Approximation bounds for quadratic maximization and max-cut problems with semidefinite programming relaxation

In this paper,we consider a class of quadratic maximization problems.For a subclass of the problems,we show that the SDP relaxation approach yields an approximation solution with the ratio is dependent on the data of the problem with α being a uniform lower bound.In light of this new bound,we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at least α δd if every weight is strictly positive,where δd ＞ 0 is a constant depending on the problem dimension and data.     

对数似然比与整值随机变量序列的一类强律

本文引进对数似然比作为整值随机变量序列相对于服从几何分布的独立随机变量序列的偏差的一种度量,并通过限制对数似然比给出了样本空间的一个子集.在此子集上得到了一类用不等式表示的强律,其中包含整值随机变量序列与相对熵密度及几何分布的熵函数有关的若干极限性质.     

保偏光纤偏振器

利用保偏光纤的弯曲损耗特性绕制而成的光纤偏振器已有过报道。但文献[1]中报道的偏振器尺寸太大(φ=100mm),不利于光纤陀螺的小型化。本文介绍一种采用“熊猫”型光纤制成的偏振器,其尺寸较小(φ=30mm),消光比可达到33dB。     

工件带到达时间的两阶段柔性流水作业的近似算法

研究了工件带到时间的两阶段柔性流水作业的排序问题,基于求解流水作业和平行机问题的算法思想,提出两个相应的近似算法H(R)和H(MR(?)),证明了这两个算法的最坏情况性能比分别为3-1/m和2/5-1/m,讨论了界的紧性,并利用数值模拟以分析算法与最优值的近似性能比.     

Risk-neutral valuation with infinitely many trading dates

The first Fundamental Theorem of Asset Pricing establishes the equivalence between the absence of arbitrage in financial markets and the existence of Equivalent Martingale Measures, if appropriate conditions hold. Since the theorem may fail when dealing with infinitely many trading dates, this paper draws on the A.A. Lyapunov Theorem in order to retrieve the equivalence for complete markets such that the Sharpe Ratio is adequately bounded.     

Corrected mirror systems with double reflection

We propose objectives consisting of two mirrors with central holes for passage of a light beam. The optical layout ensures multiple reflection of rays from both mirrors. We consider several approaches to calculating the design parameters for which three and four aberrations do not occur. The objectives can be used in optical devices operating in the UV and IR regions of the spectrum. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 267–270, March–April, 2007.     

Tests of ordered hypotheses in linkage in heredity

The asymptotic null distribution of the likelihood ratio test for two cases of ordered hypotheses in a particular genetic model is considered. A simple iterative process is proposed in order to get the restricted estimates. It is shown that both tests have asymptotically a chi-bar squared distribution and the same size. A simulation study is also conducted in order to compare the usual unrestricted test with the corresponding one of ordered hypotheses. Finally, the results are extended to some special cases.     

总延误问题顺时安排法的性能比

给定一组工件的加工时间与工期，要求确定这些工件在一台机器上的加．工排列，使相应的总延误达到最小，这就是总延误问题．该问题在近年已被证明是NP困难的．由Wilkermn和Irwin（1971），林勋（1983）等所研究的顺时安排法能得到相邻交换意义下的局部解．在本文中，我们进一步证明该算法能得到前移邻域意义下的局部解，并确定了该算法的性能比．     

A bartlett-type adjustment for the likelihood ratio statistic with an ordered alternative

For testing the equality of normal variances with an increasing alternative, under the null hypothesis the likelihood ratio test statistic is asymptotically distributed as a mixture of chi-squared distributions. In this paper a Bartlett-type adjustment is proposed to improve the approximation of the null distribution of the likelihood ratio test statistic with an ordered alternative.     

Reactions of mercury salts with benzo- and tetrafluorobenzobarrelenes

Regiochemistry and stereochemistry of the addition of mercury salts to benzobarrelene and tetrafluorobenzobarrelene have been studied in acetic acid and methanol. The effect of the substrate structure on the regiochemistry of the reaction is discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1105–1108, June, 1994.