一个增算子不动点定理及其在Banach 空间非线性方程的应用

给出了Banach空间的一个增算子不动点定理,将这一定理应用到Banach空间的积分-微分方程,给出了一类积分-微分方程的连续可微最大解和连续可微最小解的存在性定理.     

Bounds to optimal burn‐in and optimal work size

Burn‐in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, we consider the problem of determining the optimal burn‐in time and optimal work size maximizing the long‐run average amount of work saved per time unit in the computer applications. Assuming that the underlying lifetime distribution of the computer has an initially decreasing or/and eventually increasing failure rate function, an upper bound for the optimal burn‐in time is derived for each fixed work size and a uniform (with respect to the burn‐in time) upper bound for the optimal work size is also obtained. Furthermore, it is shown that a non‐trivial lower bound for the optimal burn‐in time can be derived if the underlying lifetime distribution has a large initial failure rate. Copyright © 2005 John Wiley & Sons, Ltd.     

A Fixed Point Theorem for Multi—valued Composite Increasing Operators

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Level of nodes in increasing trees revisited

Simply generated families of trees are described by the equation T(z) = ϕ(T(z)) for their generating function. If a tree has n nodes, we say that it is increasing if each node has a label ∈ { 1,…,n}, no label occurs twice, and whenever we proceed from the root to a leaf, the labels are increasing. This leads to the concept of simple families of increasing trees. Three such families are especially important: recursive trees, heap ordered trees, and binary increasing trees. They belong to the subclass of very simple families of increasing trees, which can be characterized in 3 different ways. This paper contains results about these families as well as about polynomial families (the function ϕ(u) is just a polynomial). The random variable of interest is the level of the node (labelled) j, in random trees of size n ≥ j. For very simple families, this is independent of n, and the limiting distribution is Gaussian. For polynomial families, we can prove this as well for j,n → ∞ such that n − j is fixed. Additional results are also given. These results follow from the study of certain trivariate generating functions and Hwang's quasi power theorem. They unify and extend earlier results by Devroye, Mahmoud, and others. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

FIXED POINTS AND COUPLED FIXED POINTS FOR INCREASING OPERATORS WITH APPLICMIONS TO DIFFERENTIAL INCLUSIONS IN BANACH SPACES

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Representing the mean residual life in terms of the failure rate

In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Whereas the failure rate can be expressed quite simply in terms of the mean residual life and its derivative, the inverse problem—namely that of expressing the mean residual life in terms of the failure rate—typically involves an integral of a complicated expression. In this paper, we obtain simple expressions for the mean residual life in terms of the failure rate for certain classes of distributions which subsume many of the standard cases. Several results in the literature can be obtained using our approach. Additionally, we develop an expansion for the mean residual life in terms of Gaussian probability functions for a broad class of ultimately increasing failure rate distributions. Some examples are provided to illustrate the procedure.     

Exponential distributions on semigroups

Three fundamental characterizations of the standard exponential distribution on [0, ) are the remaining life, memoryless and constant failure properties. Analogs of these properties are studied for distributions on a class of semigroups in which the semigroup operation replaces addition, a compatible partial order replaces the ordinary order, and a left-invariant measure replaces Lebesgue measure. Partial characterizations of exponential distributions on such semigroups are obtained and the semigroup formulation provides new characterizations of certain aging properties studied in reliability-increasing failure rate, new better than used, and increasing failure rate average.     

介质阻挡放电跃变升压模式下靶波斑图研究

在大气压氩气介质阻挡放电中,首次通过跃变外加电压得到了稳定的靶波斑图.实验分别研究了跃变再缓变和直接跃变升压模式下靶波斑图的稳定性和波长选择.研究发现,跃变再缓变升压之后得到的靶波斑图不稳定,其与螺旋波相互转换.在这种转换中,靶波每次出现的时间为几十毫秒.直接跃变升压得到的靶波斑图稳定性明显增强,其稳定时间通常为5 min以上.比较不同升压模式下靶波斑图的波长,发现直接跃变升压模式下波长随电压升高减小较快.综上表明,升压模式对靶波斑图的稳定性和波长都有影响. 关键词： 介质阻挡放电 靶波斑图 跃变升压 缓变升压     

Right Spread序的若干封闭性质

§1Introductionandmotivation Itisalwaysofinteresttocomparethevariabilityoftworandomvariablesinreliability theoryandeconomics.Thecomparisonsbasedonmomentssuchasvarianceandstandard deviationarenotveryinformativealthoughsuchmeasuresaresimpletouse.Meanwhile,sincethesecomparisonsarestaticones,andhencetheirapplicationsinsomefields,e.g.,reliabilityandfinance,arerestricted.Inthesefields,however,somedynamicalcomparisons areneeded.Asaresult,severalstochasticordersthataremorerefinedhavebeen establishedi…     

STUDY ON THE PROPERTIES OF BLEND OF NATURAL RUBBER LATEX/METHYL METHACRYLATE GRAFTED RUBBER LATEX BY GAMMA RADIATION

Natural rubber latex(NRL)and methyl methacrylate(MMA)grafted rubber latex were blended in different ratios and irradiated at various absorbed doses by gamma rays from Co-60 source at room temperature.The tensile properties, swelling ratio and permanent set were measured.The maximum tensile strength and modulus at 500% elongation were obtained at an absorbed dose of 8 kGy.Modulus increases from 6.99 MPa to 9.87 MPa for an increase in proportion of MMA grafted rubber from 40% to 60% in the blend at similar absorbed dose.Elongation at break and swelling ratio decrease with increasing absorbed dose as well as the MMA grafted rubber content in the blends.The decreasing trend of permanent set is high up to 5 kGy absorbed dose,and beyond that dose,it becomes almost flat.