Multivariable BC Type Askey-Wilson Polynomials With Partly Discrete Orthogonality Measure

The multivariable BC type Askey-Wilson polynomials are considered for a parameter domain such that the orthogonality measure has partly discrete and partly continuous support.     

A positive radial product formula for the Dunkl kernel

It is an open conjecture that generalized Bessel functions associated with root systems have a positive product formula for nonnegative multiplicity parameters of the associated Dunkl operators. In this paper, a partial result towards this conjecture is proven, namely a positive radial product formula for the non-symmetric counterpart of the generalized Bessel function, the Dunkl kernel. Radial here means that one of the factors in the product formula is replaced by its mean over a sphere. The key to this product formula is a positivity result for the Dunkl-type spherical mean operator. It can also be interpreted in the sense that the Dunkl-type generalized translation of radial functions is positivity-preserving. As an application, we construct Dunkl-type homogeneous Markov processes associated with radial probability distributions.

     

非线性多类变量有限元的进展

本文介绍了非线性多类变量有限元,即非线性的杂交元和拟协调元近几年来的发展及其变分基础.     

单变量有限元的新思考:精化直接刚度法

对单变量有限元和多变量有限元进行了综合分析和比较。其中包括有限元法的单元的可靠性问题:收敛性,坐标不变性,伪零能模式;单元的性能:计算精度,对畸变网格的适应性及解除闭锁、解的晃动现象等问题。进一步对单变量有限元提出新的思考,用精化直接刚度法发展单变量有限元,使之能兼备单变量有限元与多变量有限元之长,克服两者之短。     

多变量样条元法分析弹性地基板的弯曲,振动与稳定问题

本文应用双三次乘积型二元B样条函数来构造弹性地基板的位移、弯矩和扭矩等多种场函数，由混合变分原理导出多变量样条无法方程．文中，对弹性地基板的弯曲、振动与稳定问题作了分析与计算．由于，本文方法设定了各自独立的场函数，因此，所算得的场未知量如位移、弯矩和扭矩值的精度均比较高。     

Statistical identification and optimal control of thermal power plants

Statistical system identification and its use for the optimal control of thermal power plants are discussed. The analysis of the plant dynamics and derivation of the state-space representation are performed by fitting a multivariate AR model to the plant data obtained by an experiment. The basic concept of the power plant control and the motivation that necessitated the statistical approach are explained in the introduction. Practical procedure for the implementation of the method is described in detail with examples obtained from actual plants. The main items discussed are the selection of system variables by means of relative power contribution analysis, determination of the state equation and adjustment of the optimal feedback gain by digital simulation technique. Finally, excellent performance of the proposed control system is demonstrated by the operating records of 500 MW and 600 MW supercritical plants.     

Modelling of characteristic delays in multivariable control systems wcbsl

Pure time delays in multivariable control systems place severe restrictions on achievable feedback performance. This paper considers an approach to modelling distributed time-delay systems using discrete convolution. The basis for convolution algebra is briefly outlined and the new concepts of characteristic pattern and vector delays are introduced. A process control example is given that illustrates the concepts and shows typical results obtained using WCBSL (Windows Convolution-Based Simulation Language)     

Optimal Transient Response Shaping of the Servomechanism Problem

The problem of constructing a controller which gives a desirable transient response, e.g., a time response which is smooth, ripple-free, fast, and with negligible interaction effects, is considered in this paper for the servomechanism problem for continuous linear time invariant (LTI) systems. It is shown that this may be accomplished by constructing a controller which minimizes the following cheap control performance index: J=₀ {(+e)(+e)+(u)(u)}dwhere e is the error in the system and (u) is a polynomial function of u and its derivatives; here, >0 and is a diagonal matrix with nonnegative elements. A number of examples are included to illustrate the type of results which may be obtained.     

Determination of Saikosaponins in Bupleuri Radix by Micellar Electrokinetic Chromatography with Experimental Design

The important pharmacological components of Bupleuri radix include saikosaponins a–d. A multivariable approach with experimental design was employed in this study to determine four saikosaponins in different species of Bupleuri radix by cyclodextrin-modified micellar electrokinetic chromatography. Compared to traditional multiple-parameter investigations, the current experimental design can shorten the time necessary for method development, and the multivariable approach can be used to evaluate the separation capability of the method and to explore the interactions of the different parameters. The significant influences of two experimental variables, including the concentration of γ-cyclodextrin and the percentage of methanol, on the responses were investigated using chromatographic resolution statistics. The optimized conditions were as follows: 25?mM of borate (pH 9.18) containing 50?mM of sodium dodecyl sulfate, 5?mM of γ-cyclodextrin, and 15% methanol (v/v) as running buffer. After the separation conditions were optimized and good resolution was acquired, solid phase extraction was performed to reduce the interference of crude extracts of Bupleurum kaoi and Bupleurum chinense DC. The simple and rapid analytical method was successfully applied, allowing for the determination of four saikosaponins and the identification of species of Bupleuri radix.     

多重C~*-动力系统在Hilbert C~*-模上的膨胀

研究了多重C~*-动力系统在Hilbert C~*-模上表示的膨胀.设(A,α)是一个多重C~*-动力系统,(π,T,E)是(A,α)的行压缩协变表示,证明了存在(π,T,E)的等距膨胀(ρ,V,F).