Precise bounds for the petersen time-varying real parameter uncertainty system stabilized via linear static controllers

Using a class of linear static controllers, we stabilize the Petersen open-loop two-dimensional linear system (Ref. 1), which consists of one time-varying uncertainty in the state matrixA and one timevarying uncertainty in the input matrixB. We show that the worst-case uncertainty strategy for the closed-loop system is a piecewise constant strategy of the angular state with three switches on the half-turn, –/2/2; it is unique with respect to a set of measure zero. Formulas are derived for the worst-case half-turn radius gainr _HT as a function of the parameters of the class of stabilizing linear static controllers. Using the class of scalar-quadratic Lyapunov functions, we show that a necessary and sufficient condition for the closed-loop system to be robustly stable against all time-varying admissible uncertainties is thatr _HT be less than unity. The bound on the time-varying real parameter uncertainties for the closed-loop system to be robustly stable is derived for the class of linear static feedback controllers. We obtain stabilizing linear static controllers such that the bound is as close to infinity as desired. The derived results are compared with numerical results obtained using commerical robust-control software.     

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution belongs to the range of the operator (T ^* T) ^v , o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India.     

Effective electromagnetic and chiral parameters of chiral composite material

The effective parameters of chiral composite are studied using a simple model, that is, randomly oriented non-interacting wire helices embedded in a nonchiral host medium. It is found that both the effective permittivity and permeability are independent on the handedness of the chiral objects while the effective chirality admittance is dependent. It is also found that when the ratio of the radius of the chiral helix to its pitch is about 0.23, maximum chirality admittance is achieved. The effective parameters of equichiral sample are also discussed.     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.     

EHMO和模式识别法研究芬太尼衍生物的构效关系

自Hansch等创立QSAR法以来,药物构效关系的研究已获得较大的进展。本文将模式识别法用于芬太尼衍生物构效关系的研究,将该类药物的分子结构看作与生物活性具有对应关系的表现形式——模式,以药物分子结构中有关取代基的多个量子化学参数为数量化的模式向量成分。将已知生物活性的药物作为模式识别训练点,则所得模式识别分类图反映了该类药物的生物活性与其量子化学结构特征参数间的统计学意义的关系。它既可用来探寻高效药物的结构参数,又能预测新设计药物生物活性的等级或类别。     

Self aggregation of binary mixtures of sodium dodecyl sulfate and polyoxyethylene alkyl ethers in aqueous solution

The mixed micelles of sodium dodecyl sulphate (SDS) with Brij35 and Brij 97 were studied separately by fluorescence measurement using pyrene as fluorescent probe. In the range of 0–1.0 mole fraction (X) of added SDS to Brij solutions, the cmc value of the mixed micelles varies from 0.085 to 8 mmol with Brij 35 and 0.04 to 8 mmol with Brij 97. The aggregation number also changes. A measure of the stability of mixed micelles is also presented. The interaction parameter ₁₂ and the chain–chain contribution parameter (B₁) are extracted from the analysis of the results. This parameter B₁ is related to the standard free energy change associated with the introduction of one ionic species into a nonionic micelle coupled with the release of one nonionic species from the micelle. The clouding behaviour of Brij 97 in the presence of SDS was investigated and the associated thermodynamic parameters of clouding were generated and discussed.     

Thermodynamic parameters of interaction of HC1 with alcohols in water Ⅲ.HCl-ethanol-water system at 278.15-318.15 K

Pt,H2(g,p0)HCl(mE)|AgCl-AgPt, H2(g, p0)|HCl(mE), EtOH(mN)|AgCl-Ag have been measured at 10 degree intervals from 278.15 to 318.15 K, where EtOH refers to ethanol, mE=0.005-0.1 mol.kg-1, mN=0.4-1.0 mol.kg-1. The salting constant kS of EtOH by HCl and the thermodynamic parameters of interaction, fEN(gEN> hEN, sEN] cP,EN)> of EtOH with HCI in water have been evaluated. It has been shown that kS>0, gEN>0,hEN>0, SEN>0 ,and cp,EN<0.The signs of these parameters and the temperature dependence of them have been discussed on the basis of structural interaction and the group additivity models.     

THE PARAMETER KERNELS FOR THE LINEAR INVERSION OF THE FREE OSCILLATION OF THE EARTH (Ⅰ)

In the linear inversion of the radial variation of the parameters of the Earth by usingthe observed frequencies of various normal modes of free oscillation of the earth, it is neces-sary to know the values of the kernels of the parameters ρ, μ and λ. This paper describesthe methods of the derivation of the formulas of these kernels. This is the first part of thepaper in which only the toroidal oscillations are considered. They are much simpler thanthose of the spheroidal ones, that we will consider in the second part of the paper. The data of the two types of oscillations are equally important in the solution of theinversion problem, and should be employed simultaneously, and we know that the toroidaloscillations are much simpler than the spheroidal ones, it seems wise to divide the whole programof the inversion problem into steps: first, by employing the toroidal data to correct the twoparameters ρ and μ in the mantle, then by using the spheroidal data to correct the remain-ing parameters, i.e. th     

非晶高聚物对聚(ε-己内酯)在其与苯乙烯-丙烯腈共聚物相容共混物中球晶生长速率的影响

本文研究了聚(ε-己内酯)(PCL)在其与苯乙烯-丙烯腈共聚物(SAN)的相容共混物中球晶生长速率与共混组成和结晶温度的关系.发现聚己内酯的球晶生长速率随着SAN的含量增加而下降.由于PCL与SAN是相容共混物,因此在用二次成核动力学方程描述PCL球晶生长速率时,我们引进了相互作用参数X.结果由共混体系的结晶动力学方程计算到的X值与由平衡熔点下降方法计算到的X_(23)值是相同的;而PCL晶体的折叠表面自由能则随着SAN含量的增加而下降.这些结果说明非晶高聚物SAN有碍于PCL球晶的生长.     

有机试剂结构与性质的研究XII有机试剂的pKa与改进的Swain－Lupton参数

有机试剂的ｐＫ０ａ是其重要的物化参数，它是有机试剂酸碱性的度量，决定其配合物的稳定性．根据Ｓｗａｉｎ－Ｌｕｐｔｏｎ的工作，每个取代基的效应可用两个参数：场／诱导效应参数与共振效应参数来描述．本文应用Ｈａｎｓｃｈ改进的参数值研究了ｐＫａ与取代基常数的相关性，建立了下式．ｐＫａ＝ｐＫ０ａ＋ｒ１Ｆ＋ｒ２Ｒ