影响

采用瞬态信号等效替换随机激励的方法,通过计算讨论车辆在路面随机激励下双作用减振器阻尼的非对称性对车身振动的影响,并讨论了车辆在路面冲击激励下阻尼非对称对车身振动加速度响应的峰值以及总能量的影响。     

对称性对二相互作用玻色子耦合系数的制约

给出了一般形式下二体相互作用玻色系统对角化的一般方法,讨论了能对角化的条件,得到了制约耦合系数的两个关系式。     

基于三角点阵模型的自组织城市网络探讨

基于城市体系的三角点阵模型提出了自组织城市网络空间结构无标度性的数学定义和描述方法：假定区域城市是三角点阵格局上的无规分布，构造城市两两之间的空间关联函数；只要城市关联密度与码尺之间满足幂指数关系，就表明城市体系是无标度网络，可以用标度指数进行度量。以河南省为研究区，对城市空间关联进行了实证分析，发现在双对数坐标图上存在明确的无标度区，从而在揭示自组织城市网络内在复杂规律的同时，证实了上述方法刻画无标度城市网络的有效性。     

冰箱试验包传热过程的仿真计算

建立了一个用于描述冰箱试验包传热过程的三维非稳态数学模型,模型考虑了试验包降温过程的物性变化,通过引入一个试验包边界导热系数折算因子来考虑由于其体积变化而造成的接触热阻.试验包的降温试验结果与预测值的比较表明:采用Morgan关联式计算试验包的表面传热系数精度较高,其值约为5～7W/(m2·K);试验包边界导热折算因子在10×10×10的网格划分下,其值约为0 1;试验包的温度预测值与实测值吻合得较好,模型可靠,可用于相变蓄能等类似问题的仿真计算.     

分形几何中的美--分形理论哲学探索之一

从美学角度指出了分形几何是科学与艺术的结合.进而,探讨了分形几何中美的特征:统一性、对称性与奇异性.