Computational complexity of LCPs associated with positive definite symmetric matrices

Murty in a recent paper has shown that the computational effort required to solve a linear complementarity problem (LCP), by either of the two well known complementary pivot methods is not bounded above by a polynomial in the size of the problem. In that paper, by constructing a class of LCPs—one of ordern forn 2—he has shown that to solve the problem of ordern, either of the two methods goes through 2 ⁿ pivot steps before termination.However that paper leaves it as an open question to show whether or not the same property holds if the matrix,M, in the LCP is positive definite and symmetric. The class of LCPs in whichM is positive definite and symmetric is of particular interest because of the special structure of the problems, and also because they appear in many practical applications.In this paper, we study the computational growth of each of the two methods to solve the LCP, (q, M), whenM is positive definite and symmetric and obtain similar results.This research is partially supported by Air Force Office of Scientific Research, Air Force Number AFOSR-78-3646. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon.     

Second order algorithms for the posynomial geometric programming dual,part I: Analysis

In this paper we analyse algorithms for the geometric dual of posynomial programming problems, that make explicit use of second order information. Out of two possible approaches to the problem, it is shown that one is almost always superior. Interestingly enough, it is the second, inferior approach that has dominated the geometric programming literature.This work was partially supported by the National Research Council of Canada, Grant A3552 and National Science Foundation Grant ENG78-21615.Earlier versions of this paper were presented at the Optimization Days Conference in Montreal (May 1976) and the TIMS meeting in Athens (July 1977).     

The a posteriori error estimates of Chebyshev–Petrov–Galerkin methods for second-order equations

In this paper, the a posteriori error estimates of Chebyshev–Petrov–Galerkin approximations are investigated. For simplicity, we choose the Poisson equation with Dirichlet boundary conditions to discuss the a posteriori error estimators, and deduce their efficient and reliable properties. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error estimators.     

KClO_4/Zr在石英管内的燃烧发射光谱与燃烧产物分析

为了研究燃烧条件对KClO_4/Zr烟火剂燃烧过程中光辐射性能的影响,考察了KClO_4/Zr在开放环境和不同规格封闭石英管内的燃烧发射光谱和燃烧产物。借助光纤光谱仪、光电二极管和示波器测试了烟火剂燃烧过程中的光辐射能量分布和闪光时间-强度曲线,分析了所得发射光谱在(590±10),(750±10)和(808±10)nm三个主吸收波段内的光谱效率,借助SEM表征了不同燃烧条件下KClO_4/Zr燃烧产物的形貌。结果表明:在开放条件下燃烧时,KClO_4/Zr的燃烧发射光谱在可见光到近红外的宽波段内,最强辐射出现在730~820nm波段。在石英管内封闭燃烧时,随着石英管体积的减少,在石英管外检测到的燃烧发射光谱强度逐渐减弱,光谱能量分布也呈现不同的变化规律,而且对火焰发射光谱分布进行处理后,随着石英管体积的变化,得到(590±10),(750±10)和(808±10)nm波段的光谱效率也呈现不同的变化规律。但是,随着石英管体积的减少,KClO_4/Zr烟火剂的爆燃闪光辐射时间逐渐缩短,峰值辐射强度逐渐提高。增加石英管的直径,有利于在管外获得更高的有效光辐射能量,减少石英管的直径,则有利于提高烟火剂的峰值辐射强度。随着管直径的增大,KClO_4燃烧更加充分,产物粒径较小,呈规则的球状。而管长度的改变对反应并无太大影响。     

Macromodeling of high-speed interconnects by positive interpolation of vertical segments

In this paper a novel macromodeling scheme is presented to model the per unit of length (p.u.l.) parameters of uniform transmission lines. In particular, it is focused on single on-chip interconnects, because their p.u.l. parameters are influenced by the presence of semiconductor (s) and as such exhibit a strong frequency-dependency, making the modeling process harder. Starting from a set of very accurate tabulated data samples, obtained by two-dimensional electromagnetic modeling, rational models for the four p.u.l. parameters are constructed. The novelty of the approach lies in the fact that the rational models are positive by construction and that a controllable accuracy is obtained. These models can then further be used to construct multivariate models, e.g., for variability analysis. Here, the novel scheme is applied to an on-chip inverted embedded microstrip line, of which the signal integrity behavior is assessed in both the frequency and the time domain, demonstrating the applicability of the macromodels.     

晶硅太阳电池原位光老化及热致输运机理

为研究晶体硅太阳电池在标准模拟光条件下的输出特性变化规律和电池内部载流子输运特性,采用原位光老化技术对被测电池进行光照处理,按标准测试实验流程测量电池的伏安特性及光谱响应等参量,发现原位光老化后太阳电池伏安特性各项参量衰减,导致电池效率降低;短波段光谱响应微量下降,是由于原位光老化过程中电池表面产生极微量的面缺陷导致经过硅表面的微量载流子被复合;而长波段响应明显降低,是由于晶硅内大量体缺陷被激活导致长波载流子在经过硅材料内部时被复合.随后将光老化后电池退火并测量比对电池各项特性参量,结果表明,退火对光老化后电池内部深层体缺陷具有较好的修复功能,但对浅层面缺陷没有修复功能,最终造成电池伏安特性参量和光谱响应只得到部分恢复.     

Spectral characterization and biocidal activity of organotin(IV) (E)-3-[(2′,6′-dichlorophenylamido)]propenoates

Biocidal and spectroscopic aspects of organotin(IV) complexes with (E)-3-[(2′,6′-dichlorophenylamido)]propenoic acid are described with support of elemental analysis. IR, ¹H, ¹³C, ¹¹⁹Sn NMR and mass spectral data suggest that the ligand is bidentate, coordinating through oxygen atoms and that diorganotin(IV) complexes are six-coordinate. Triorganotin(IV) carboxylates exist as pentacoordinated trigonal bipyramidal complexes in the solid state and tetrahedral ones in solution. The complexes have been screened against bacteria, fungi and brine-shrimp larvae to assess their biological activity.     

An unprecedented tetranuclear Zn(ΙΙ) complex with an unsymmetric Salen-type bisoxime ligand: synthesis,crystal structure,and spectral properties

A tetranuclear Zn(ΙΙ) complex, [Zn₄L₂(OAc)₂(CH₃OH)₂] with an unsymmetric Salen-type bisoxime (H₃L?=?6-hydroxy-4′,6′-dibromo-2,2′-[ethylenediyldioxybis(nitrilomethylidyne)]diphenol), has been synthesized and structurally characterized. There are two kinds of coordination geometry (trigonal bipyramidal and square pyramidal) in the Zn(ΙΙ) complex. The molecule has serious distortion probably from the asymmetry. The complex exhibits blue emission with the maximum emission wavelength λ _max?=?423?nm when excited with 340?nm.