Optimal lower eigenvalue estimates for Hodge-Laplacian and applications

We consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold M isometrically immersed into another Riemannian manifold $\overline{M}$. We first assume the pull back Weitzenböck operator of $\overline{M}$ bounded from below, and obtain an extrinsic lower bound for the first eigenvalue of Hodge-Laplacian. As applications, we obtain some rigidity results. Second, when the pull back Weitzenböck operator of $\overline{M}$ bounded from both sides, we give a lower bound of the first eigenvalue by the Ricci curvature of M and some extrinsic geometry. As a consequence, we prove a weak Ejiri type theorem, that is, if the Ricci curvature bounded from below pointwisely by a function of the norm square of the mean curvature vector, then M is a homology sphere. In the end, we give an example to show that all the eigenvalue estimates are optimal when $\overline{M}$ is the space form.     

Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes–Darcy model

Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes–Darcy model with Beavers–Joseph–Saffman interface condition in literatures, the numerical analysis only gets the optimal error order for porous media flow and a non-optimal error order that is half order lower than the optimal one in fluid flow. The purpose of this paper is to fill in the gap between the numerical results and the theoretical analysis.     

The MAP/PH/N retrial queue in a random environment

We consider the MAP/PH/N retrial queue with a finite number of sources operating in a finite state Markovian random environment. Two different types of multi-dimensional Markov chains are investigated describing the behavior of the system based on state space arrangements. The special features of the two formulations are discussed. The algorithms for calculating the stationary state probabilities are elaborated, based on which the main performance measures are obtained, and numerical examples are presented as well.     

蒙特卡罗计算中颗粒型燃料的随机分布模型比较

高温气冷堆是新一代反应堆系统的热门候选堆型，已经受到国际上越来越多的关注。为设计和分析这种堆型，因其特有的包覆颗粒燃料引入了双重非均匀性，需要应用随机分布模型。对粗网格模型、细网格随机(FLS)模型、随机顺序添加(RSA)模型、子网格随机(Sub-FLS)模型和Metropolis模型等进行了研究，通过计算分析比较给出了各种模型的优缺点。结果表明:子网格随机模型和连续的RSA模型非常接近参考值，但是连续RSA模型的建模时间随着燃料体积份额的增加连续快速上升。 Key words: coated particle fuels; stochastic transport model; Monte Carlo; random distribution     

A class of random field memory models for mortality forecasting

This article proposes a parsimonious alternative approach for modeling the stochastic dynamics of mortality rates. Instead of the commonly used factor-based decomposition framework, we consider modeling mortality improvements using a random field specification with a given causal structure. Such a class of models introduces dependencies among adjacent cohorts aiming at capturing, among others, the cohort effects and cross generations correlations. It also describes the conditional heteroskedasticity of mortality. The proposed model is a generalization of the now widely used AR-ARCH models for random processes. For such a class of models, we propose an estimation procedure for the parameters. Formally, we use the quasi-maximum likelihood estimator (QMLE) and show its statistical consistency and the asymptotic normality of the estimated parameters. The framework being general, we investigate and illustrate a simple variant, called the three-level memory model, in order to fully understand and assess the effectiveness of the approach for modeling mortality dynamics.     

Effect of deuteron density distribution on the deduction of screening potential from the D(d,p)T reaction in Be metals

The D(d,p)T reaction in Be metal environments has been measured to investigate the electron screening effect in metals in an energy region of from 5.5 keV to 10 keV in a center of mass system(CMS)at a temperature of 121 K.The depth distribution of deuteron density in Be metals has an impact on the observed reaction yields.A model of deuteron density distribution in metal has been proposed to obtain the original yields.A screening energy of(116±46)eV has been obtained with the assumed deuteron density distribution model.     

A Mixed Mann Iteration Process for Fixed Points of Mixed Increasing Operators in Ordered Banach Spaces

In this paper, we develop a new mixed Mann iteration process to approximate the fixed points of mixed increasing operators in ordered Banach spaces and discuss the convergence analysis of the iterative sequences generated by the iteration process. As an application, we develop a new iterative method for solving a class of nonlinear integral equations.     

Bayesian knowledge base tuning

For a knowledge-based system that fails to provide the correct answer, it is important to be able to tune the system while minimizing overall change in the knowledge-base. There are a variety of reasons why the answer is incorrect ranging from incorrect knowledge to information vagueness to incompleteness. Still, in all these situations, it is typically the case that most of the knowledge in the system is likely to be correct as specified by the expert (s) and/or knowledge engineer (s). In this paper, we propose a method to identify the possible changes by understanding the contribution of parameters on the outputs of concern. Our approach is based on Bayesian Knowledge Bases for modeling uncertainties. We start with single parameter changes and then extend to multiple parameters. In order to identify the optimal solution that can minimize the change to the model as specified by the domain experts, we define and evaluate the sensitivity values of the results with respect to the parameters. We discuss the computational complexities of determining the solution and show that the problem of multiple parameters changes can be transformed into Linear Programming problems, and thus, efficiently solvable. Our work can also be applied towards validating the knowledge base such that the updated model can satisfy all test-cases collected from the domain experts.     

DRDF analysis of wide-angle x-ray scattering of natural rubber

A differential radial distribution function (DRDF) of molten natural rubber (NR) was derived from its wide-angle x-ray scattering (WAXS) data. Three peaks with Bragg spacings 4.85, 2.31, and 1.23 Å corresponding, respectively, to interchain, C₁-C₃ and C₁ -C₂ distances are present in the corrected WAXS curve. The derived DRDF, which is shown to be greatly improved than the ones published so far, contains six peaks located at 1.51, 2.48, 3.98, 5.68, 10.65, and 15.25 Å. Maximum contributions of intramolecular atomic distances to the radial distribution peaks were estimated and compared with the experimental results. The comparison shows that the first three peaks are intramolecular in origin and the remaining peaks are predominantly due to intermolecular regularities. A periodicity of an approximately constant interval of 5.26 Å is found between the intermolecular peaks and is attributable to the organizations of more or less parallel chain segments in the material. This finding provided additional evidence for the presence of local lateral ordering to the extent of about 30 Å in molten-state natural rubber.     

State of the art and research development prospects of energy and resource-efficient environmentally safe chemical process systems engineering

In this focus overview, the main types and directions of engineering, methods and techniques of intensification of chemical process systems (CPS) and process optimization of energy- and resource-efficient processes for the representative production of titanium compounds, mining waste processing systems, electrochemical coating technologies, combined technologies for the treatment of industrial effluents and energy-and resource-efficient technologies for cleaning soils from petroleum and chemical pollution products are reviewed. The following issues have been discussed: methods of complex assessment of production energy efficiency and software and information support for automated synthesis of optimal energy-efficient regenerative heat exchange systems using pinch analysis; methods and algorithms for fractal-statistical characteristics analysis of nonstationary gas flows in complex gas pipelines; methods of ecological and economic optimization of production, infrastructure supply chains; methods for assessing and preventing the dangerous environmental impact assessment of chemical pollution; organization and logistics management of business processes engineering for improving the energy efficiency of plants; engineering of problem oriented computer systems, heuristic-computational models and algorithms for intelligent integrated logistics support of the equipment life cycle; engineering developments in the field of digital transformation of energy-efficient CPS and technological production systems; application of methods for optimizing reliability factors optimization, digitalized risk and safety management in the engineering of energy- and resource efficient CPS.