时空Chaos研究中的CML模型

通过对有关差分格式的稳定性分析，我们提出了一类新的格点耦合映射（ＣＭＬ）模型。数值试验表明：我们提出的ＣＭＬ模型是一类有效的研究时空复杂性的模型，特别是对于强耦合系统。     

具有磁场效应的非线性Schroedinger方程组的拟谱方法

考察一类具有磁场效应的非线性Ｓｃｈｒｏｅｄｉｎｇｅｒ方程组的周期初值问题，构造了全离散地Ｆｏｕｒｉｅｒ拟谱格式，利用有界延拓法，证明了其格式的收敛性与稳定性，并给出了误差估计及其算法分析，为对此模型的数值分析提供了理论基础和一个有效的算法，最后，通过数值例子，检验了理论结果的可信性。     

随机固定资产模型有限元降维格式的数值解

将特征正交分解(Proper Orthogonal Decomposition,简记为POD)方法应用于固定资产模型,简化其为一个具有较低维数和较高精度的有限元格式,并给出简化的有限元解的误差分析.数值例子表明在简化格式解和通常格式解之间的误差足够小的情况下,简化格式能大大的降低维数,提高计算速度和计算精度,从而验证固定资产模型的简化格式是可行和有效的.     

具有磁场效应的非线性Schrdinger方程组的拟谱方法

考察一类具有磁场效应的非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程组的周期初值问题，构造了全离散的Ｆｏｕｒｉｅｒ拟谱格式，利用有界延拓法，证明了其格式的收敛性与稳定性，并给出了误差估计及其算法分析，为对此模型的数值分析提供了理论基础和一个有效的算法．最后，通过数值例子，检验了理论结果的可信性．     

时空离散FitzHugh-Nagumo方程解的渐近行为

本文用有限差分格式对FitzHugh-Nagumo方程的时间变量和空间变量同时离散，给出了离散模型整体吸引子存在的条件。     

一维气液两相漂移模型全隐式AUSMV算法研究

气液两相漂移模型显式AUSMV（advection upstream splitting method combined with flux vector splitting method）算法的时间步长受限于CFL（Courant-Friedrichs-Lewy）条件，为了提高计算效率，建立了一种全隐式AUSMV算法求解气液两相漂移模型.采用AUSM格式结合FVS（flux vector splitting）格式构造连续方程和运动方程的对流项数值通量，AUSM格式构造压力项数值通量.离散控制方程是非线性方程组，采用六阶Newton(牛顿)法结合数值Jacobi矩阵求解.计算经典算例Zuber-Findlay激波管问题和复杂漂移关系变质量流动问题，结果分析表明:全隐式AUSMV算法，色散效应小，无数值震荡，计算精度高.在压力波波速高的条件下，可以显著提高计算效率，耗散效应小.     

规定水平下重置期权的有限差分解

利用Black—Scholes偏微分方程,结合重置期权与关卡期权的关系,建立了规定水平下的重置期权定价模型,最后运用C—N格式和θ法构造该模型的有限差分格式．     

时间分数阶期权定价模型的一类有效差分方法

时间分数阶期权定价模型(时间分数阶Black-Scholes方程)数值解法的研究具有重要的理论意义和实际应用价值.对时间分数阶Black-Scholes方程构造了显-隐格式和隐-显差分格式,讨论了两类格式解的存在唯一性,稳定性和收敛性.理论分析证实,显-隐格式和隐-显格式均为无条件稳定和收敛的,两种格式具有相同的计算量.数值试验表明:显-隐和隐-显格式的计算精度与经典Crank-Nicolson(C-N)格式的计算精度相当,其计算效率(计算时间)比C-N格式提高30%.数值试验验证了理论分析,表明本文的显-隐和隐-显差分方法对求解时间分数阶期权定价模型是高效的,证实了时间分数阶Black-Scholes方程更符合实际金融市场.     

粘弹性本构模型的准静力位移识别

对一类边界条件，建立粘弹性准静力位移与本构参数的显式关系，给出优化识别的叠代格式，从二阶微分模型出发，识别粘弹性本构模式，讨论了信息误差对反演结果的影响     

守恒型双曲方程的中心差分TVD格式研究

研究了如何利用迎风格式的耗散性构造中心差分ＴＶＤ格式的方法，给 相应的定理，构造出新的耗散表达式。新格式既保留了二阶中心差分格式灵活方便的优点，又吸收了迎风格式耗散项比较精细的特点，同时具有ＴＶＤ性质，使得新格式具有较同的激波分辨率。     

Financial Risk Modelling and Econometric Inference

In finance, the explicit modelling of uncertainty takes on a particularly important role. The values of financial derivatives increase in the return volatility of the underlying security. This notion requires a concept of volatility and hence uncertainty. In addition, the choice between modelling in discrete and continuous time is not arbitrary, since it corresponds to a distinction between incomplete and complete markets, respectively, and this distinction matters for asset pricing, financial risk modelling, and inference. Risk and volatility are closely connected, and implied volatility, volatility forecasting, volatility in term structure models, stochastic volatility, and portfolio analysis are considered and related to a more general interplay between cross-sectional and dynamic aspects in finance. Stocks, bonds, and options are considered and placed in the context of efficiency and separation in inference.     

