灰色组合模型及其应用

本建立了GM(1．1)与线性回归模型的组合模型，改进了单一模型的局限性，并用此模型预测了郑州市粮食总产量，得到了较为满意的结果。     

敏感性问题“随机变量和”回答模型

孔圣元，孟生旺．敏感性问题“随机变量和”回答模型．数理统计与管理，１９９８，１７（２），３５～３９．本文依据概率论中“随机变量和”的分布理论，对敏感性问题的调查，提出了一个新模型，即“随机变量和”回答模型，实现了敏感性问题的问卷调查。本文给出了模型的最优估计量及其方差的计算公式，讨论了模型参数的合理选择，同时还得出了一个有趣的结果：“随机化回答模型”包含在“随机变量和”回答模型之中。     

开发区居民分布模型研究

本文从规划区土地利用状况出发，建立了居民分布的引力模型和概率模型，在规划区就业人口分成就业区就业人口和居住区服务就业人口的基础上，研究了运用模型分布这两种就业人口的方法，并建立分布全部居民的模型，最后给出了模型应用实例．     

软件可靠性M-O模型和逆线性模型的参数估计

Musa-Okumoto模型和逆线性模型是研究软件可靠性的重要模型，给出了在分组数据下，M－O模型和逆线性模型中参数的最大似然估计及其存在的充分性条件，指出了[4]中的错误，并且给出了一个实例。     

具有测量误差的非线性模型的Bayes估计

测量中大量的函数模型都是非线性回归模型．当回归变量含有一定的测量误差时，我们得到非线性测量误差模型．本讨论了这种模型中未知参数具有正态先验分布时的参数Bayes估计方法，并对这种估计进行了影响分析，证明了删除模型与均值漂移模型中参数的Bayes估计相同，利用Cook统计量给出了删除模型下参数的Bayes估计的影响度量．     

项目投资组合的风险度及其最优决策

本文针对项目组合投资问题引入了风险度概念，并建立其风险度模型．在无零风险度项目的情况下，给出了该模型的最优项目组合投资策略并证明该策略为马氏有效．在有零风险度项目的情况下，讨论了该模型的有效前沿的结构、性质和有效性，同时还论证了该模型的有效前沿与威廉·夏普提出的资本资产定价模型的有效前沿相一致的线性关系．最后作为本模型的应用，构造了”保证还本”模型，给出了其最优项目投资组合的策略．     

基于模糊数变换的DEA模型与应用

在数据包络分析(DEA)的C^2R模型的基础上，建立FC^2R模型。但现有的FC^2R模型，要求模糊输入输出指标值之间满足一定的严格条件，这在实际应用中有一定的局限性。为此本文在FC^2R模型的基础上，提出了一种基于模糊数变换的DEA模型(α-FC^2R模型)，拓展了传统DEA的应用范围，并将其应用于综合评价，取得了很好效果。     

股票价格波动的塑性性质及模型探讨

首先基于股票价格和成交量，根据股票的量价规律，分析了股价波动的塑性性质；然后使用计量经济学方法建立描述股价波动的塑性模型，包括股价塑性基本模型、基本模型的一阶自回归模型、幂指数模型及幂指数模型的一阶自回归模型，基于12支样本股对这些模型进行参数估计和检验；最后对4种形式的股价塑性模型进行了总结。由4种模型均能够通过经济学检验和统计学检验可知股价波动具有塑性性质，且幂指数模型描述股价塑性较为科学、合理。     

考虑时间效应的机器负荷分配模型

机器人高低负荷分配问题是动态规划的应用之一，但该问题的动态规划模型一般都没有考虑资金，产值的时间价值效应，本在机器负荷分配的原动态规划模型基础之上，加入了时间因索，建立了考虑时间效应的机器高低负荷分配的动态规划模型，从而扩大了原模型的适应范围。     

