奇异协方差阵下有效前沿及有效组合的解析解

利用广义逆矩阵研究了协方差阵奇异时的投资组合问题,突破了传统方法中要求协方差阵可逆的限制,得到了证券市场存在有效组合的充要条件,并给出了有效前沿和有效组合的解析解,成功地推广了经典Markowitz模型,同时还将有助于证券组合有效子集的深入研究.     

光纤—自聚焦棒—反射器耦合系统的后向耦合系数

用光线矩阵方法推导了光纤-自聚焦棒-反射器在共轴耦合情况下的后向耦合系数;分析了它与耦合系统结构参数之间的关系.用计算机模拟画出了反射器为平面镜的系统的后向耦合系数和后向耦合损耗的曲线分布,计算曲线与实验结果大致符合.     

Estimating the covariance matrix and the generalized variance under a symmetric loss

For estimating the power of a generalized variance under a multivariate normal distribution with unknown means, the inadmissibility of the best affine equivariant estimator relative to the symmetric loss is shown, and a class of improved estimators is given. The problem of estimating the covariance matrix is also discussed.     

任意除环上一矩阵方程组的一般解与中心和反中心对称解

Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.     

Photocatalytic membrane of a novel high surface area TiO2 synthesized from titanium triisopropanolamine precursor

Photocatalytic membrane was successfully prepared using an efficiently high surface area TiO₂ catalyst, dispersed into polyacrylonitrile matrix. The catalyst was directly synthesized using titanium triisopropanolamine as a precursor. The membranes were characterized using FT‐IR, TGA, SEM and their photocatalytic performance tested, viz. stability, permeate flux and photocatalytic degradation of 4‐NP. We find that polyacrylonitrile is an effective matrix, showing high stability and low permeate flux. The amount of TiO₂ loaded in the membrane was varied between 1, 3 and 5 wt% to explore the activity and stability of membranes in the photocatalytic reaction of 4‐NP. As expected, the higher the loading of TiO₂ loaded, the higher the resulting catalytic activity. Copyright © 2006 John Wiley & Sons, Ltd.     

Decentralized Guaranteed Cost Control for Uncertain Large-Scale Systems Using Delayed Feedback: LMI Optimization Approach

In this paper, we propose a design method of guaranteed cost controllers for uncertain large-scale systems with time delays in subsystem interconnections using delayed feedback. Using the Lyapunov method, a linear matrix inequality (LMI) optimization problem is formulated to design a delayed feedback controller which minimizes the upper bound of a given quadratic cost function. A numerical example is included to illustrate the design procedures.Communicated by Q. C. ZhaoThe authors thank the Associate Editor and three anonymous referees for careful reading and useful suggestions.     

Determining Causal Skeletons with Information Theory

Modeling a causal association as arising from a communication process between cause and effect, simplifies the discovery of causal skeletons. The communication channels enabling these communication processes, are fully characterized by stochastic tensors, and therefore allow us to use linear algebra. This tensor-based approach reduces the dimensionality of the data needed to test for conditional independence, e.g., for systems comprising three variables, pair-wise determined tensors suffice to infer the causal skeleton. The only thing needed is a minor extension to information theory, namely the concept of path information.     

Adaptive synchronization of chaotic systems with less measurement and actuation

We investigate the synchronization problem between identical chaotic systems only when necessary measurement(output) and actuation(input) are needed to be implemented by the adaptive controllers. A sufficient condition is derived based on the Lyapunov stability theory and Schur complementary lemma. Moreover, the theoretic result is applied to the Rikitake system and the hyperchaotic Liu system to show its effectiveness and correctness. Numerical simulations are presented to verify the results.     

Phase-shift interferometry measured transmission matrix of turbid medium: Three-step phase-shifting interference better than four-step one

Transmission matrix(TM) is an important tool for controlling light focusing, imaging, and communication through turbid media. It can be measured by 3-step(TM3) or 4-step(TM4) phase-shifting interference, but the similarities and differences of the transmission matrices obtained by the two methods are rarely reported. Therefore, we make a quantitative comparison of the peak light intensity, signal-to-noise ratio, and average background of 24 × 24 = 576 focal points between paired samples(TM3–TM4) through the Wilcoxon rank sum test, and discuss the singular value of the transmission matrix and the focal peak. The comparative results of peak light intensity and signal-to-noise ratio show that there is a significant difference between the 3-step phase shift and the 4-step phase shift transmission matrixes. The focusing effect of the former is significantly better than that of the latter; interest concentrates on the focal intensity and singular value. The reciprocal of the singular value is proportional to the squared intensity, which is in accordance with singular value theory. The results of comparison of peak light intensity and signal-to-noise ratio strongly suggest that 3-step phase shift should be selected and used in applying the phase shift method to the measurement of the transmission matrix; and the singular value is of great significance in quantifying the focusing, imaging, and communication quality of the transmission matrix.     

An adsorption study of Sr2+ from saline sources by coconut shell charcoal

The adsorption potential of charcoal for the removal of heavy metal ions is well documented in the literature. However, its exploration for uptake of technologically valuable metal ions such as Sr²⁺ is poorly known. In this work, the batch adsorption study of Sr²⁺ ion from aqueous solution as well as from saline matrix (>3% of NaCl) onto charcoal has been carried out. The experiments were conducted with two charcoals, i.e., our prepared charcoal (coconut shell charcoal) and commercial charcoal. Strontium adsorption has been investigated as a function of its initial concentration, contact time, and varied mass of adsorbent. Equilibrium adsorption data were evaluated for Langmuir and Freundlich isotherm models. The adsorption capacities (mg/g) of Sr²⁺ present in the salt matrix onto coconut shell charcoal and commercial charcoal was found to be 18.4 and 22.2, respectively. Uptake of Sr²⁺ from subsoil brine onto coconut shell charcoal has been successfully demonstrated in this work.