Asymptotic Expansions for Large Deviation Probabilities of Noncentral Generalized Chi-Square Distributions

Asymptotic expansions for large deviation probabilities are used to approximate the cumulative distribution functions of noncentral generalized chi-square distributions, preferably in the far tails. The basic idea of how to deal with the tail probabilities consists in first rewriting these probabilities as large parameter values of the Laplace transform of a suitably defined function f_k; second making a series expansion of this function, and third applying a certain modification of Watson's lemma. The function f_k is deduced by applying a geometric representation formula for spherical measures to the multivariate domain of large deviations under consideration. At the so-called dominating point, the largest main curvature of the boundary of this domain tends to one as the large deviation parameter approaches infinity. Therefore, the dominating point degenerates asymptotically. For this reason the recent multivariate asymptotic expansion for large deviations in Breitung and Richter (1996, J. Multivariate Anal.58, 1–20) does not apply. Assuming a suitably parametrized expansion for the inverse g⁻¹ of the negative logarithm of the density-generating function, we derive a series expansion for the function f_k. Note that low-order coefficients from the expansion of g⁻¹ influence practically all coefficients in the expansion of the tail probabilities. As an application, classification probabilities when using the quadratic discriminant function are discussed.     

Bounds for the tail distribution in a queue with a superposition of general periodic Markov sources: theory and application

An efficient yet accurate estimation of the tail distribution of the queue length has been considered as one of the most important issues in call admission and congestion controls in ATM networks. The arrival process in ATM networks is essentially a superposition of sources which are typically bursty and periodic either due to their origin or their periodic slot occupation after traffic shaping. In this paper, we consider a discrete-time queue where the arrival process is a superposition of general periodic Markov sources. The general periodic Markov source is rather general since it is assumed only to be irreducible, stationary and periodic. Note also that the source model can represent multiple time-scale correlations in arrivals. For this queue, we obtain upper and lower bounds for the asymptotic tail distribution of the queue length by bounding the asymptotic decay constant. The formulas can be applied to a queue having a huge number of states describing the arrival process. To show this, we consider an MPEG-like source which is a special case of general periodic Markov sources. The MPEG-like source has three time-scale correlations: peak rate, frame length and a group of pictures. We then apply our bound formulas to a queue with a superposition of MPEG-like sources, and provide some numerical examples to show the numerical feasibility of our bounds. Note that the number of states in a Markov chain describing the superposed arrival process is more than 1.4 × 10⁸⁸. Even for such a queue, the numerical examples show that the order of the magnitude of the tail distribution can be readily obtained.     

The Product of Independent Random Variables with Regularly Varying Tails

A distribution is said to have regularly varying tail with index – (0) if lim _x(kx,)/(x,)=k ^– for each k>0. Let X and Y be independent positive random variables with distributions and , respecitvely. The distribution of product XY is called Mellin–Stieltjes convolution (MS convolution) of and . It is known that D() (the class of distributions on (0,) that have regularly varying tails with index –) is closed under MS convolution. This paper deals with decomposition problem of distributions in D() related to MS convolution. A representation of a regularly varying function F of the following form is investigated: F(x)= _k=0 ^n–1 b _k f(a ^k x), where f is a measurable function and a and b _k (k=1,...,n–1) are real constants. A criterion is given for these constants in order that f be regularly varying. This criterion is applicable to show that there exist two distributions and such that neither nor belongs to D() (>0) and their MS convolution belongs to D().     

A Comparison of Methods for Estimating the Extremal Index

The extremal index, (01), is the key parameter when extending discussions of the limiting behavior of the extreme values from independent and identically distributed sequences to stationary sequences. As measures the limiting dependence of exceedances over a threshold u, as u tends to the upper endpoint of the distribution, it may not always be informative about the extremal dependence at levels of practical interest. Therefore we also consider a threshold-based extremal index, (u). We compare the performance of a range of different estimators for and (u) covering processes with < 1 and = 1. We find that the established methods for estimating actually estimate (u), so perform well only when (u) . For Markov processes, we introduce an estimator which is as good as the established methods when (u) but provides an improvement when (u) < = 1. We illustrate our methods using simulated data and daily rainfall measurements.     

