ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {X_n, n≥1} be a strictly stationary sequence of random variables, whichare either associated or negatively associated, f(·) be their common density. In this paper,the author shows a central limit theorem for a kernel estimate of f(·) under certain regularconditions.     

论鲍照的咏物赋

鲍照是一位伟大的诗人,同时亦是一位杰出的辞赋家。咏物赋是鲍照赋中数量最多的类型,最能体现鲍赋的艺术魅力;鲍照咏物赋的艺术特质:一,体物特征,包括动态的生命之美、流动的画面美、形似与神似之美、修辞之美以及险奇之美等;二,言志特征,包括言志的复杂性以及言志的方式等。体物与言志结合,真正达到了《文心雕龙.诠赋》所称赏的“符采相胜”的艺术境界。     

ON THE PRODUCT OF GATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Frechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.     

有限循环群的Fuzzy子群的等价类数

有限循环群G的F子群可以有无数个．但是．若当两个F子群的水平集构成的集合相等就称其等价的话，那么其等价类数是有限的。通过研究群的合成群列、商群列以及数的因数列和极大因数列找出了有限循环群的极大F子群和F子群的等价类数的求解公式．并给出二者之间的关系式．     

Synthesis of bioactive indolocarbazoles: synthesis, nucleophilic ring-opening and chiral base desymmetrisation of a cyclic sulfate intermediate

A number of new functionalised bridged indolocarbazole systems have been prepared by ring-opening reactions of a key cyclic sulfate intermediate, prepared from the corresponding diol by the action of sulfuryl diimidazole and DBU. The same cyclic sulfate also undergoes an unprecedented asymmetric rearrangement to a chiral ketone, on treatment with a chiral lithium amide base.     

Measurements of Time-Varying Characteristics of Optical Signals and Inhomogeneities of Tested Substances with Additional Phase Modulation

The problem of investigation of the amplitude and phase structure of a time-varying probing optical signal and the structure of time-varying inhomogeneities of a substance tested by this signal is considered. The analysis is concerned, in particular, with determination of the structure of signals and processes with resolution in the pico- and femtosecond range. The scheme used for the analysis is based on registration of four spatially separated spectra of the studied radiation. The spectra are formed in a four-channel scheme with a twin-wave Michelson interferometer and a spectral device. Modulators based on electrooptical crystals (perovskites) are placed in the channels. The sum spectra are formed: without modulators, with the effect of either of the modulators, and with both of them affecting the radiation. The effect of the studied substance implies either modulating the radiation (in this case it is described by multiplication) or redistributing the radiation (then it is described by convolution).     

Cl/HN3/I2全气相化学激光体系的化学动力学模拟计算

 对Cl/HN₃/I₂产生NCl(a)/I激光的过程进行了化学动力学计算，主要考察了Cl,HN₃和I₂的初始粒子数密度及其配比对小信号增益系数的影响。结果发现,当温度为400K, 初始Cl粒子数密度为1×10¹⁵，1×10¹⁶和1×10¹⁷cm^-3时,小信号增益系数分别达到1.6×10^-4,1.1×10^-3和1.1×10^-2cm^-1，获得最佳小信号增益系数的HN₃和I₂的初始粒子数密度分别为初始Cl粒子数密度的1～2倍和2%～4%。同时，对Cl，HN₃和I₂配比对小信号增益系数和增益持续时间的影响进行了讨论。     

The long‐time behaviour of the thermoconvective flow in a porous medium

For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd.     

Existence and uniform decay for Euler–Bernoulli beam equation with memory term

In this article we prove the existence of the solution to the mixed problem for Euler–Bernoulli beam equation with memory term. The existence is proved by means of the Faedo–Galerkin method and the exponential decay is obtained by making use of the multiplier technique combined with integral inequalities due to Komornik. Copyright © 2004 John Wiley & Sons, Ltd.     

Uniformity in Computable Structure Theory

We investigate the effects of adding uniformity requirements to concepts in computable structure theory such as computable categoricity (of a structure) and intrinsic computability (of a relation on a computable structure). We consider and compare two different notions of uniformity, previously studied by Kudinov and by Ventsov. We discuss some of their results and establish new ones, while also exploring the connections with the relative computable structure theory of Ash, Knight, Manasse, and Slaman and Chisholm and with previous work of Ash, Knight, and Slaman on uniformity in a general computable structure-theoretical setting.