PROMETHEE: A comprehensive literature review on methodologies and applications

In recent decades, several Multi-Criteria Decision Aid (MCDA) methods have been proposed to help in selecting the best compromise alternatives. In the meantime, the PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) family of outranking methods and their applications has attracted much attention from academics and practitioners. In this paper, a classification scheme and a comprehensive literature review are presented in order to uncover, classify, and interpret the current research on PROMETHEE methodologies and applications. Based on the scheme, 217 scholarly papers from 100 journals are categorized into application areas and non-application papers. The application areas include the papers on the topics of Environment Management, Hydrology and Water Management, Business and Financial Management, Chemistry, Logistics and Transportation, Manufacturing and Assembly, Energy Management, Social, and Other Topics. The last area covers the papers published in several fields: Medicine, Agriculture, Education, Design, Government and Sports. The scholarly papers are also classified by (1) year of publication, (2) journal of publication, (3) authors’ nationality, (4) PROMETHEE as applied with other MCDA methods, and (5) PROMETHEE as applied with GAIA (Geometrical Analysis for Interactive Aid) plane. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of PROMETHEE methodologies and applications, and hence promote the future of PROMETHEE research.     

环境治理政策的减排、增效与结构优化效果动态评价

为测度环境治理政策波动对产出、减排、要素配置、消费与产业结构的影响及其传导机制,将异质性消费偏好、产出差异性、环境效用和环境损失函数引入E-DSGE模型。政策强度分析发现,技术进步、排污税和消费税政策效果较强,环境控制和治污支出冲击效果较弱。政策效应分析发现,技术进步政策效应最优,能实现增产和减排双重目标,促进要素配置和居民消费、产出与消费结构改进;排污税和政府治污支出政策次优,能实现增产和减排的双赢目标,促进要素供给和产出结构清洁化,不利于消费提升和消费结构优化;环境控制与消费税政策效果最差,以牺牲产出实现减排,不利于要素配置,产出与消费结构改进效果较弱,消费税会抑制居民消费,但消费税政策效果随环境友好型家庭比例提升而加强。     

Simulating the effect of nepotism on political risk taking and social unrest

Nepotism has been the primary influence on political behavior throughout human history. Despite the spread of democracy in the 20th century, nepotistic regimes have hardly disappeared. Nepotism heavily influences political activity throughout the developing world, Middle East, and central Asia where family ties are essential for gaining access to power, state resources, and privileges. Rebelling against such nepotistic regimes is difficult and risky. RiskTaker is an agent-based model we developed for testing the influences of various social forces on risk taking behavior, including the formulation of rebellious coalitions. We use RiskTaker to examine the influence of nepotism on the distribution of wealth and social status. Nepotism heavily skews the distribution of wealth and status, leading to the formation of opposing coalitions and exacerbating social unrest.This paper was tied for Best Paper, NAACSOS (North American Association for Computational Social and Organizational Science) Annual Conference 2005, June 26–28, Notre Dame. Robert Sedlmeyer, Department of Computer Science, Indiana University – Purdue University, Fort Wayne provided programming for the RiskTaker model. Lawrence A. Kuznar is a professor of anthropology and director of the Decision Sciences and Theory Institute at Indiana University—Purdue University, Fort Wayne. He has conducted fieldwork among Aymara Indians in Andean Peru and the Navajo of the American southwest. His research interests include computer modeling, theories of risk taking and conflict, terrorism, social evolution, and scientific epistemology. He has authored articles in Ecological Economics (with W. Frederick), Current Anthropology, American Anthropologist, Mathematical Anthropology and Culture Theory and Journal of Anthropological Research, and published two books (Awatimarka Harcourt Brace, 1995 and Reclaiming a Scientific Anthropology Altamira Press, 1997) and two edited volumes. William Frederick has served as a faculty member in the departments of mathematical sciences and the department of computer sciences at Indiana University—Purdue University, Fort Wayne since 1979. His primary interests include mathematical modeling, game theory, and genetic algorithms.     

Supply chain coordination with downstream operating costs: Coordination and investment to improve downstream operating efficiency

There are many conceptualizations and formalizations of decision making. In this paper we compare classical decision theory with qualitative decision theory, knowledge-based systems and belief–desire–intention models developed in artificial intelligence and agent theory. They all contain representations of information and motivation. Examples of informational attitudes are probability distributions, qualitative abstractions of probabilities, knowledge, and beliefs. Examples of motivational attitudes are utility functions, qualitative abstractions of utilities, goals, and desires. Each of them encodes a set of alternatives to be chosen from. This ranges from a small predetermined set, a set of decision variables, through logical formulas, to branches of a tree representing events through time. Moreover, they have a way of formulating how a decision is made. Classical and qualitative decision theory focus on the optimal decisions represented by a decision rule. Knowledge-based systems and belief–desire–intention models focus on an alternative conceptualization to formalize decision making, inspired by cognitive notions like belief, desire, goal and intention. Relations among these concepts express an agent type, which constrains the deliberation process. We also consider the relation between decision processes and intentions, and the relation between game theory and norms and commitments.     

