Ethnomathematics: Why, and what else?

Ethnomathematics—we all have some notions of what it is, but should it be influencing school mathematics? This paper considers a justification for the influence from a constructivist perspective, and considers the implications of enactivism and other ways of thinking on ethnomathematics. My conclusion is that the influence should be broader—that different cultural groups may have different ways of knowing, that we may be asking the wrong questions, and that we might need to consider ‘ethno-education’     

Efficient Genetic Algorithms Using Simple Genes Exchange Local Search Policy for the Quadratic Assignment Problem

In this paper, we describe an approach for solving the quadratic assignment problem (QAP) that is based on genetic algorithms (GA). It will be shown that a standard canonical GA (SGA), which involves genetic operators of selection, reproduction, crossover, and mutation, tends to fall short of the desired performance expected of a search algorithm. The performance deteriorates significantly as the size of the problem increases. To address this syndrome, it is common for GA-based techniques to be embedded with deterministic local search procedures. It is proposed that the local search should involve simple procedure of genome reordering that should not be too complex. More importantly, from a computational point of view, the local search should not carry with it the full cost of evaluating a chromosome after each move in the localized landscape. Results of simulation on several difficult QAP benchmarks showed the effectiveness of our approaches.     

Costing communication standards in information systems using a minimum cut approach

On a very abstract level, an information system consists of a set of system elements which communicate with each other. Communication is an unproductive operation, so the time needed to communicate data should be kept as short as possible and, to put it in monetary terms, the opportunity costs for communication should be kept small. Now, communicating data is more than just transmitting it; it consists in large parts of converting data structures that are used by one system element into data structures that are used by another system element. Such conversion can be avoided, if the system elements, use a common standard of data structures. Since establishing a standard at a system element incurs standardization costs, a decision-maker has to check, if the cost savings gained by standardized communication outweigh the costs for installing the standard. In a recent paper by Buxmann et al¹, it is claimed that this so-called standardization problem is an NP-hard optimization problem without giving a formal proof for it. We will demonstrate that this claim is not true, but in fact the standardization problem can be solved in polynomial time by solving a minimum cut problem.     

Optimal Mission Duration for Partially Repairable Systems Operating in a Random Environment

As a system failure during a mission can result in considerable penalties, at some instances it is more cost-effective to terminate operation of a system than to attempt to complete its mission. This paper analyzes the optimal mission duration for systems that operate in a random environment modeled by a Poisson shock process and can be minimally repaired during a mission. Two independent sources of failures are considered and for both cases, the failures are classified as minor or terminal in accordance with the Brown-Proschan model. Under certain assumptions, an optimal time of mission termination is obtained. It is shown that, if for some reason a termination is not technically possible at this optimal time, the mission should be terminated within a specific time interval and, if this is not possible, it should not be terminated beyond this interval. Illustrative examples are presented. The influence of mission and system parameters on the mission termination interval is demonstrated.     

Mechanisms and Difference-Making

I argue that difference-making should be a crucial element for evaluating the quality of evidence for mechanisms, especially with respect to the robustness of mechanisms, and that it should take central stage when it comes to the general role played by mechanisms in establishing causal claims in medicine. The difference-making of mechanisms should provide additional compelling reasons to accept the gist of Russo-Williamson thesis and include mechanisms in the protocols for Evidence-Based Medicine (EBM), as the EBM+ research group has been advocating.     

用于枪炮射表整体解析逼近的一列基函数

本文提出用于枪炮射表整体解析逼近的一列基函数.在一个具体型号的火炮的射表上作出的数值试验表明效果良好.这列基函数对于其它型号枪炮射表的逼近应该同样有参考价值.为得出这列基函数而提出的开拓与不变性的分析方法,在数学模型工作中对于其它许多表函数的整体解析逼近应该同样有参考价值.     

On semigroups admitting ring structure

A multiplicative semigroup S with 0 is said to be a R-semigroup if S admits a ring structure. Isbell proved that if a finitely generated commutative semigroup is a R-semigroup, then it should be finite. The non-commutative version of this theorem is unsettled. This paper considers semigroups, not necessarily commutative, which are principally generated as a right ideal by single elements and semigroups which are generated by two independent generators and describes their structure. We also prove that if a cancellative 0-simple semigroup containing an identity is a R-semigroup, then it should be a group with zero. Communicated by A. H. Clifford     

A psychomathematically‐based teaching method†

Mathematical education is concerned with two questions: what to teach and how to teach. In this article the question of how will be discussed.

