Types of likelihood maxima in mixture models and their implication on the performance of tests

In two-component mixtures of exponential distributions, different strategies for starting the likelihood maximization algorithm converge to different types of maxima. The power of an LR test of homogeneity against such a mixture strongly depends on the considered strategy, and global maximization need not result in the largest power. An explanation is given on basis of a systematic investigation of the likelihood function in a large number of simulations, using a variety of diagnostic tools. Thereby, we also gain a deeper insight into the properties of the samples that generate particular types of solutions of the likelihood equation. In particular, “spurious solutions” often occur; these are mainly responsible for the fact that global maximization may not result in a statistically meaningful estimator. Removing the smallest elements of a sample may drastically increase the power of previously inferior strategies. This research has been supported by a grant from the Deutsche Forschungsgemeinschaft.     

Nonlinear acoustics of bounded solid

Reflection and refraction are investigated when the incidental angles of transverse waves are larger than the critical one. An interesting result is obtained that at this angle all the second-order displacements on the stress-free surface have a very strong maximum module and a phase leap; thereupon an appropriate second-order harmonic surface wave could be produced. Project supported by the National Natural Science Foundation of China (Grant No. 19334062).     

高频红外分析低碳低硫的影响因素

对影响低碳(0.0x9／5)、低硫(0.00x9／5)分析的若干问题进行了探讨，提出了低碳低硫分析的注意事项。     

Arithmetic of the Integer Quantum Hall Effect

The integer quantum Hall effect (IQHE) is analysed, considering the degeneracies of localized and extended states separately. Occupied localized and extended states are counted, and their variation is studied as a function of magnetic field. The number of current-carrying electrons is found to have a saw-tooth variation with magnetic field. The analysis addresses certain basic questions in the IQHE, particularly the one about floatation of extended states as the magnetic field tends to zero.     

Some Observations on the Early History of Equilibrium Statistical Mechanics

The article begins with some personal comments by the author on the outstanding contributions of Michael Fisher to statistical mechanics and critical phenomena. Its major aim is to trace the contributions of a number of pioneering personalities to the early history of equilibrium statistical mechanics. Four different areas are considered: (1) Classical Statistical Mechanics, (2) Quantum Statistical Mechanics, (3) Interacting Systems, and (4) The Ising Model. The article is concerned with the development and applications of statistical mechanics when certain basic assumptions are made. It does not deal with the justification of these assumptions which is a sophisticated discipline of its own.     

Evaluation of a total reflection set-up by an interface geometric model

We have studied the total reflection regime through a model represented by a region separating two dielectric bulk media with well-defined refraction indexes. This region is considered to be an interface in which the following hypotheses are established: – Refraction index linear variation with the transition from one medium to the other. – The thickness depends on the optical phenomenon supposedly produced in the interface. The results we obtained were in close agreement with those obtained by authors who have studied this regime through a fundamentally different treatment.     

TN approximation to reflected slab and computation of the critical half thicknesses

The criticality solution to one-speed neutron transport equation using the T_N approximation is described for reflected slab. In the solution, Marshak type boundary condition is used. The critical half thicknesses are computed for different values of c and reflection coefficients. Computations are made by using the both T_N and P_N approximation for the comparison.     

NONTRIVIAL SOLUTION FOR A CLASS OF SEMILINEAR BIHARMONIC EQUATION INVOLVING CRITICAL EXPONENTS

In this article,the authors prove the existence and the nonexistence of non- trivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequality.     

一类复映射$z\leftarrow e^{i\phi}(\bar{z})^\alpha+c~ (\alpha<0)$的广义M集

本文分析了一类复映射$z \leftarrow e^{i\phi }(\bar {z})^\alpha +c\{\alpha < 0,\phi \in [0,2\pi)\}$的临界点的性质,给出了广义Mandelbrot集 (简称广义M集)的定义,并构造出一系列广义M集.利用复变函数理论和计算机制图相结合的实验数学的方法,本文对广义M集的结构和演化进行了研究,结果表明: 1). 广义M集的几何结构依赖于参数$\alpha$, $R$和$\phi$; 2). 整数阶广义M集具有对称性和分形特征; 3). 小     

Light-scattering studies on phase separation in a binary blend with addition of diblock copolymers

Time-resolved light-scattering measurements have been conducted to investigate the influence of a diblock copolymer additive on the phase boundaries and the kinetics of the phase separation of a polymer blend. The blend studied was a polystyrene-d₈/polybutadiene (PSD/PB) mixture with a diblock copolymer composed of the same homopolymers. It was observed that the critical temperature of the blend, which has an upper critical solution temperature (UCST), decreased with increasing copolymer content and the kinetics of the phase separation via a spinodal decomposition mechanism slowed down in the presence of the copolymer. The features of the spinodal peak position and intensity as a function of time with and without copolymer additive were analyzed for near and off-critical compositions in various temperature jumps. The intermediate and late-stage growth rates do not follow a universal scaling function with the addition of diblock copolymers. © 1995 John Wiley & Sons, Inc.