On guaranteed stability of uncertain linear systems via linear control

This paper addresses the problem of stabilizing an uncertain linear system. The uncertaintyq(·) which enters the dynamics is nonstistical in nature. That is, noa priori statistics forq(·) are assumed; only boundsQ on the admissible variations ofq(·) are taken as given. The results given here applied to so-called matched systems differ from previous results in two ways. Firstly, the stabilizing control in this paper is linear; for this same class of problems, many of the existing results would require a nonlinear control. Furthermore, those results which do in fact yield linear controls are only valid when a certain matrix (q) (formed using the given data) is negative definite for allq Q. In contrast, the theory given here only requires compactness of the bounding setQ. Secondly, we show that the so-called matching conditions (used in earlier work) can be generalized so as to encompass a larger class of dynamical systems.This research was supported by the US Department of Energy under Contract No. ET-78-S-01-3390.     

茜素红与壳聚糖的相互作用机理研究

应用光谱法研究在pH=5.0的反应体系中壳聚糖（CTS）与茜素红（AR）的结合 反应，考察了反应体系中AR/CTS摩尔比、NaCl浓度及CTS的脱乙酰度对茜素红与壳 聚糖相互作用的影响，通过实验测得CTS对AR的最大结合数N_E=4.78×10~3，理论 模型预测最大结合数N_c=4.73×10~3，实验值与理论值一致，并对壳聚糖与茜素红 的相互作用机理提出了合理的解释。     

Three-dimensional aromaticity in deltahedral boranes and carboranes

Methods derived from topology and graph theory indicate that the deltahedral boranes B _n H _n ^2– and the corresponding carboranes C₂B_n–2H _n (6 n 12) may be regarded as three-dimensional delocalized aromatic systems in which surface bonding and core bonding correspond to -bonding and -bonding, respectively, in planar polygonal two-dimensional hydrocarbons CinnH _n ^(n–6)+ (n=5/7). The two extreme types of topologies which may be used to model core bonding in deltahedral boranes and carboranes are the deltahedral (D _n ) topology based on the skeleton of the underlying deltahedron and the complete (K _n ) topology based on the corresponding complete graph. Analyses of the Hoffmann-Lipscomb LCAO extended Hückel computations, the Armstrong—Perkins—Stewart self-consistent molecular orbital computations, and SCF MOab initio GAUSSIAN-82 computations on B₆H₆ ^2– indicate that the approximation of the atomic orbitals by the sum of the molecular orbitals, as is typical in modernab initio computations, leads to significantly weaker apparent core bonding approximated more closely by deltahedral (D _n ) topology than by complete (K _n ) topology.This work was presented at the Workshop The Modern Problems of Heteroorganic Chemistry sponsored by the A. N. Nesmeyanov Institute of Organoelement Compounds of the Russian Academy of Sciences (May 8–13, 1993).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1353–1360, August, 1993.     

Infinitesimal obstructions to weakly mixing

Let ^t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M ⁿ , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d ^t and, for each x M, we define a smooth real function _x (t) : (1 + _i (t)), where the _i(t) are the eigenvalues of AA ^T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d^2t , restricted to v at the point _x ^-t M ⁿ.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that _x ^' (t) 0 for all x M and real t; then, if _x ^t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.     

Time-resolved fluorescence analysis of the mobile flavin cofactor in p -hydroxybenzoate hydroxylase

Conformational heterogeneity of the FAD cofactor in p-hydroxybenzoate hydroxylase (PHBH) was investigated with time-resolved polarized flavin fluorescence. For binary enzyme/substrate (analogue) complexes of wild-type PHBH and Tyr222 mutants, crystallographic studies have revealed two distinct flavin conformations; the ‘in’ conformation with the isoalloxazine ring located in the active site, and the ‘out’ conformation with the isoalloxazine ring disposed towards the protein surface. Fluorescence-lifetime analysis of these complexes revealed similar lifetime distributions for the ‘in’ and ‘out’ conformations. The reason for this is twofold. First, the active site of PHBH contains various potential fluorescence-quenching sites close to the flavin. Fluorescence analysis of uncomplexed PHBH Y222V and Y222A showed that Tyr222 is responsible for picosecond fluorescence quenching free enzyme. In addition, other potential quenching sites, including a tryptophan and two tyrosines involved in substrate binding, are located nearby. Since the shortest distance between these quenching sites and the isoalloxazine ring differs only little on average, these aromatic residues are likely to contribute to fluorescence quenching. Second, the effect of flavin conformation on the fluorescence lifetime distribution is blurred by binding of the aromatic substrates: saturation with aromatic substrates induces highly efficient fluorescence quenching. The flavin conformation is therefore only reflected in the small relative contributions of the longer lifetimes.     

Dynamic surface tension of micellar solutions studied by the maximum bubble pressure method

A theoretical model for the dynamic surface tension of an air bubble expanding in micellar surfactant solution is proposed. The model accounts for the effect of expansion of the bubble surface during the adsorption of surfactant molecules (monomers) and the effect of disintegration of polydisperse micelles on the surfactant diffusion. Assuming small deviations from equilibrium and constant rate of expansion analytical expression for the surface tension and the subsurface concentration of monomers as a function of time is derived. The characteristic time of micellization is computed from the experimental data for two surfactants (sodium dodecyl sulfate and nonylphenol polyglycol ether) obtained by the maximum bubble pressure method.     

Hamiltonian graphs of given order and minimum algebraic connectivity

In this paper, we study the algebraic connectivity of a Hamiltonian graph, and determine all Hamiltonian graphs whose algebraic connectivity attain the minimum among all Hamiltonian graphs on n vertices.     

多对一双方匹配市场中的最优化

在双方市场中定义的博弈概念，可以使市场同方参与者的收益同时达到最大．这种最优化存在的理论依据是选择匹配的稳定性．用博弈论的分析与证明方法研宄多对一双方匹配市场中的最优化．在替代偏好和LAD（Law of Aggregate Demend）偏好下，证明由企业作选择的选择函数一定是个稳定匹配，由工人做选择的选择函数也是一个稳定匹配．