Foreword to the Special Focus on Mathematics,Data and Knowledge

There is a growing interest in applying mathematical theories and methods from topology, computational geometry, differential equations, fluid dynamics, quantum statistics, etc. to describe and to analyze scientific regularities of diverse, massive, complex, nonlinear, and fast changing data accumulated continuously around the world and in discovering and revealing valid, insightful, and valuable knowledge that data imply. With increasingly solid mathematical foundations, various methods and techniques have been studied and developed for data mining, modeling, and processing, and knowledge representation, organization, and verification; different systems and mechanisms have been designed to perform data-intensive tasks in many application fields for classification, predication, recommendation, ranking, filtering, etc. This special focus of Mathematics in Computer Science is organized to stimulate original research on the interaction of mathematics with data and knowledge, in particular the exploration of new mathematical theories and methodologies for data modeling and analysis and knowledge discovery and management, the study of mathematical models of big data and complex knowledge, and the development of novel solutions and strategies to enhance the performance of existing systems and mechanisms for data and knowledge processing. The present foreword provides a short review of some key ideas and techniques on how mathematics interacts with data and knowledge, together with a few selected research directions and problems and a brief introduction to the four papers published in the focus.     

维修保障船与修船厂维修远海受损舰船的定价博弈

维修保障船能够实现远海受损舰船的现场维修,当其进入舰船维修市场时将与修船厂形成一定程度的竞争。为解决维修保障船模式与修船厂模式维修远海受损舰船的最优定价问题,通过分析这两种维修模式在时空以及成本方面的差异,建立维修保障船与修船厂的定价博弈双层规划模型,并设计迭代算法实现模型的求解。以维修远海船体受损的舰船为例,求得了两者的最优定价、最大收益以及船东对两种维修模式的需求,验证了模型与算法的有效性,并分析了调遣距离、舰船受损程度、海上维修技术难度等因素对维修保障船与修船厂定价博弈的影响。该方法能够为维修保障船与修船厂的经营者提供最优定价策略,为两种维修模式的定价博弈提供理论支持。     

准正交基与准正交变换

利用内积给出了准正交基,准正交变换与准对合变换的概念,研究了它们的性质及其之间的联系,获得了许多新的结果,推广了正交基,正交变换,对合变换的概念,性质以及张禾瑞,郝新,邹本强等先生的相关结果。     

小区域科技实力及其评估体系

科技实力是运作主体能够进行并完成科技活动的能力。科技实力是一个评估性概念，它反映了科学技术的创新，发展，转移，推广，储备条件以及管理，效果等不同层面的综合性的特征，科技实力由科技潜在能力（科技势能），科技显现能力（科技动能）构成，它包含了对科技资源及分布状态，科技资源保障能力，科技创新能力，科技开发能力，科技转移能力和科技活动运作能力的综合描述。     

动态投入产出模型及其在高等教育成本分析中的应用

高等院校教育成本核算一直是人们关心的重要问题.把高等院校大学生培养过程,看作人才的生产与加工过程,投入高中毕业生(原材料)以及教学、办公楼等固定资本与教职员工等劳动工时,生产或毕业高校大学毕业生,从而建立高等教育的动态投入产出模型,并由此推导高等院校大学生教育成本的计算公式,指出在计算教育成本时,固定资本租金率与高校规模扩张速度之间的关系,指出进一步深入研究的方向.     

复杂装备研制协调超网络均衡与实现路径

复杂装备研制主体间呈现社会关系、合作关系、协调关系等网络关系,并且相互影响相互作用,其影响复杂装备研制的重要参数。为有效描述在资源环境约束下制造商和供应商的关系,探讨复杂装备研制协调机理与实现路径,本文利用超网络方法,设计了相互影响、相互作用的社会关系网络、协调网络和合作网络的复杂装备研制协调超网络,并将社会关系水平、协调度和合作水平作为超网络的3个决策变量,建立基于关系价值最大、协调成本最低、协调风险最小、合作收益最大、合作风险最小和成本最小等不同偏好下的多目标最优决策模型,构建了复杂装备研制超网络均衡模型,并利用其探讨超网络均衡和实现路径。     

Which is more fundamental: Outward peace or being true to our humanity?

How we perceive and define concepts should be a major concern for teachers and educators in general and for math teachers and educators in particular. This issue, however, is usually ignored or marginalised in curricula and classrooms, where textbooks form the major source of information, knowledge, meanings and definitions. The two words in the theme of this ZDM-issue—math and peace—are themselves good examples to explore. “What do we include in the math curriculum and what do we exclude, and why?” and “What do we mean by peace, and whose peace, and at what human and environmental cost?” are questions that the article raises and tries to point out how we should go about dealing with them. The article challenges the absolute meanings of concepts and stresses the importance of discussing meanings only within context. This concern requires giving teachers and students a greater say in the curriculum, to explore and discuss issues that affect their lives profoundly. The article challenges current values and goals, and suggests what it considers more fundamental values. In particular, it suggests that when there is conflict between peace and being true to our humanity, the latter should be given priority as a guiding value.     

