Understanding the shape of the mixture failure rate (with engineering and demographic applications)

Mixtures of distributions are usually effectively used for modelling heterogeneity. It is well known that mixtures of DFR distributions are always DFR. On the other hand, mixtures of IFR distributions can decrease, at least in some intervals of time. As IFR distributions often model lifetimes governed by ageing processes, the operation of mixing can dramatically change the pattern of ageing. Therefore, the study of the shape of the observed (mixture) failure rate in a heterogeneous setting is important in many applications. We study discrete and continuous mixtures, obtain conditions for the mixture failure rate to tend to the failure rate of the strongest populations and describe asymptotic behaviour as t→∞. Some demographic and engineering examples are considered. The corresponding inverse problem is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

A Small Molecule Affecting the Replication of Trinucleotide Repeat d(GAA)n

A newly designed ligand, methylcarbamoylnaphthyridine dimer (MCND), was synthesized and characterized. Ligand binding to d(GAA)₁₀ was investigated by UV thermal denaturation, circular dichroism spectroscopy, surface plasmon resonance, and cold‐spray‐ionization time‐of‐flight mass spectrometry. The results indicated that MCND bound to the d(GAA)_n repeat to form a stable hairpin structure with a major binding stoichiometry of 3:1. The most likely binding site was identified as the G? G mismatch in the AGA/AGA triad. The polymerase stop assay showed that MCND binding to the d(GAA)_n repeat effectively interfered with the extension of the primer at the first two GAA sites on the template with both prokaryotic Taq DNA polymerase and human DNA polymerase α.     

Sawyer's duality principle for grand Lebesgue spaces

The aim of this paper is to extend Sawyer's duality principle from the cone of decreasing functions of the Lebesgue space to the cone of decreasing functions of the grand Lebesgue space and to prove the boundedness of classical Hardy operators in the grand Lebesgue spaces.     

基于多步长梯度特征的红外弱小目标检测算法

针对低信噪比红外图像中弱小目标检测难的问题,在分析红外弱小目标各向梯度特征的基础上,提出了一种新的红外弱小目标检测算法.该算法基于红外弱小目标各向梯度均快速下降的特征,首先根据目标大小在待检测点上、下、左、右选取4个参考点,根据多步长下待检测点与参考点之间的最大梯度特征,判定潜在目标;然后通过连续3帧检测信息的融合,确...     

Characterization of the nanopore structures of PAN-based carbon fiber precursors by small angle X-ray scattering

The nanopore structures in precursors are crucial to the performance of PAN-based carbon fibers. Four carbon-fiber precursors are prepared. They are bath-fed filaments (A), water-washing filaments (B), hot-stretching filaments (C) and drying-densification filaments (D). Synchrotron radiation small angle X-ray scattering is used to probe and compare the nanopore structures of the four fibers. The nanopore size, discrete volume distribution, nanopore orientation degree along the fiber axis and the porosity are obtained. The results demonstrate that the nanopores are mainly formed in the water-washing stage. During the processes of the subsequent production technologies, the slenderness ratio of nanopores and their orientation degree along the fiber axis increase further and simultaneously, the porosity decreases. These results are helpful for improving the performance of the final carbon fibers.     

Maximising entropy on the nonparametric predictive inference model for multinomial data

The combination of mathematical models and uncertainty measures can be applied in the area of data mining for diverse objectives with as final aim to support decision making. The maximum entropy function is an excellent measure of uncertainty when the information is represented by a mathematical model based on imprecise probabilities. In this paper, we present algorithms to obtain the maximum entropy value when the information available is represented by a new model based on imprecise probabilities: the nonparametric predictive inference model for multinomial data (NPI-M), which represents a type of entropy-linear program. To reduce the complexity of the model, we prove that the NPI-M lower and upper probabilities for any general event can be expressed as a combination of the lower and upper probabilities for the singleton events, and that this model can not be associated with a closed polyhedral set of probabilities. An algorithm to obtain the maximum entropy probability distribution on the set associated with NPI-M is presented. We also consider a model which uses the closed and convex set of probability distributions generated by the NPI-M singleton probabilities, a closed polyhedral set. We call this model A-NPI-M. A-NPI-M can be seen as an approximation of NPI-M, this approximation being simpler to use because it is not necessary to consider the set of constraints associated with the exact model.     