Phenomenology of neutrino oscillations

The phenomenology of solar, atmospheric, supernova and laboratory neutrino oscillations is described. Analytical formulae for matter effects are reviewed. The results from oscillations are confronted with neutrinoless double beta decay.     

环氧树脂/层状无机物纳米复合材料

概述了近年来国内外环氧树脂／层状无机物纳米复合材料的研究现状，详细介绍厂环氧树脂／蒙脱土、环氧树脂／水滑石及环氧树脂／石墨三种代表性环氧树脂纳米复合材料的制备、性能及研究进展。     

HPLC检测器的线性动态范围及其测试方法的研究

简单论述了ＨＰＬＣ检测器（ＨＰＬＣＤ）的线性动态范围（ＬＤＲ）的重要性，提出了对光学式ＨＰＬＣＤ的ＬＤ测试的一种新方法，同时对有关问题进行了讨论。     

The further crystallographic refinement of trichosanthin at 2.7A resolution and the comparison among the three molecular structures in two crystal forms

The three-dimensional structure of trichosanthin at 2.7A resolution has been improved further, by refitting one of the C-terminal tails, adjusting 16 residues in the molecular surface regions, discarding some water molecules with high B values, and adjusting weights during the further refinement. The R-factor has been reduced to 18.5% and the r.m.s deviations from ideal geometry are also improved. The structures of the two molecules in the monoclinic asymmetric unit and the only molecule in the orthorhombic asymmetric unit are compared with one another. The main-chain structures for most of the residues in the three molecules are substantially the same. However, the courses of the three C-terminal tails are completely different, and the intermolecular interactions resulting from the particular packing of the molecules in the crystals account for the differences. The strand Be-2 and the preceding B-turn in small domain show large r.m.s. deviations among the three molecules and they are also involved in i     

高Al含量Ni/Al双氢氧化物的结构及循环伏安特性

为了合成具有优良电化学性能的Ni系列碱性电池氢氧化镍正极活性物质,本文以硫酸镍和硫酸铝以及硝酸镍和硝酸铝为原料,在搅拌及同时超声波作用的条件下,用共沉淀方法合成了Al含量为Ni含量30(mol)%～50(mol)%的高Al含量的NiAl层状双氢氧化物(HACNiAlLDHs)。用XRD技术表征了HACNiAlLDHs样品的晶体结构特征;采用粉末微电极循环伏安(CV)技术研究了典型HACNiAlLDHs样品的电化学性能。结果表明,合成的HACNiAlLDHs样品为αNi(OH)2;观察到HACNiAlLDHs电极在反向扫描过程中的“第2个还原电流峰”,该还原峰可能为γNiOOH—→αNi(OH)2的还原电流和γNiOOH—→αNi(OH)2还原“滞后”的电流的重叠电流峰;Al3 以及SO42-杂质离子对“第2个还原电流峰”的出现起到重要作用;SO42-在电化学反应过程中使γNiOOH的还原“滞后”,并使得αNi(OH)2在碱性介质中更加稳定;以硝酸盐为原料合成的LNHACNiAlLDHs样品具有优良的电化学性能,如可逆性、电极活性物质利用率、放电性能、循环性能和析氧过电位。     

双抗体夹心酶联免疫检测法测定蓖麻毒素

建立了双抗体夹心酶联免疫法检测蓖麻毒素的方法。优化了最佳蓖麻毒素多克隆抗体包被浓度和包被方法、蓖麻毒素单克隆抗体工作浓度、酶标记二抗体工作浓度和显色时间等实验条件。方法的线性范围在1.2~10.0μg/L之间,线性回归方程y=0.05x 0.42,相关系数为0.9962,检出限为0.2μg/L。将该方法用于检测实际水样蓖麻毒素加标样品,回收率为91.7%~104.0%;检测实际土壤加标样品,回收率为83.3%~98.0%;检测奶粉加标样品,回收率为83.3%~94.0%;检测实际血液加标样品,回收率为75.0%~82.0%。