OUTPUT VERSUS INPUT CONTROLS UNDER UNCERTAINTY: THE CASE OF A FISHERY

Abstract The paper compares the management outcomes with a total allowable catch (TAC) and a total allowable effort (TAE) in a fishery under uncertainty. Using a dynamic programming model with multiple uncertainties and estimated growth, harvest, and effort functions from one of the world's largest fisheries, the relative economic and biological benefits of a TAC and TAE are compared and contrasted in a stochastic environment. This approach provides a decision and modeling framework to compare instruments and achieve desired management goals. A key finding is that neither instrument is always preferred in a world of uncertainty and that regulator's risk aversion and weighting in terms of expected net profits and biomass, and the trade‐offs in terms of expected values and variance determine instrument choice.     

Market-based pricing in grids: On strategic manipulation and computational cost

Grid technologies and the related concepts of utility computing and cloud computing enable the dynamic sourcing of computer resources and services, thus allowing enterprises to cut down on hardware and software expenses and to focus on key competencies and processes. Resources are shared across administrative boundaries, e.g. between enterprises and/or business units. In this dynamic and inter-organizational setting, scheduling and pricing become key challenges. Market mechanisms show promise for enhancing resource allocation and pricing in grids. Current mechanisms, however, are not adequately able to handle large-scale settings with strategic users and providers who try to benefit from manipulating the mechanism. In this paper, a market-based heuristic for clearing large-scale grid settings is developed. The proposed heuristic and pricing schemes find an interesting match between scalability and strategic behavior.     

双渠道供应链中的价格决策与服务决策研究

在集中式和分散式决策条件下,应用两阶段优化技术和Stackelberg博弈的理论与方法,对一个制造商与一个零售商组成的双渠道供应链,重点考虑了制造商在网络渠道的服务决策,建立了利润最大化模型,得到了最优的价格策略和服务策略,研究表明,网络渠道的服务水平对制造商和零售商的价格决策有着重要影响,而且消费者对网络直销渠道的偏好对制造商和零售商价格决策和服务决策会产生很大影响．     

基于投人产出分析的中国能源消费分行业碳排放系数因素分解

采用投入产出分析法,结合部门能源消费数据,从最终需求的角度评估和计算了中国1997年、2002年和2007年的碳排放量、碳排放系数、直接碳排放系数和完全碳排放系数.研究结果表明,金属冶炼及压延加工业、燃气生产和供应业、非金属矿物制品业、电力、热力的生产和供应业、水的生产和供应业以及煤炭开采和洗选业的直接碳排放系数历年均是最高的,能源强度是影响这些行业直接碳排放系数变化的主要因素;金属冶炼及压延加工业、非金属矿物制品业、金属制品业、化学工业、电力、热力的生产和供应业、水的生产和供应业以及煤炭开采和洗选业的完全碳排放系数历年均居前列,中间产品投入和能源强度是影响完全碳排放系数变化的主要因素.针对实证结果,现阶段我国节能减排的重点方向在于调控金属冶炼及压延加工业、化学工业等高碳排放行业,并通过提高能源效率、调整产业结构及优化能源结构来达到降低碳排放系数的目的.     

Reexamination of processing time uncertainty

This paper presents the insights gained from the use of data mining and multivariate statistical techniques to identify important factors associated with a country's competitiveness and the development of knowledge discovery in databases (KDD) models to predict it. In addition to stepwise regression and weighted non-linear programming techniques, intelligent learning techniques (artificial neural networks), and inferential techniques (classification and regression trees), were applied to a dataset of 43 countries from the World Competitiveness Yearbook (WCY). The dataset included 55 variables on economic, internationalization, governmental, financial, infrastructure, management, science and technology, as well as demographic and cultural characteristics. Exploratory data analysis and parameter calibration of the intelligent method architectures preceded the development and evaluation of reasonably accurate models (mean absolute error <5.5%), and subsequent out-of-sample validations. The strengths and weaknesses of each of the KDD techniques were assessed, along with their relative performance and the primary input variables influencing a country's competitiveness. Our analysis reveals that the primary drivers of competitiveness are lower country risk rating and higher computer usage, in entrepreneurial urbanized societies with less male dominance and basic infrastructure, with higher gross domestic investment, savings and private consumption, more imports of goods and services than exports, increased purchase power parity GDP, larger and more productive but not less expensive labor force, and higher R&;D expenditures. Without diminishing the role and importance of WCY reports, our approach can be useful to estimate the competitiveness of many countries not included in WCY, while our findings may benefit policy makers and international agencies to expand their own abilities, insights and establish priorities for improving country competitiveness.     