关于可信性模型的若干评注

可信性模型是经验费率厘定中最重要的方法，本文在简述可信性概念的发展简史并强调了有限扰动可信性和最精确可信性的区别后，重点剖析了最精确可信性的理论基础，且详尽地解释了导出（修正）Buehlmann单合同可信性模型的基本思路，在阶段性地展示了建立此模型基本假定的过程后，给出了风险保费与预测值的可信性估计的简明公式，现今最基础的Buehlmann-Straub可信性模型可视为由多个相互独立，且具有相同的结构函数的（修正）Buhlmann单合同模型相嵌而成，这种组嵌方式使得估计该模型的未知结构参数成为可能，本文最后概述了可信性模型的主要进展，全文的叙述是说明性的，不步及技术性证明过程，目的在于为理解可信性模型提供一个直观与清晰的思路。     

煤层注水非线性渗流方程的解析解及应用

本文运用流体力学,多孔介质流体动力学,渗流理论等理论知识,结合实验室和现场试验,从理论上对煤层注水预湿煤体机理进行了研究.分析了煤层注水过程,建立起了煤层注水的数学模型;对煤层注水的边界条件进行了描述.由于描述煤层注水的方程组为非线性的,为简化它们,利用了因次分析理论,引入了注水压力,渗透速度,煤水份增加量等无因次量.之后讨论了其解析和近似解.另外:结合实际煤层注水的科研项目,说明了该理论指导煤层注水及设计的作用和重要性.     

Dynamical analysis of chemotherapy models with time-dependent infusion

Classical mathematical models for chemotherapy assume a constant infusion rate of the chemotherapy agent. However in reality the infusion rate usually varies with respect to time, due to the natural (temporal or random) fluctuation of environments or clinical needs. In this work we study a non-autonomous chemotherapy model where the injection rate and injection concentration of the chemotherapy agent are time-dependent. In particular, we prove that the non-autonomous dynamical system generated by solutions to the non-autonomous chemotherapy system possesses a pullback attractor. In addition, we investigate the detailed interior structures of the pullback attractor to provide crucial information on the effectiveness of the treatment. The main analytical tool used is the theory of non-autonomous dynamical systems. Numerical experiments are carried out to supplement the analysis and illustrate the effectiveness of different types of infusions.     

Continuum-Mechanical Analysis of Human Brain Tissue

The effective treatment of brain diseases, such as malignant brain tumours, is generally constricted by the controlled contribution of therapeutic agents. Novel brain tumour therapy proceeds from a direct infusion of the drug into the extra-vascular space of the nervous brain tissue (convection-enhanced delivery). This is carried out using catheter to bypass the blood-brain barrier, which effectively separates brain tissue from the intra-vascular space and hence hamper drug delivery through the bloodstream. The dilation of the target tissue, as response to the local pressure increase, initiates interstitial fluid flow and, thus, the distribution of the chemical agents. An adequate constitutive model of the complex tissue aggregate in the framework of the Theory of Porous Media is essential in order to assist modern clinical application via numerical simulations. The presented model consists of an elastically deformable solid skeleton, provided by the tissue cells, permeated by two viscous, materially incompressible pore-liquid phases, interstitial fluid and blood plasma. Both liquids are mobile within the solid skeleton and separated from each other. With regard to simulate a drug infusion process in the extra-vascular space, the interstitial fluid is treated as a solution of a liquid solvent and a dissolved therapeutic solute. The constitutive assumptions for the involved constituents are adjusted in order to describe the physical behaviour of human brain tissue. The presented numerical examples illustrate the fundamental effects during an infusion process. Therefore, the resulting set of coupled partial differential equations is spatially discretised using hexahedral mixed finite elements with an implicit (backward) Euler time integration scheme to solve the considered problem in a monolithic manner for the primary variables. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multi-component modelling and simulation of metastases proliferation within brain tissue

Originated from a lung tumour, cancer cells can spread via the blood-vessel system, travel to the cerebrum and may pass the blood-brain barrier. The extravasation is followed by migration, and the formation of micrometastases. Further proliferation causes interveined metastases. A pressure-driven infusion of a therapeutic solution counteracts the disturbance by the metastases within the brain. These processes are described with a continuum-mechanical model based on the Theory of Porous Media. Numerical applications demonstrate the feasibility of the model and include multicellular-tumour spheroid experiments in the macroscopic simulation of metastases growth and atrophy. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling the response of spatially structured tumours to chemotherapy: Drug kinetics

