Bayesian sequential reliability for Weibull and related distributions

Assume that the probability density function for the lifetime of a newly designed product has the form: [H(t)/Q()] exp{–H(t)/Q()}. The Exponential(), Rayleigh, WeibullW(, ) and Pareto pdf's are special cases.Q() will be assumed to have an inverse Gamma prior. Assume thatm independent products are to be tested with replacement. A Bayesian Sequential Reliability Demonstration Testing plan is used to eigher accept the product and start formal production, or reject the product for reengineering. The test criterion is the intersection of two goals, a minimal goal to begin production and a mature product goal. The exact values of various risks and the distribution of total number of failures are evaluated. Based on a result about a Poisson process, the expected stopping time for the exponential failure time is also found. Included in these risks and expected stopping times are frequentist versions, thereof, so that the results also provide frequentist answers for a class of interesting stopping rules.This research was supported by NSF grants DMS-8703620 and DMS-8923071, and forms part of the Ph.D. Thesis of the first author, the development of which was supported in part by a David Ross grant at Purdue University. The authors thank the editors and a referee for insightful comments and suggestions.     

The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

Derivative of the exponential mapping for infinite dimensional lie groups

It is proved that for infinite dimensional Lie groups in the sense of the differential calculus of Frölicher and Kriegl the derivative of the exponential mappings is given by the formula d(exp)(X)Y=d_exp(X)(e) ₀ ¹ Ad_exp(–tX) Y dt, where stands for the left translation ande is the neutral element.This work was supported by the Alexander von Humboldt-Stiftung.     

Convergence of splitting and Newton methods for complementarity problems: An application of some sensitivity results

This paper is concerned with two well-known families of iterative methods for solving the linear and nonlinear complementarity problems. For the linear complementarity problem, we consider the class of matrix splitting methods and establish, under a finiteness assumption on the number of solutions, a necessary and sufficient condition for the convergence of the sequence of iterates produced. A rate of convergence result for this class of methods is also derived under a stability assumption on the limit solution. For the nonlinear complementarity problem, we establish the convergence of the Newton method under the assumption of a pseudo-regular solution which generalizes Robinson's concept of a strongly regular solution. In both instances, the convergence proofs rely on a common sensitivity result of the linear complementarity problem under perturbation.This work was based on research supported by the National Science Foundation under grant ECS-8717968.     

On the convergence of the exponential multiplier method for convex programming

In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy proximal term in place of a quadratic. We strengthen substantially the available convergence results for these methods, and we derive the convergence rate of these methods when applied to linear programs.Research supported by the National Science Foundation under Grant DDM-8903385, and the Army Research Office under Grant DAAL03-86-K-0171.     

PHOTOCATALYTIC HYDROGEN EVOLUTION FROM WATER SPLITTING UNDER VISIBLE LIGHT IRRADIATION ON NOVEL PHOTOCATALYST FULLENES-PVP-ZN0.999NI0.001S

Fullerenes (C60/C70) linked up to Ni-doped ZnS through the medium of an amphalic polymer polyvinyl pyrrolidone (PVP) to form a new kind of photocatalyst for hydrogen evolution from aqueous Na2S/Na2SO3 solution under visible light irradiation, the photocatalytic activities of this novel photocatalyst C60/C70-PVP-Zn0.999Ni0.001S are 3-5 fold higher compared with that of precurse catalyst Zn0.999Ni0.001S. This result could be attributed to Schottky barrier layer built between C60/C70 and Zn0.999Ni0.001S due to the electro-negativity of C60 and characteristic of being used as a multiple electron acceptor. C60 or C60/C70, its moiety, with its low energy first excited singlet state, is a good energy acceptor and in addition readily accepts multiple electrons, making it a potential electron accumulate as we know, which could protect the separation between electrons and holes against combination. This is an important reason for the marked increase of amount of H2 evolution during the photocatalytic process for the composite system C60/C70-PVP-Zn0.999Ni0.001S.     

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利用太阳能光解水制氢和降解有机污染物对解决能源和环境问题具有重要意义，而可见光响应催化剂的研制是实现太阳光高效利用的关键。本文从可见光响应光催化剂的设计思路出发，从电子能带结构、固溶体结构和微观复合结构三方面介绍了目前光催化剂的研究进展和发展方向。     

呋喃西林水溶液在光和热作用下的稳定性

The influence of both light and heat on the stability of nitrofurazone aqueous solution was studied. Results show that in either heating experiments or the exposure to light at high temperatures, the degradation rate obeyed zero-order kinetics. The total rate constant ktotal caused by both light and heat can be divided into two parts: ktotal =kdark klight, where kdark and klight are the degradation rate constants caused by heat and light, respectively. The klight can be expressed as klight=Alight*exp(-Ea,light/RT)*E, where E is the illuminance of light, and Alight and Ea,light both are experimental constants. The values of these kinetic parameters were determined based on the experiments in the dark and upon exposure to three different light sources. Results show that the values of Alight and Ea, light varied with the light source. To save time, labor, and drugs, exponential heating experiments were employed and compared with the isothermal experiments. Results indicated that kinetic parameters obtained by exponential heating experiments are comparable to those obtained by isothermal experiments either in the dark or upon exposure to light.     

对一个大单轴磁各向异性镍(Ⅱ)配合物中的磁跃迁的直接观察

最近Ruamps和同事发现三角双锥构型的Ni（Ⅱ）配合物[Ni（Me₆tren）Cl]ClO₄（1，Me₆tren=tris（2-（dimethylamino）ethyl）amine）具有大的单轴磁各向异性（J.Am.Chem.Soc.，2013，135：3017-3026）。他们利用HF-EPR研究获得横向零场分裂（ZFS）参数E=1.56（5）cm^-1但未能确定轴向零场分裂参数D。在本工作中，我们利用0~17.5 T和5 K的变磁场远红外光谱（FIRMS）来检测自旋基态S=1中的M_S=±1和M_S=0态之间的磁跃迁。在FIRMS中直接观察到Zeeman分裂态之间的跃迁，得出轴向ZFS参数D=-110.7（3）cm^-1。我们对1的晶体结构进行了Hirshfeld表面分析，揭示了1分子中的阳离子与阴离子之间以及分子之间的相互作用。     

Band splitting in overloaded isocratic elution chromatography I. The experimental evidence

A series of samples of increasing volume (from 0.001 to 4.0 cm3), containing the same constant concentration (40 g/l) of two simple compounds, ethylbenzoate and 4-tert.-butylphenol were injected on a Kromasil-C18 column with methanol-water (62:38. v/v) as the mobile phase. Complex band profiles were observed when the volume of the sample became large enough and strong band interference took place. The analysis of the fractions collected during the elution of the mixed band demonstrates that, for samples larger than 2 cm3, the band of 4-tert.-butylphenol is split into two separate bands, one eluted before and the other eluted after the band of ethylbenzoate. Such a phenomenon has never been observed yet in RPLC, under isocratic elution conditions.