Bayes估计的进一步研究及其Pitman最优性

对线性模型参数,讨论了Bayes估计的Pitman最优性,将已有结果进行了改进,去掉了附加条件,证明了在Pitman准则下,Bayes估计一致优于最小二乘估计(LSE),在此基础上,提出了一种基于先验信息的方差分量估计,通过和基于LSE的方差分量估计作比较,证明了新估计是无偏估计且有更小的均方误差．最后,证明了在Pitman准则下生长曲线模型参数的Bayes估计优于最佳线性无偏估计．     

基于ARX模型的压电智能结构振动预测控制

采用预测控制法对压电智能结构的振动主动控制进行了实验研究，通过实验方法建立了系统的ARX模型，并在此基础上设计了预测控制器对结构进行振动主动控制。实验结果验证了该方法在压电智能结构振动主动控制中的可行性和有效性。     

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??We study the linear quadratic optimal stochastic control problem which is jointly driven by Brownian motion and L\'{e}vy processes. We prove that the new affine stochastic differential adjoint equation exists an inverse process by applying the profound section theorem. Applying for the Bellman's principle of quasilinearization and a monotone iterative convergence method, we prove the existence and uniqueness of the solution of the backward Riccati differential equation. Finally, we prove that the optimal feedback control exists, and the value function is composed of the initial value of the solution of the related backward Riccati differential equation and the related adjoint equation.     

Vector-Orthogonality and Lanczos-Type Methods

A method for solving a linear system is defined. It is a Lanczos-type method, but it uses formal vector orthogonality instead of scalar orthogonality. Moreover, the dimension of vector orthogonality may vary which gives a large freedom in leading the algorithm, and controlling the numerical problems. The ideas of truncated and restarted methods are revisited. The obtained residuals are exactly orthogonal to a space of increasing dimension. Some experiments are done, the problem of finding automaticaly good directions of projection remains partly open.     

Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors

Bayesian inference is considered for the seemingly unrelated regressions with an elliptically contoured error distribution. We show that the posterior distribution of the regression parameters and the predictive distribution of future observations under elliptical errors assumption are identical to those obtained under independently distributed normal errors when an improper prior is used. This gives inference robustness with respect to departures from the reference case of independent sampling from the normal distribution.     

基于单纯形方法的双层线性规划全局优化算法

通过分析双层线性规划可行域的结构特征和全局最优解在约束域的极点上达到这一特性,对单纯形方法中进基变量的选取法则进行适当修改后,给出了一个求解双层线性规划局部最优解方法,然后引进上层目标函数对应的一种割平面约束来修正当前局部最优解,直到求得双层线性规划的全局最优解.提出的算法具有全局收敛性,并通过算例说明了算法的求解过程.     

Restorations of punctured languages and similarity of languages

Punctured languages are languages whose words are partial words in the sense that the letters at some positions are unknown. We investigate to which extent restoration of punctured languages is possible if the number of unknown positions or the proportion of unknown positions per word, respectively, is bounded, and we study their relationships for different boundings. The considered restoration classes coincide with similarity classes according to some kind of similarity for languages. Thus all results we can also formulate in the language of similarity. We show some hierarchies of similarity classes for each class from the Chomsky hierarchy and prove the existence of linear languages which are not δ ‐similar to any regular language for any δ < ½. For δ ≥ ½ this is unknown but it could only be possible in the case of non‐slender linear languages. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

线性方程组通解并行数值方法

1预备知识 线性方程组消息传递MIMD算法是20世纪90年代至今的活跃课题，但尚无此问题 的通用有效算法发表.用!.}.}表示矩阵列分块划分，记AX=b为[AI司.定理1、2是文 {l]、[s]成果综述和推广. 定理i[‘]设有线性方程组!e}己l，e〔尺”“m，d〔R”“‘，rank(e)=r.当且仅当rank(!     

多元线性回归应用于近代物理实验

本文介绍非线性方程转化直线性方程和多元线性回归法来分析近代物理实验中塞曼效应分裂干涉圆环多处选点测量的处理过程。     

Bayesian Probabilities and the Histories Algebra

We attempt a justification of a generalisation of the consistent histories programme using a notion of probability that is valid for all complete sets of history propositions. This consists of introducing Cox's axioms of probability theory and showing that our candidate notion of probability obeys them. We also give a generalisation of Bayes' theorem and comment upon how Bayesianism should be useful for the quantum gravity/cosmology programmes. PACS: 02.50.Cw;03.65.Ta;04.60.-m.