Modelling of unilateral constraints using power-based restriction functions within Lagrangian mechanics

The consideration of unilateral contacts within multi-body systems is a common but also difficult task. Established modelling approaches such as the rigid body theory or the Hertzian contact are suitable for single-body systems but show serious problems with increasing system complexity. Indeed, there are different approaches to extend the existing models to multi-body systems, but with a growing number of contacts and the consideration of tangential friction, those enhancements are hardly applicable, showing numeric problems or becoming unmanageable. Thus, to overcome these limitations, a new modelling approach for unilateral contacts defined by power-based restriction functions is proposed in this contribution. The proposed contact model is based on continuous functions, making it numerically robust as well as applicable within Lagrangian mechanics. The approach is easily applicable and even remains manageable for multiple contacts since each constraint can be independently adapted by four physical parameters. The simple applicability and generalizability of the approach is demonstrated by several examples.     

A classification of time scales and analysis of the general delays on time scales with applications

In this paper, we present five classes/categories of time scales. Then, on each class, we introduce and analyze delays that not only lead to new types of delay systems on time scales but also reveal the limitations of the known results in the literature. To show the importance and significance of our analysis, several examples are illustrated. We conclude our paper with some interesting open problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Modelling and analysis of haemoglobin catalytic reaction kinetic system

ABSTRACT

In order to study whether haemoglobin (Hb) can replace peroxidase and has good catalytic properties. The key to exploring the characteristics of Hb peroxidase is to establish a suitable kinetic model, which is studied in this paper. First, according to the Hb catalytic reaction, a nonlinear system is established and improved. It is proved that the established system is in line with the practical significance. The stability of the original system is judged by analysing the stability of the simplified system. Then, considering the effect of time delay on Hb catalytic reaction, a nonlinear time-delay catalytic reaction system is obtained. For convenient application, the system is linearized using Taylor’s formula, and the dynamic characteristics of Hopf bifurcation are analysed. The response diagrams of three system are plotted by setting perturbation parameters, and their variations are observed to analyse the differences among them. The results show that the nonlinear time-delay system can better describe the characteristics of the catalytic reaction.     

利用故障数据和估计的检查数据建立维修优化模型

利用时间延迟概念,根据故障记录数据和估计的检查数据建立了预防维修模型.通过对故障记录数据统计分析,提出了模型的假定条件.采用最大似然估计法,估计参数,包括缺陷发生率、不完全检查概率和时间延迟分布.建立了有关预防维修间隔期和总停机时间之间关系的检查模型,并根据估计参数和检查模型,计算最佳维修间隔期.     

基于异步次梯度法的LR算法及其在多阶段HFSP的应用

为降低求解复杂度和缩短计算时间,针对多阶段混合流水车间总加权完成时间问题,提出了一种结合异步次梯度法的改进拉格朗日松弛算法。建立综合考虑有限等待时间和工件释放时间的整数规划数学模型,将异步次梯度法嵌入到拉格朗日松弛算法中,从而通过近似求解拉格朗日松弛问题得到一个合理的异步次梯度方向,沿此方向进行搜索,逐渐降低到最优点的距离。通过仿真实验,验证了所提算法的有效性。对比所提算法与传统的基于次梯度法的拉格朗日松弛算法,结果表明,就综合解的质量和计算效率而言,所提算法能在较短的计算时间内获得更好的近优解,尤其是对大规模问题。     

基于FUDAN-CCDC模型对新冠肺炎的建模和确诊人数的预测

科学地预测疫情发展趋势对疫情防控至关重要.在新时滞动力学模型(TDD-NCP)的基础上,提出基于随机动力学的时滞卷积模型和离散卷积模型,并基于中国疾病预防控制中心的相关研究结果及公开数据以及Wallinga和Lipsitch的工作,反演出COVID-19的重要参数,拟合了武汉及上海市疫情发展趋势.     

Modelling the probability assessment of system state prognosis using available condition monitoring information

^** Email: w.wang{at}salford.ac.uk This paper reports on a model to assess the current and futurestates of a monitored system based on measured condition monitoringinformation to date. The true state of the system is unobservable,but is assumed to be related to the measured condition monitoringinformation in a stochastic way. We further assume that thetransition of the system state follows a time-dependent Markovchain which has only three states, namely good, defective andfailed. This assumption effectively defines a two-stage failureprocess which is widely used in delay time modelling of maintainedsystems. Three modelling techniques are used to establish themodel. First, we use a hidden Markov model to describe the transitionsbetween system states. Second, the transition matrix is establishedbased on the well-known delay time concept. The last one isthe use of the filtering technique to construct the relationshipbetween measured condition information and the underlying truestate of the system. We also discuss the procedure for modelparameter estimation. A numerical example is presented to demonstratethe modelling ideas.     

Stabilization of a one‐dimensional wave equation with variable coefficient under non‐collocated control and delayed observation

In this paper, we consider stabilization of a 1‐dimensional wave equation with variable coefficient where non‐collocated boundary observation suffers from an arbitrary time delay. Since input and output are non‐collocated with each other, it is more complex to design the observer system. After showing well‐posedness of the open‐loop system, the observer and predictor systems are constructed to give the estimated state feedback controller. Different from the partial differential equation with constant coefficients, the variable coefficient causes mathematical difficulties of the stabilization problem. By the approach of Riesz basis property, it is shown that the closed‐loop system is stable exponentially. Numerical simulations demonstrate the effect of the stable controller. This paper is devoted to the wave equation with variable coefficients generalized of that with constant coefficients for delayed observation and non‐collocated control.     

