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.     

Synthesis, crystal structure and magnetic property of a new 1D molecular material [1-(4′-chlorobenzyl)-4-aminopyridinium](+) bis(maleonitriledithiolato)nickel(-)

A new ion-pair complex, [1-(4′-chlorobenzyl)-4-aminopyridinium](+)bis(maleonitrile-dithiolato)nickel(−),[ClbzPyNH₂][Ni(mnt)₂] (1), has been prepared and characterized. X-ray single crystal structure conforms that the Ni(mnt)₂⁻ anions and [ClbzPyNH₂]⁺ cations of 1 form completely segregated uniform stacking columns with the Ni?Ni distance 3.944 Å in the Ni(mnt)₂⁻ stacking column. The temperature dependence of the magnetic susceptibility reveals that 1 undergoes a magnetic transition, and exhibits ferromagnetic interaction in the high-temperature phase and spin gap system in the low-temperature phase.     

Syntheses, structures, optical properties, and theoretical calculations of Cs2Bi2ZnS5, Cs2Bi2CdS5, and Cs2Bi2MnS5

Three new compounds, Cs₂Bi₂ZnS₅, Cs₂Bi₂CdS₅, and Cs₂Bi₂MnS₅, have been synthesized from the respective elements and a reactive flux Cs₂S₃ at 973 K. The compounds are isostructural and crystallize in a new structure type in space group Pnma of the orthorhombic system with four formula units in cells of dimensions at 153 K of a=15.763(3), b=4.0965(9), c=18.197(4) Å, V=1175.0(4) Å³ for Cs₂Bi₂ZnS₅; a=15.817(2), b=4.1782(6), c=18.473(3)  Å, V=1220.8(3)  ų for Cs₂Bi₂CdS₅; and a=15.830(2), b=4.1515(5), c=18.372(2) Å, V=1207.4(2) Å³ for Cs₂Bi₂MnS₅. The structure is composed of two-dimensional _∞²[Bi₂MS₅²⁻] (M=Zn, Cd, Mn) layers that stack perpendicular to the [100] axis and are separated by Cs⁺ cations. The layers consist of edge-sharing _∞¹[Bi₂S₆⁶⁻] and _∞¹[MS₃⁴⁻] chains built from BiS₆ octahedral and MS₄ tetrahedral units. Two crystallographically unique Cs atoms are coordinated to S atoms in octahedral and monocapped trigonal prismatic environments. The structure of Cs₂Bi₂MS₅, is related to that of Na₂ZrCu₂S₄ and those of the AMM′Q₃ materials (A=alkali metal, M=rare-earth or Group 4 element, M′= Group 11 or 12 element, Q=chalcogen). First-principles theoretical calculations indicate that Cs₂Bi₂ZnS₅ and Cs₂Bi₂CdS₅ are semiconductors with indirect band gaps of 1.85 and 1.75 eV, respectively. The experimental band gap for Cs₂Bi₂CdS₅ is ≈1.7 eV, as derived from its optical absorption spectrum.     

Nanocrystals for large Stokes shift-based optosensing

The influence of Stokes shift in optosensing was discussed. Then, the current status of large Stokes shift-based optosensing was reviewed here.     

Length of the flooded zone in the column inlet and evaluation of different retention gaps for capillary gas chromatography

In on-column or in splitless injection with recondensation of the solvent, the length of the flooded zone in the column inlet depends primarily on the wettability of the internal wall of the inlet. For columns with a coated inlet this explains why peak distortion due to band broadening in space by a certain sample volume is pronounced in one case and hardly observable in another. Glass or fused silica capillaries silylated with diphenyltetramethyldisilazane were found to give optimal retention gaps. They combine thorough and thermostable deactivation with good wettability and low retention power. On the other hand it is very easy to deactivate fused silica capillaries with Carbowax. The resulting retention gaps are suitable for a wide range of applications and are particularly attractive for the analysis of dirty samples which require frequent replacement of the inlet.     

内含式化合物X@B12P12的结构与稳定性研究

采用B3LYP/6-31G*方法，对内含式化合物X@B₁₂P₁₂(X=Li^0/+、Na^0/+、K^0/+、Be^0/2+、Mg^0/2+、Ca^0/2+、H和He)的不同对称性构型进行了计算，讨论其最稳定构型的几何参数、布居分析、偶极矩、电离势、包含能、振动频率、能隙和自旋密度． 发现在X@B₁₂P₁₂化合物中，客体X=Li、Na^0/+、K^0/+、Mg^0/2+、Ca^0/2+和He处在偏离笼的中心0.006 nm的半径内． Be²⁺沿着C₃轴偏离中心点0.279 nm． 在Be@B₁₂P₁₂和H@B₁₂P₁₂的基态结构中，Be和H与笼上的B原子成键． 除Li@B₁₂P₁₂、 Be²⁺@B₁₂P₁₂和He@ B₁₂P₁₂外， 其余结构为C_s对称稳定构型．     

