Large Deviations Rate Function for Polling Systems

In this paper, we identify the local rate function governing the sample path large deviation principle for a rescaled process n ^–1 Q _nt , where Q _t represents the joint number of clients at time t in a polling system with N nodes, one server and Markovian routing. By the way, the large deviation principle is proved and the rate function is shown to have the form conjectured by Dupuis and Ellis. We introduce a so called empirical generator consisting of Q _t and of two empirical measures associated with S _t , the position of the server at time t. One of the main step is to derive large deviations bounds for a localized version of the empirical generator. The analysis relies on a suitable change of measure and on a representation of fluid limits for polling systems. Finally, the rate function is solution of a meaningful convex program. The method seems to have a wide range of application including the famous Jackson networks, as shown at the end of this study. An example illustrates how this technique can be used to estimate stationary probability decay rate.     

The quickest path problem with batch constraints

The quickest path problem has been proposed to cope with flow problems through networks whose arcs are characterized by both travel times and flowrate constraints. Basically, it consists in finding a path in a network to transmit a given amount of items from a source node to a sink in as little time as possible, when the transmission time depends on both the traversal times of the arcs and the rates of flow along arcs. This paper is focused on the solution procedure when the items transmission must be partitioned into batches with size limits. For this problem we determine how many batches must be made and what the sizes should be.     

双限制Tobit自回归GARCH模型和价格限制下股票日收益率模型估计

本文提出了一个在价格限制即涨跌停板制度存在的情况下，股票日收益率可能遵循的时间序列模型一双限制Tobit自回归GARCH模型，建立了此模型的最大似然估计法(MLE)，用Monte Carlo实验研究了最大似然估计量性质．作为此模型应用，我们对一个上海股市的股票日收益率模型参数进行了估计。     

带警戒限的均值控制图中警戒参数的优化

带警戒限的均值控制图中 ,如何恰当选取警戒参数B1、B2 的值是实际应用的关键。本文提供了两个计算机程序 ,可根据不同的要求设计出恰当的方案。     

Viscous limits for piecewise smooth solutions of the p-system

We study the zero-dissipation problem for a one-dimensional model system for the isentropic flow of a compressible viscous gas, the so-called p-system with viscosity. When the solution of the inviscid problem is piecewise smooth and having finitely many noninteracting shocks satisfying the entropy condition, there exists unique solution to the viscous problem which converges to the given inviscid solution away from shock discontinuities at a rate of order ε as the viscosity coefficient ε goes to zero. The proof is given by a matched asymptotic analysis and an elementary energy method. And we do not need the smallness condition on the shock strength.     

薄壁结构屈曲和初始后屈曲的局部分析及其精度

为了解决大型复杂薄壁结构稳定性有限元分析中方程阶数过高的问题,本文建议用结构局部代替整体进行计算,证明局部分析方法可以得到整体结构线性分支点的上限和下限,以及整体结构渐近后屈曲行为的近似解,给出了算例。     

Localized analysis of thin-walled structure's buckling/initial post-buckling and its accuracy

A method of localization is proposed to lower the high order of equations in FEM calculation for the stability of a complex thin-walled structure. The localized analysis enables us to obtain both the upper and lower limits for the bifurcating point in a whole linear-elastic structural system, as well as an approximate solution to asymptotic post-buckling problem. Some numerical examples are included. Project supported by National Natural Science Foundation of China     

Constraints, Constitutive Limits, and Instability in Finite Thermoelasticity

This paper examines all the possible types of thermomechanical constraints in finite-deformational elasticity. By a thermomechanical constraint we mean a functional relationship between a mechanical variable, either the deformation gradient or the stress, and a thermal variable, temperature, entropy or one of the energy potentials; internal energy, Helmholtz free energy, Gibbs free energy or enthalpy. It is shown that for the temperature-deformation, entropy-stress, enthalpy-deformation, and Helmholtz free energy-stress constraints equilibrium states are unstable, in the sense that certain perturbations of the equilibrium state grow exponentially. By considering the constrained materials as constitutive limits of unconstrained materials, it is shown that the instability is associated with the violation of the Legendre–Hadamard condition on the internal energy. The entropy-deformation, temperature-stress, internal energy-stress, and Gibbs free energy-deformation constraints do not exhibit this instability. It is proposed that stability of the rest state (or equivalently convexity of internal energy) is a necessary requirement for a model to be physically valid, and hence entropy-deformation, temperature-stress, internal energy-stress, and Gibbs free energy-deformation constraints are physical, whereas temperature-deformation constraints (including the customary notion of thermal expansion that density is a function of temperature only), entropy-stress constraints, enthalpy-deformation constraints, and Helmholtz free energy-stress constraints are not.     

Quantitative analysis of trace levels of surface contamination by X‐ray photoelectron spectroscopy. Part II: Systematic uncertainties and absolute quantification

We discuss analyses of trace levels of surface contamination using X‐ray photoelectron spectroscopy (XPS). The problem of quantifying common sources of statistical and systematic uncertainties for these measurements is formulated in terms of the needs of extreme ultraviolet lithography, but the results and conclusions are applicable to a broad range of XPS applications. We quantify the systematic uncertainties introduced by particular cases of overlapping peaks on different substrate structures by simulating measured spectra with the National Institute of Standards and Technology Database for the Simulation of Electron Spectra for Surface Analysis (SESSA). One example demonstrates that the relative atomic concentrations of trace elements such as S, P, and halogens on a Ru surface could be dramatically overestimated if the fitting of the overlapping Ru 3d and C 1s peaks excludes the contribution from carbon. We also show how spectra generated by SESSA can be compared with measured spectra to determine absolute amounts of surface impurities on layered samples of the type used for extreme ultraviolet lithography. We provide estimates of the total uncertainty for such measurements by considering the systematic limitations of SESSA and the statistical uncertainties of the measurements. The same procedure can be employed for other multilayered materials. Finally, we describe two approaches for converting XPS detection limits for an elemental impurity in an elemental matrix to the corresponding detection limits for the impurity as a thin film on the surface of the matrix material.     

Methanol Mitigation during Manufacturing of Fruit Spirits with Special Consideration of Novel Coffee Cherry Spirits

Methanol is a natural ingredient with major occurrence in fruit spirits, such as apple, pear, plum or cherry spirits, but also in spirits made from coffee pulp. The compound is formed during fermentation and the following mash storage by enzymatic hydrolysis of naturally present pectins. Methanol is toxic above certain threshold levels and legal limits have been set in most jurisdictions. Therefore, the methanol content needs to be mitigated and its level must be controlled. This article will review the several factors that influence the methanol content including the pH value of the mash, the addition of various yeast and enzyme preparations, fermentation temperature, mash storage, and most importantly the raw material quality and hygiene. From all these mitigation possibilities, lowering the pH value and the use of cultured yeasts when mashing fruit substances is already common as best practice today. Also a controlled yeast fermentation at acidic pH facilitates not only reduced methanol formation, but ultimately also leads to quality benefits of the distillate. Special care has to be observed in the case of spirits made from coffee by-products which are prone to spoilage with very high methanol contents reported in past studies.