Eliciting density ratio classes

The probability distributions of uncertain quantities needed for predictive modelling and decision support are frequently elicited from subject matter experts. However, experts are often uncertain about quantifying their beliefs using precise probability distributions. Therefore, it seems natural to describe their uncertain beliefs using sets of probability distributions. There are various possible structures, or classes, for defining set membership of continuous random variables. The Density Ratio Class has desirable properties, but there is no established procedure for eliciting this class. Thus, we propose a method for constructing Density Ratio Classes that builds on conventional quantile or probability elicitation, but allows the expert to state intervals for these quantities. Parametric shape functions, ideally also suggested by the expert, are then used to bound the nonparametric set of shapes of densities that belong to the class and are compatible with the stated intervals. This leads to a natural metric for the size of the class based on the ratio of the total areas under upper and lower bounding shape functions. This ratio will be determined by the characteristics of the shape functions, the scatter of the elicited values, and the explicit expert imprecision, as characterized by the width of the stated intervals. We provide some examples, both didactic and real, and conclude with recommendations for the further development and application of the Density Ratio Class.     

Synchronous working vacation policy for finite-buffer multiserver queueing system

This paper presents modeling and analysis of unreliable Markovian multiserver finite-buffer queue with discouragement and synchronous working vacation policy. According to this policy, c servers keep serving the customers until the number of idle servers reaches the threshold level d; then d idle servers take vacation altogether. Out of these d vacationing servers, d_W servers may opt for working vacation i.e. they serve the secondary customers with different rates during the vacation period. On the other hand, the remaining d − d_W = d_V servers continue to be on vacation. During the vacation of d servers, the other e = c − d servers must be present in the system even if they are idle. On returning from vacation, if the queue size does not exceed e, then these d servers take another vacation together; otherwise start serving the customers. The servers may undergo breakdown simultaneously both in regular busy period and working vacation period due to the failure of a main control unit. This main unit is then repaired by the repairman in at most two phases. We obtain the stationary performance measures such as expected queue length, average balking and reneging rate, throughput, etc. The steady state and transient behaviours of the arriving customers and the servers are examined by using matrix analytical method and numerical approach based on Runge-Kutta method of fourth order, respectively. The sensitivity analysis is facilitated for the transient model to demonstrate the validity of the analytical results and to examine the effect of different parameters on various performance indices.     

A thermodynamical gradient theory for deformation and strain localization of porous media

In this work, a thermodynamically consistent gradient formulation for partially saturated cohesive-frictional porous media is proposed. The constitutive model includes a classical or local hardening law and a softening formulation with state parameters of non-local character based on gradient theory. Internal characteristic length in softening regime accounts for the strong shear band width sensitivity of partially saturated porous media regarding both governing stress state and hydraulic conditions. In this way the variation of the transition point (TP) of brittle-ductile failure mode can be realistically described depending on current confinement condition and saturation level. After describing the thermodynamically consistent gradient theory the paper focuses on its extension to the case of partially saturated porous media and, moreover, on the formulation of the gradient-based characteristic length in terms of stress and hydraulic conditions. Then the localization indicator for discontinuous bifurcation is formulated for both drained and undrained conditions.     

舰船舷侧复合装甲结构抗动能穿甲模拟实验

以均质钢板前置复合材料板模拟舰船舷侧复合装甲结构,结合低速弹道冲击实验,分析了结构的 破坏模式和吸能机理,比较了复合材料板与均质钢板的抗弹性能。在此基础上,根据靶板破坏模式,得到了球 头弹穿透组合靶板的剩余速度预测公式,并与实验结果进行了比较。结果表明,复合材料板的面密度吸能远 大于均质钢板的;组合靶板中前置复合装甲板的破坏模式主要为纤维拉伸断裂,而钢质背板则由于前置复合 装甲板的影响,破坏模式主要为花瓣开裂破坏;将剩余速度理论预测值与实验数据进行比较,两者吻合较好。