Generalized Bayes minimax estimators of the mean of multivariate normal distribution with unknown variance

We construct a broad class of generalized Bayes minimax estimators of the mean of a multivariate normal distribution with covariance equal to σ²I_p, with σ² unknown, and under the invariant loss δ(X)−θ²/σ². Examples that illustrate the theory are given. Most notably it is shown that a hierarchical version of the multivariate Student-t prior yields a Bayes minimax estimate.     

Elimination of surface scratch/texture on the surface of single crystal Si substrate in chemo-mechanical grinding (CMG) process

Si wafers are widely used as a substrate material for fabricating ICs. The quality of ICs depends on the quality of Si wafers. The chemo-mechanical grinding (CMG) with soft abrasive grinding wheels (SAGW) has been recently found to be a great potential process for machining Si wafers to generate superior surface quality at low cost. However, there have been very few studies on observing variation of topography of scratch/texture and understanding basic eliminating process of scratch/texture on the ground Si wafer. Furthermore, few reports on the variation of surface roughness and material removal rate (MRR) during CMG process and relationship between MRR and surface roughness during CMG process are presented. In this paper, a series of CMG experiments have been conducted to study the elimination process of artificial scratches created on etched Si surfaces and residual textures induced by SD1500 diamond wheel in CMG process, and to understand the topography variations of Si surfaces and some basic grinding characteristics during CMG process.     

Existence of positive solutions for a singular <Emphasis Type="Italic">p</Emphasis>-Laplacian differential equation

In this paper, we are concerned with the existence of positive solutions for a singular p-Laplacian differential equation
（φp（u＇））＇＋β/r φp（u＇）-γ ｜u＇｜^p/u ＋ g（r）=0,0〈r〈1,
subject to the Dirichlet boundary conditions： u（0） = u（1） =0, where φp（s） = ｜sl^P-2s,p 〉 2,β 〉0, γ〉（p-1）/p （β ＋ 1）, and g（r） ∈ C^1 [0, 1] with g（r） 〉 0 for all τ ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution.     

Statistical properties of world investment networks

We have performed a detailed investigation on the world investment networks constructed from the Coordinated Portfolio Investment Survey (CPIS) data of the International Monetary Fund, ranging from 2001 to 2006. The distributions of degrees and node strengths are scale-free. The weight distributions can be well modeled by the Weibull distribution. The maximum flow spanning trees of the world investment networks possess two universal allometric scaling relations, independent of time and the investment type. The topological scaling exponent is 1.17±0.02 and the flow scaling exponent is 1.03±0.01.     

A two-step estimator of the extreme value index

In this paper, we build a two-step estimator , which satisfies , where is the well-known maximum likelihood estimator of the extreme value index. Since the two-step estimator can be calculated easily as a function of the observations, it is much simpler to use in practice. By properly choosing the first step estimator, such as the Pickands estimator, we can even get a shift and scale invariant estimator with the above property. The author thanks Laurens de Haan for motivating this work and giving helpful comments. The author also thanks two anonymous referees for their useful comments.     

Distortion of optical feedback signals in microchip Nd:YAG lasers subjected to external multi-beam interference feedback

This paper proposes a theoretical analysis for the characteristics of an external cavity Nd:YAG laser with feedback of multiple-beam interference, which is induced by the multi-reentrance of the light from the external Fabry--Perot cavity. The theoretical model considers the multiple beam interference of the external Fabry--Perot cavity. It is found that the optical feedback signals are distorted to pulse waveforms instead of the sinusoidal ones in conventional feedback. The experimental results are in good agreement with the theoretical analysis. The obtained theoretical and experimental results can advance the development of a laser feedback interferometer.     

On simultaneous approximation by lagrange interpolating polynomials

This paper considers to replace △_m(x)=(1-x~2)~2(1/2)/n +1/n~2 in the following result for simultaneousLagrange interpolating approximation with (1-x~2)~2(1/2)/n: Let f∈C_(-1.1)~0 and r=[(q+2)/2],then|f~(k)(x)-P_~(k)(f,x)|=O(1)△_(n)~(a-k)(x)ω(f~(a),△(x))(‖L_n-‖+‖L_n‖),0≤k≤q,where P_n( f ,x)is the Lagrange interpolating polynomial of degree n+ 2r-1 of f on the nodes X_nU Y_n(see the definition of the text), and thus give a problem raised in [XiZh] a complete answer.     

胆囊癌的傅里叶变换红外光谱研究

运用衰减全反射(attenuated total reflection,ATR)探头与傅里叶变换红外(Fourier transform infra-red,FTIR)光谱仪,测定并分析了新鲜离体的胆囊癌组织18例和良性组织139例的FTIR光谱。结果表明:(1)胆囊癌的1 167和1 123 cm-1谱带的峰位显著地向低波数移动(P0.05),而1 309 cm-1谱带的峰位显著地向高波数移动(P0.05)。(2)胆囊癌组织光谱多个峰的相对强度I2 856/I1 461,I1 167/I1 461,I1 123/I1 461和I1 082/I1 461明显升高(P0.05)。(3)1 167和1 082 cm-1谱带的半高宽显著升高(P0.05),谱带1 461 cm-1的半高宽则显著降低(P0.05)。(4)癌组织1 750 cm-1谱带的出现几率明显增加(P0.05)。与胆囊良性组织相比较,癌组织光谱中与脂类、糖和核酸相关的谱带均发生了明显的变化。     

相对论磁控管中自磁场的影响

针对相对论磁控管中自磁场的产生与分布、自磁场对电子运动的影响以及自磁场对互作用的影响进行了深入分析。分析认为,由于自磁场分布的不对称,自磁场对不同区域电子束的作用不同。加速器一侧的电子束受到更明显的自磁场作用,促使此区域的电子束角向速度增加,直接激化模式竞争。同时,如果阴极比较靠近加速器一侧的1/4区域(距磁控管对称中心大约1/4高度）,模式竞争将进一步被激化。     

基于原始波形测量的脉冲电场探测器

介绍了脉冲电场微分测量和原始波形测量的基本原理,设计研制了一系列不同灵敏度的脉冲电场原始波形测量系统,分析了脉冲电场探测器的理论修正模型。该测量系统主要包括天线模块、积分器模块、放大和驱动模块以及光电传输模块,利用同轴型TEM小室对测量系统进行了时域标定。结果表明:测量系统的前沿响应时间小于1.0 ns,系统输出脉冲平顶在10.0μs内下降不超过5%,测量系统输出幅度与电场强度在20 dB的动态范围内呈线性关系,该系列探测器可以用来测量最小10 V/m、最大100 kV/m的电场强度,满足高空电磁脉冲标准环境的测量要求。