再论Mobius变换中的n阶循环群判据

用二阶方阵的幂运算取代Mobius变换的迭代运算,导出了Mobius变换为n阶循环群的判据,并对判据进行了简化,最后给出了它们的应用.     

散射体排列方式对二维磁振子晶体带隙结构的影响

本文采用平面波展开法数值计算了由铁圆柱分别按正方排列、三角排列以及六角排列在氧化铕基底材料中构成的二维磁振子晶体带结构,讨论了散射体的不同排列方式对磁振子晶体带隙结构的影响.计算结果表明,三角排列散射体的磁振子晶体能够获得最大的自旋波带隙结构. 关键词： 磁振子晶体 带隙 排列方式     

均聚物结晶与熔融化转变的稳态和亚稳态统计理论Ⅴ 分子分凝统计结晶动力学—结晶增长速率对结晶生长机制和高聚物起始结构的依赖性

首先对结晶增长速率同浓度、分子量和链柔性依赖性进行总结，然后基于微晶核和粒——高分子键组网络结构模型和高分子分子分凝统计结晶动力学，根据高分子链组是微晶粒同连接链段复合体的结构特征及它们间存在的四个相关性（并存性、简并性、顺反式构象共存性和物料守恒性）的事实，成功地把连接链段缩短增长动力方程同微晶粒体积增大增长动力方程有机结合在一起，从理论上创建出一种微晶粒数增长速率和微晶粒尺寸增长速率表达的一般化计算法，推导出结晶体系的微晶粒数增长速率和微晶粒尺寸增长速率同四种增长机制（近邻折叠，近邻伸直，近邻折叠同近邻伸直并联并存和近邻折叠同近邻伸直串联并存）、结晶温度和高分子起始结构（分子量）间定量表达式．当把分子量的指数同链的构象分数相连后，就又从理论上得到了分子量指数同温度和链柔性间的关系式，并讨论了它们同增长机制间的关系，最后以大量结晶动力学实验数据对上述所得到的关系式进行了验证，结果表明它们均能同实验结果很好符合．     

Spherically symmetric static inhomogeneous cosmological models

Spherically symmetric static cosmological models filled with black-body radiation are considered. The models are isotropic about a central observer but inhomogeneous. It is suggested that the energy density of the free gravitational field, which is coupled to the isotropic radiation energy density, might play an important role in generating sufficient field (vacuum) energy (when converted into thermal energy) and initiate processes like inflation. On the central world line the energy density of the free gravitational field vanishes whereas the proper pressure and density of the isotropic black-body radiation are constants. Further, it is shown that the cosmological constant is no more arbitrary but given in terms of the central pressure and density. Also, at its maximum value the energy density of the free gravitational field is proved to be equal to one third of the combined value of radiation pressure and density.     

Patterns at the onset of electroconvection in freely suspended smectic films

We report the results of experiments on electrically driven convection that occurs in a thin, freely suspended film of smectic A liquid crystal when an electric field is applied in the plane of the film. Convection in a vortex pattern is found above a well-defined critical voltage. The film behaves as a two-dimensional isotropic liquid: neither its thickness nor the director field are modified by the flow. We present measurements of the critical voltage at the onset of convection in two experimental configurations—one which allows the injection of charges into the film from the electrodes, and one which does not. When injection is present, the critical voltage for the onset of flow increases monotonically with increasing frequency of applied field. With no injection, there is no instability at DC and the critical voltage diverges there. The nature of the flow pattern observed at onset changes with frequency. Below a certain frequency the film flows in vortices that extend over the width of the film; above this frequency the flow is confined to two lines of smaller vortices localized along the electrodes. We present a simple discussion of the mechanisms which drive the convection.     

The effect of a coriolis force on Taylor-Couette flow

Taylor-Couette flow subject to a Coriolis force is studied experimentally and numerically. In the experiment, the Couette apparatus is mounted on a turntable with the axis of the cylinders orthogonal to the rotation vector of the turntable. The Coriolis force stabilizes the fluid against the onset of Taylor vortices and alters the velocity fields, both above and below the transition from the initial flow. At small dimensionless turntable frequencies, the transition yields time-independent Taylor vortices which are tilted with respect to the cylinder axis. At larger there is a direct transition to turbulence. We determine the first-order correction to the classical Couette initial flow, to account for the effects of the Coriolis force, by expanding in powers of. We present numerical results for the axial velocity (the only nonvanishing correction term to order) in the infinite-cylinder approximation.     

High-density properties of hard spheres within a modified Percus-Yevick theory: The role of thermodynamic consistency

Using an integral-equation approach based upon an approximation for the tail function, the equilibrium properties of a system of hard spheres are studied with special concern for the behavior in the region of close packing. The closure adopted is such that full, internal consistency is ensured in the thermodynamics of the model with respect to both the two zero-separation theorems as well as to the more standard virial and fluctuation routes to the equation of state. The scheme also makes use of the continuity properties of the tail function and of the cavity distribution function at contact. These properties are explictly tested in the low-density limit up to the fourth derivative. The theory generates an equilibrium branch bounded on the high-density side by a point corresponding to a packing fraction0.78, a value which closely matches Rogers' least upper bound for the densest packing of spheres. The pair structure of the fluid in the state of random close packing is also compared to the type of local order predicted by the theory at similar densities.     

Sufficiency and fuzziness in random experiments

In previous papers, the consequences of the “presence of fuzziness” in the experimental information on which statistical inferences are based were discussed. Thus, the intuitive assertion «fuzziness entails a loss of information» was formalized, by comparing the information in the “exact case” with that in the “fuzzy case”. This comparison was carried out through different criteria to compare experiments (in particular, that based on the “pattern” one, Blackwell's sufficiency criterion). Our purpose now is slightly different, in the sense that we try to compare two “fuzzy cases”. More precisely, the question we are interested in is the following: how will different “degrees of fuzziness” in the experimental information affect the sufficiency? In this paper, a study of this question is carried out by constructing an alternative criterion (equivalent to sufficiency under comparability conditions), but whose interpretation is more intuitive in the fuzzy case. The study is first developed for Bernoulli experiments, and the coherence with the axiomatic requirements for measures of fuzziness is also analyzed in such a situation. Then it is generalized to other random experiments and a simple example is examined.     

Some exact expressions for the mean and higher moments of functions of sample moments

Examples of exact expressions for the moments (mainly of the mean) of functions of sample moments are given. These provide checks on alternative developments such as asymptotic series for n, and simulation processes. Exact expressions are given for the mean of the square of the sample coefficient of variation, particularly in uniform sampling; Frullani integrals studied by G. H. Hardy arise. It should be kept in mind that exact results for (joint) moment generating functions (mgfs) are of interest as they produce a means of obtaining exact results for (cross) moments—including moments with negative indices. Thus an exact expression for the joint mgf of the 1st two noncentral moments can be used to obtain the mean of the (c.v.)² (but not for the mean of the c..). A general expression is given for the moment generating function of the sample variance. The limitations of Fisher's symbolic formula for the characteristic function of sample moments (or more general statistics) are noted.This research was sponsored by the Applied Mathematical Sciences Research program, Office of Energy Research, U. S. Department of Energy under contract DE-AC0584OR21400 with the Martin Marietta Energy Systems. Inc.     

Bernstein算子导数与高阶光滑性

借助于r阶光滑模ωφ^r(f,t)φ是一般的步权函数，给出了Bernstein算子导数与函数高阶光滑性之间的等价关系。