In this paper we consider the effects of a single anticancer agent on the growth of a solid tumour in the context of a simple mathematical model for the latter. The tumour is assumed to comprise a single cell population which reproduces and dies at a rate dependent on the local drug concentration. This causes cell movement and so establishes a velocity field within the tumour. We investigate the action of a single chemotherapeutic drug on the tumour and explore how different drug kinetics and treatment regimes may affect the final treatment outcome. A single infusion of drug is shown to be more effective than repeated short applications. We are able to construct asymptotic solutions to the model in the limit of a small drug degradation rate; these closely match solutions obtained numerically and provide additional insight into the behaviour of the tumour, in particular allowing the prediction of the strength of drug required to achieve tumour regression.     

Problem of the infusion of a fluid in an elastic deformable medium

The problem of the infusion of a fluid in an elastic coal seam via a hole drilled from the daylight surface is solved. Analytical expressions that make it possible to investigate the effect of the stress—strain state, physicomechanical and collecting properties of the coal, and the rate of injection on the process of fluid infusion under prescribed conditions, are obtained.Donetsk. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 112–116, 1190.     

Theoretical and numerical aspects in the multiphasic modelling of human brain tissue

A surgical intervention is often required if the functionality of the sensitive human brain tissue is seriously compromised, e. g., due to the occurrence of malignant brain tumours. A promising method for an effective tumour-treatment procedure is given by the so-called convection-enhanced drug delivery (CED), cf. [1]. In this regard, the aim of this contribution is to simulate the expected effects as well as coupled impacts of a (scheduled) CED-procedure with the help of numerical computations, which base on a sophisticated multiphasic and multi-physical modelling strategy applied to human brain tissue. In particular, a quaternary porous-media model, cf. [3–5], is used for the discussion of selected numerical examples and demonstrates the applicability of the model. In detail, the optimal catheter placement and the application of multiple infusion catheters are studied in terms of the occurring anisotropic therapeutic spreading of the infused drug. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A technological,organisational, and environmental analysis of decision making methodologies and satisfaction in the context of IT induced business transformations

Although Operational Research (OR) has successfully provided many methodologies to address complex decision problems, in particular based on the rationality principle, there has been too little discussion regarding their limited consideration in IT evaluation practice and associated decision making satisfaction levels in an organisational context. The aim of this paper is to address these issues through providing a current account of diffusion and infusion of OR methodologies in IT decision making practice, and by analysing factors affecting decision making satisfaction from a Technological, Organisational, and Environmental (TOE) framework in the context of IT induced business transformations. We developed a structural equation model and conducted an empirical survey, which supported four out of five developed research hypotheses. Our results show that while Decision Support Systems (DSSs), holistic IT evaluation methods, and management support seem to positively affect individual satisfaction, legislative regulation has an adverse effect. Results also revealed a persistent methodology diffusion and infusion gap. The paper discusses implications in each of these aspects and presents opportunities for future work.     

Estimating the delay-time distribution of faults in repairable machinery from failure data

This paper considers a repairable machine that may fail or sufferbreakdown many times during the course of its service lifetime,and is inspected for visible faults at intervals. The delay-timeconcept of Christer & Waller provides a means of modellingthe behaviour of the system, and predicting such useful quantitiesas reliability and cost, under various putative inspection regimes. Hitherto, model parameters have been estimated mainly from subjectivedata. In this paper, we show that it is both theoretically andpractically possible to estimate model parameters, and makeuseful predictions, purely from objective data, i.e. the historyof breakdown times and the findings of inspections. Model parameters are fitted by the method of maximum likelihood,and selection of the 'best' model made using the Akaike informationcriterion (AIC). Initially, Monte-Carlo studies were made, andshowed that the p r d u r e did enable unbiased and asymptoticallyaccurate estimates of model parameters to be recovered fromdata. Manual records of inspections and failures of a sampleof hospital infusion pumps were then analysed, and values ofmodel parameters estimated. Tests of fit were derived and carriedout. Finally, the reliability of infusion-pump components underdifferent inspection intervals was derived from the delay-timemodel with 95% confidence limits, as a demonstration that themethod does indeed provide a practical tool for optimizing inspectionpolicies. The practical details of the relevant computations are givenin some detail throughout, to enable other workers to followour procedure.