Development and application of Halanay-type theory: Evolutionary differential and difference equations with time lag

We consider extensions, developments and modifications of a result due to Halanay, and the application of “Halanay-type inequalities” in the analysis and numerics of retarded functional-differential equations, difference equations, and retarded functional-difference equations. Our emphasis is on the variety, structure and development, and future development, of Halanay-type results and their applications. We classify and present novel results of Halanay type (linear and non-linear, discrete, semi-discrete, and continuous) and establish their relevance to delay-differential equations, discretized analogues (we consider ?-methods), and difference equations. A rôle for such results in stability and contractivity analysis is made apparent.     

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。     

Aggregation functions and generalized convexity in fuzzy optimization and decision making

In this paper triangular norms and conorms are introduced and suitable definitions and properties are mentioned. Then, aggregation functions and their basic properties are defined. The averaging aggregation operators are defined and some interesting properties are derived. Moreover, we have extended concave and quasiconcave functions introducing t-quasiconcave and upper and lower starshaped functions. The main results concerning aggregation of generalized concave functions are presented and some extremal properties of compromise decisions by adopting aggregation operators are derived and discussed.     

定积分概念中蕴涵的对立统一思想

讨论了定积分定义中所蕴涵的对立统一思想,并从直与曲、整体与局部、近似与精确、有限与无限、特殊与一般、常量与变量等十个方面进行了论述.     

农业科技资源错配对农业科技创新全要素生产率影响的空间溢出效应

为研究农业科技资源错配与农业科技创新全要素生产率之间的空间溢出效应,利用2005-2017年所选取的25个省份的面板数据,通过动态空间杜宾模型进行实证研究.研究显示:①农业科技人力、财力资源错配与农业科技创新全要素生产率存在较强的空间相关性且分别呈现负向的区域内和区域间空间溢出效应.②农业科技财力资源错配程度每提升1%,农业科技创新全要素生产率就会下降0.264%,其中直接效应贡献0.255%,空间溢出效应贡献0.009%;农业科技人力资源错配对于农业科技创新全要素生产率的影响中间接效应起主要作用.③农业科技资源错配对于农业科技创新全要素生产率的空间效应存在显著的地区差异.     

ESTIMATING A STOCHASTIC MODEL OF POPULATION DYNAMICS WITH AN APPLICATION TO KANGAROOS

In this study, we derive stochastic models of population dynamics and devise a new method of estimating the models. The models allow growth and harvest to be nonlinear functions of stochastic processes and the error terms to be nonlinear and heteroskedastic. Ordinary least-squares estimates would be biased and inefficient and generalized least-squares estimates cannot be calculated. Therefore, we implement nonlinear maximum likelihood methods to find unbiased and efficient estimates of parameters. The method is applied to the population dynamics of kangaroos in South Australia. Aerial survey data of kangaroo numbers are combined with harvest, effort and rainfall data to estimate the growth and harvest functions and the variances of the stochastic processes which drive the system. Results suggest that growth and harvest should be modeled as functions of stochastic processes and that observations on kangaroo numbers are critical for estimating population dynamics. The results also indicate that the estimation method works well and is a viable alternative to ARIMA and GARCH models, particularly for small data sets.     

Collaborative Curriculum Investigation as a Vehicle for Teacher Enhancement and Mathematics Curriculum Reform

The Missouri Middle Mathematics (M³) Project is an NSF-funded 3-year professional development project involving teacher/administrator teams from districts statewide. Project activities focus on collaborative investigation of emerging reform-based middle school mathematics curricula to support individual and systemic reform. Collaborative review and field-testing of material facilitates awareness and exploration of alternative instructional and assessment strategies and informed decision making. Early indicators of the model's success are reflected in participants’ enthusiasm and professional growth. Project activities stimulate discussions of critical topics including questioning appropriateness of various teaching practices, research about teaching and learning, tracking policies, appropriate assessment models for gauging student learning and the importance of calculators and manipulatives as teaching and learning tools. These discussions transcend curriculum materials being reviewed and serve as a powerful vehicle for professional growth and development for individual teachers and districts.     

Maintenance models in warranty: A literature review

Along with increasing the warranty period for complex systems, reducing the warranty servicing costs has become an issue of great importance to the manufacturers. One possible way to reduce the expected warranty servicing cost is by making sound decision on the product warranty and maintenance strategies. Therefore, warranties (basic warranty and extended warranty) and maintenance (corrective and preventive) are strongly interlinked and of great interest to both manufacturers and customers. This paper is the first identifiable academic literature review to deal with warranty and maintenance. It provides a classification scheme for the articles that link warranty and maintenance published between 2001 and 2011 covering 44 journals and proposes a taxonomy scheme to classify these articles. Nine hundred articles were identified for their relevance to warranty and were carefully reviewed. One-hundred and twenty-two articles were subsequently selected for their relevance to maintenance and included in the classification.