具有变时滞的五种群Lotka-Volterra混合系统的正周期解

本文研究了具有变时滞的五种群Lotka-Volterra混合模型.通过使用泛函微分方程的单调流理论和Schauder不动点定理,获得了该系统的正周期解的存在性的充分条件,并建立了正周期解全局渐近稳定判别准则,改进和推广了已有的结果.     

可变产量的理性产出范围研究

本从机会成本损失最小化的角度出发，对可变立量的三个阶段的两种划分方法所确定的两种不同的理性产出范围进行了分析，分析结果表明。可变产量的理性产出范围应在最小边际成本所对应的产出量到边际成本与产品的预期价格相等所对应的产出量之间。     

可变抽样区间的二项EWMA控制图

在制造过程中,对产品的不合格品数进行监控时,通常选用计数性控制图-np图,它是基于过程服从二项分布建立的,一般对于过程中出现的较大波动效果明显。为了提高控制图对不合格品数较小波动的监控效果,本文设计了产品不合格品数服从二项分布的EWMA控制图。提出可变抽样区间的二项EWMA控制图,并采用马可夫链法计算其平均报警时间。对固定抽样区间以及可变抽样区间二项EWMA控制图对比研究,表明当过程失控时,可变抽样区间二项EWMA控制图具有较小的失控平均报警时间,能够迅速监测出过程中的异常波动,明显优于固定抽样区间的二项EWMA控制图。     

Dynamic thermoviscoelastic thermistor problem with contact and nonmonotone friction

Abstract

The paper studies the evolution of the thermomechanical and electric state of a thermoviscoelastic thermistor that is in frictional contact with a reactive foundation. The mechanical process is dynamic, while the electric process is quasistatic. Friction is modeled with a nonmonotone relation between the tangential traction and tangential velocity. Frictional heat generation is taken into account and so is the strong dependence of the electric conductivity on the temperature. The mathematical model for the process is in the form of a system that consists of dynamic hyperbolic subdifferential inclusion for the mechanical state coupled with a nonlinear parabolic equation for the temperature and an elliptic equation for the electric potential. The paper establishes the existence of a weak solution to the problem by using time delays, a priori estimates and a convergence method.     

Problems for parabolic equations with variable exponents of nonlinearity and time delay

The initial-boundary value problems for parabolic equations with variable exponents of nonlinearity and time depended delay are considered. Existence and uniqueness of solutions of these problems are proved.     

A Mixed Problem for a Hyperbolic System on the Plane with Delay in the Boundary Conditions

We examine well-posedness of the boundary value problem in a half-strip for a first-order linear hyperbolic system with delay (lumped and distributed) in the boundary conditions. In the case of the negative real parts of the eigenvalues of the corresponding spectral problem we prove a time uniform estimate for a solution to the homogeneous problem which enables us to justify the linearization principle for analysis of stability of stationary solutions to the nonlinear problem.     

On the Modelling of the Adoption of Process Innovations

An alternative view on the modelling of diffusion processesof process innovations has been introduced by Nooteboom (1989). Thebasic idea in that paper is to model the process of adoption ofprocess innovations as a gambling model with odds in favourdepending on expected returns and odds against depending on risk.In this paper it is investigated under which theoretical conditions posed on the expected return function the usual adopted assumptions Nooteboom (1989) with respect to the parameters of the gambling model are in fact reasonable. It is shown that only under certainconditions the assumptions made on the gambling model are true ontheoretical grounds. In all other cases a nonexample shows that theresults as mentioned in literature are in general not true.     

Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents北大核心CSCD

该文考虑了一类带有变指数非局部项的反应扩散方程的爆破问题。首先,由不动点原理,证明了问题解的局部存在性和唯一性。其次,利用上下解方法,给出在齐次Dirichlet边界条件下,问题的解在有限时间发生爆破的充分条件,即变指数大于零且初始值足够大,并对爆破时间的上下界进行了估计。     

An algorithm for achieving proportional delay differentiation

We consider the implementation of the proportional delay differentiation model with adaptive waiting time priority scheduler and we address the problem of finding the appropriate scheduler differentiation parameters that achieve this model. In this paper, we propose an algorithm that can compute an analytical solution of this problem.     

Variable selection in high‐dimensional regression: a nonparametric procedure for business failure prediction

Business failure prediction models are important in providing warning for preventing financial distress and giving stakeholders time to react in a timely manner to a crisis. The empirical approach to corporate distress analysis and forecasting has recently attracted new attention from financial institutions, academics, and practitioners. In fact, this field is as interesting today as it was in the 1930s, and over the last 80 years, a remarkable body of both theoretical and empirical studies on this topic has been published. Nevertheless, some issues are still under investigation, such as the selection of financial ratios to define business failure and the identification of an optimal subset of predictors. For this purpose, there exist a large number of methods that can be used, although their drawbacks are usually neglected in this context. Moreover, most variable selection procedures are based on some very strict assumptions (linearity and additivity) that make their application difficult in business failure prediction. This paper proposes to overcome these limits by selecting relevant variables using a nonparametric method named Rodeo that is consistent even when the aforementioned assumptions are not satisfied. We also compare Rodeo with two other variable selection methods (Lasso and Adaptive Lasso), and the empirical results demonstrate that our proposed procedure outperforms the others in terms of positive/negative predictive value and is able to capture the nonlinear effects of the selected variables. Copyright © 2017 John Wiley & Sons, Ltd.