Analysis of petroleum fractions by on-line micro HPLC-HRGC coupling,involving increased efficiency in using retention gaps by partially concurrent solvent evaporation

Two-dimensional chromatography of gasoline by on-line coupled HPLC-HRGC, as described in this paper, allows separate GC analysis of paraffins and aromatics. The GC system contains a retention gap of only 10 m length for introducing HPLC fractions of 100 μl volume. This becomes possible through evaporation of part of the solvent during introduction of the HPLC eluent. This “partially concurrent solvent evaporation” technique allows transfer of large volumes of HPLC eluent into relatively short retention gaps, maintaining the full efficiency of the solvent effects in reconcentrating the bands of the early eluted solutes.     

Optical and Electrical Properties of Polymerizing Plasmas and Their Correlation with DLC Film Properties

Diamond-like carbon (DLC) films were grown from radiofrequency plasmas of acetylene-argon mixtures, at different excitation powers, P. The effects of this parameter on the plasma potential, electron density, electron temperature, and plasma activity were investigated using a Langmuir probe. The mean electron temperature increased from about 0.5 to about 7.0 eV while the mean electron density decreased from about 1.2 × 10⁹ to about 0.2 × 10⁹ cm^–3 as P was increased from 25 to 150 W. Both the plasma potential and the plasma activity were found to increase with increasing P. Through actinometric optical emission spectrometry, the relative concentrations of CH, [CH], and H, [H], in the discharge were mapped as a function of the applied power. A rise in [H] and a fall in [CH] with increasing P were observed and are discussed in relation to the plasma characteristics and the subimplantation model. The optical properties of the films were calculated from ultraviolet-visible spectroscopic data; the surface resistivity was measured by the two-point probe method. The optical gap, E _G, and the surface resistivity, _s, fall with increasing P. E _G and _s are in the ranges of about 2.0–1.3 eV and 10¹⁴–10¹⁶ /, respectively. The plasma power also influences the film self-bias, V _b, via a linear dependence, and the effect of V _b on ion bombardment during growth is addressed together with variation in the relative densities of sp² and sp³ bonds in the films as determined by Raman spectroscopy.     

Photophysics of ruthenium(II) complexes with 2-(2′-pyridyl) pyrimidine and 2,2′-bipyridine ligands in fluid solution

The photophysics of three complexes of the form Ru(bpy)₃₋(pypm)²⁺ (where bpy2,2′-bipyridine, pypm 2-(2′-pyridyl)pyrimidine and P=1, 2 or 3) was examined in H₂O, propylene carbonate, CH₃CN and 4:1 (v/v) C₂H₅OH---CH₃OH; comparison was made with the well-known photophysical behavior of Ru(bpy)₃²⁺. The lifetimes of the luminescent metal-to-ligand charge transfer (MLCT) excited states were determined as a function of temperature (between −103 and 90 °C, depending on the solvent), from which were extracted the rate constants for radiative and non-radiative decay and ΔE, the energy gap between the MLCT and metal-centered (MC) excited states. The results indicate that ^*Ru(bpy)₂(pypm)²⁺ decays via a higher lying MLCT state, whereas ^*Ru(pypm)₃²⁺ and ^*Ru(pypm)₂(bpy)²⁺ decay predominantly via the MC state.     

Properties of the random search in global optimization

From theorems which we prove about the behavior of gaps in a set ofN uniformly random points on the interval [0, 1], we determine properties of the random search procedure in one-dimensional global optimization. In particular, we show that the uniform grid search is better than the random search when the optimum is chosen using the deterministic strategy, that a significant proportion of large gaps are contained in the uniformly random search, and that the error in the determination of the point at which the optimum occurs, assuming that it is unique, will on the average be twice as large using the uniformly random search compared with the uniform grid. In addition, some of the properties of the largest gap are verified numerically, and some extensions to higher dimensions are discussed. The latter show that not all of the conclusions derived concerning the inadequacies of the one-dimensional random search extend to higher dimensions, and thaton average the random search is better than the uniform grid for dimensions greater than 6.This paper is based on work started in the Statistics Department of Princeton University when the first author was visiting as a Research Associate. Part of this research was supported by the Office of Naval Research, Contract No. 0014-67-A-0151-0017, and by the US Army Research Office—Durham, Contract No. DA-31-124-ARO-D-215.2 The authors wish to thank B. Omodei for his careful work in preparing the programs for the results of Figs. 1–2 and Table 1. The computations were performed on the IBM 360/50 of the Australian National University's Computer Centre. Thanks are also due to R. Miles for suggestions regarding the extension of the results to multidimensional regions, and to P. A. P. Moran and R. Brent for suggestions regarding the evaluation of the integral ₀ ¹ ... ^0/1 (x ₁ ² + ... +x _n ^/2 )^1/2 dx ₁ ...dx _n.