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.     

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.     

固相配位化学反应研究 L ⅩⅩⅢ.等温电导法研究醋酸锰和草酸的室温固相化学反应

本文利用等温电导法考察了醋酸锰和草酸的室温固相配位化学反应的制样方法对实验结果的影响，并获得了该反应的动力学参量。     

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.     

Thermoanalytical study of glibenclamide and excipients

Summary Taking into account the problems of desertification and agricultural practices able to provide income to the population at the semi-arid region of North-East Brazil, this work presents the results of the chemical and thermal characterization by TG and DSC of the seed derivatives of Cnidoscolus quercifolius, hereinafter called faveleira, aiming at the application of these materials as an alternative of food source for animals and for the human population at this region. The faveleira seed derivatives present thermodynamic properties similar to the ones of other foods utilized for human use, as well as an acceptable calorific value. According to TG and DSC results, was verified that the faveleira derivatives presents good thermal and oxidative stabilities.     

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     

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