RUMINATIONS ON THE DEVELOPMENT AND FUTURE OF POPULATION DYNAMICS MODELS IN FISHERIES

ABSTRACT. I trace the development of fisheries models (i.e., fish population dynamics models of species subject to fisheries) to the 21st century. The first real efforts occurred in the period 1900 1920 with the work of Baranov (the “Grandfather” of fisheries population dynamics) and the formation of the International Council for the Exploration of the Sea (ICES). The establishment of the science occurred between 1920 1960 with multi‐species modeling, age‐ and size‐structure dynamics, and production models. Fundamental work during this time was done by Ricker (the “Father” of fisheries population dynamics), Beverton and Holt (the “Prophets” of fisheries population dynamics), Chapman, Dickie, DeLury, Graham, Gulland, Leslie, Lotka and Volterra, Russell, Schaefer, and Thompson. During this time, most of the workwas deterministic and mathematical. Between 1960 and 1980, statistical methodology evolved greatly but was separate from mathematical advances for the most part. The development of statistical principles for the estimation of animal abundance was further enhanced by Arnason, Buckland, Burnham and Anderson and White, Cormack, Eberhardt, Jolly, Manly, Pollock, Ricker, Robson, and Seber, among others. Fisheries models evolved in a deterministic setting, with advances in age‐structured models (Gulland, Pope, Doubleday), surplus production models (Pella, Tomlin‐son, Schnute, Fletcher, Hilborn), growth models, bioeconomic models (C. Clark) and management control models (Hilborn, Walters). The period 1980 2000 was the Golden Age. The integration between mathematics and statistics occurred when likelihood and least squares techniques were formally combined with mathematical models of population change. The number of fisheries modelers grew exponentially during this time, resulting in a concomitant increase in publications. A major advance in the 1990s has been the development of Bayesian and time series methods, which have allowed explicit specification of uncertainty. Currently, theory allows realistic modeling of age‐ and size‐structured populations, migratory populations and harvesting strategies. These models routinely incorporate measurement error, process error (stochasticity) and time variation. But data needs often overwhelm the performance of models, and greater demands are being placed on models to answer complex questions. There has been poor communication between fisheries and ecological modelers, between fisheries researchers and statisticians, and among fisheries researchers in different geographic locales. Future models will need to deal better with habitat and spatial concerns, genetics, multispecies interactions, environmental factors, effects of harvesting on the ecosystem, model misspecification and so‐cioeconomic concerns. Meta‐analysis, retrospective analysis and operating models are some modern approaches for dealing with uncertainty and providing for sustainable fisheries. However, I fear that current attacks on single‐species models and management may result in rejection of these advances and an attempt to substitute a less scientific approach.     

Conservation laws of turbulence models

The conservation of mass, momentum, energy, helicity, and enstrophy in fluid flow are important because these quantities organize a flow, and characterize change in the flow's structure over time. In turbulent flow, conservation laws remain important in the inertial range of wave numbers, where viscous effects are negligible. It is in the inertial range where energy, helicity (3d), and enstrophy (2d) must be accurately cascaded for a turbulence model to be qualitatively correct. A first and necessary step for an accurate cascade is conservation; however, many turbulent flow simulations are based on turbulence models whose conservation properties are little explored and might be very different from those of the Navier-Stokes equations.We explore conservation laws and approximate conservation laws satisfied by LES turbulence models. For the Leray, Leray deconvolution, Bardina, and Nth order deconvolution models, we give exact or approximate laws for a model mass, momentum, energy, enstrophy and helicity. The possibility of cascades for model quantities is also discussed.     

Mechanics of Delaminations in Laminate Composite Structures

A survey of the literature and state of the art of the mechanical aspects of delaminations in laminate composite structures is presented. Surface and internal delaminations of various origin, shape, and location are discussed. The origination, stability, and postcritical behavior of delaminations under quasi-static, cyclic, and dynamic loads are analyzed. Some problems for further investigations are discussed.     

基于线性代数的大规模快速量纲分析算法及其在爆炸与冲击工程研究中的应用

量纲分析是科学研究,特别是工程应用中非常重要的一个理论分析工具.从E.Buckingham提出Π定理开始算起,量纲分析已有一百多年历史,其基本理论和方法已经非常成熟,在各个领域也取得了显著的成果并且仍然有着广泛的应用.然而,随着研究的深入,面对的问题越来越复杂和细致,人们越来越关注在传统量纲分析中忽略掉的一些所谓次要因素的影响,因此涉及的物理量变得越来越多,导致按传统的量纲分析方法处理时常常显得非常繁琐甚至困难.本文从线性代数的观点出发,将量纲分析转换为线性空间问题,通过矩阵运算,完成量纲分析的关键过程.给出了量纲分析对应的线性代数问题的基本定理,并基于这些定理建立了程序化的量纲分析算法,将原本复杂的量纲分析问题转化为借助计算机代数系统能够快速方便解决的矩阵运算问题.最后,结合笔者多年的工作经历,给出了上述方法在爆炸与冲击工程研究领域中的若干应用实例,详细表述了具体操作步骤,验证了算法的优越性.