We begin with the statement that a necessary, though insufficient, condition for any progress in mathematical education is that it should be based on psychomathematical research, rather than tradition or the imitation of a ‘ good ‘ teacher.

One of the results of psychomathematical research is that a secondary school student's immediate (i.e. direct) memory is very limited. On the other hand, a teaching method is useless if it demands that more items be kept in the immediate (i.e. direct) memory than is possible. Of course, it is not enough merely to say what should not be demanded; we must also explain what should be done. A psychomathematically‐based teaching method (PBTM) has been developed with this aim in view. It suggests the use of external sources of memory in a special form, the details of which are given in this paper. Experience shows that recurrent usage of the external source of memory fixes its contents in the auxiliary (long‐term) memory without any effort.

The method was investigated in a controlled experiment. The difference between the results of the experimental and control groups was significant in most of the cases at the 0‐001 level.

     

Species extinction problem: genetic vs ecological factors

Conservation biologists have been facing an intriguing question: whether it is genetic or ecological factors which govern the ecological systems. In this paper, we have constructed a few model systems describing real ecological situations and analysed them using a methodology designed for the purpose. Simulation experiments suggest that both these factors should be given equal weightage in working out strategies for any conservation effort. We conclude that the complex ecosystems are safe places for species belonging to the higher life forms, especially, generalist predators. On the contrary, simple (small) ecosystems cannot harbour these species for long. Another useful observation is that the vertebrate predators should be preferred to their invertebrate counterparts while aiming at conserving endangered prey species.     

Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update

A group of agents have claims on a resource but there is not enough of it to honor all of the claims. How should it be divided? A group of agents decide to undertake a public project that they can jointly afford. How much should each of them contribute? This essay is an update of Thomson (2003), a survey of the literature devoted to the study of such problems.     

非对称信息条件下的企业人力资源规划研究

本论针对企业管理中存在的员工工作表现难考核和信息不对称的问题，提出企业首先要根据各类职务的工作性质制定出可量化的标准(合理)的工作绩效水平，其次在信息不对称的情况下，考虑管理成本的节约，建立博弈模型，最后得出企业应选取的最优监督概率和员工的违规概率，据此采取相应的策略以取得最好的经济效益。     

Searching for multiobjective preventive maintenance schedules: Combining preferences with evolutionary algorithms

Heavy industry maintenance facilities at aircraft service centers or railroad yards must contend with scheduling preventive maintenance tasks to ensure critical equipment remains available. The workforce that performs these tasks are often high-paid, which means the task scheduling should minimize worker idle time. Idle time can always be minimized by reducing the workforce. However, all preventive maintenance tasks should be completed as quickly as possible to make equipment available. This means the completion time should be also minimized. Unfortunately, a small workforce cannot complete many maintenance tasks per hour. Hence, there is a tradeoff: should the workforce be small to reduce idle time or should it be large so more maintenance can be performed each hour? A cost effective schedule should strike some balance between a minimum schedule and a minimum size workforce.     

On parametric polynomial circle approximation

In the paper, the uniform approximation of a circle arc (or a whole circle) by a parametric polynomial curve is considered. The approximant is obtained in a closed form. It depends on a parameter that should satisfy a particular equation, and it takes only a couple of tangent method steps to compute it. For low degree curves, the parameter is provided exactly. The distance between a circle arc and its approximant asymptotically decreases faster than exponentially as a function of polynomial degree. Additionally, it is shown that the approximant could be applied for a fast evaluation of trigonometric functions too.     

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.     

Auditing Shaked and Shanthikumar’s ‘excess wealth’

A notion called “excess wealth” was introduced by Shaked and Shanthikumar around 1998 (Probab. Eng. Inf. Sci. 12:1–23, 1998). Subsequent to this, much has been written on it, mostly by Shaked and his colleagues; see Sordo (Insur. Math. Econ. 45(3):466–469, 2009) for a recent review. These works have appeared in the literatures of reliability theory and stochastic orderings. Since the term excess wealth connotes a measure of income inequality—much like its dual, poverty—it should have had an impact in economics and the econometric literature. This, it appears is not the case, at least to the extent that it should be. The purpose of this paper is to investigate the above disconnect by looking at the notion of excess wealth more carefully, but keeping in mind the angle of economics and income. Our conclusion is that an alternative definition of excess wealth better encapsulates what one means by a colloquial use of the term. Our motivation for being attracted to this topic arises from two angles. The first is that the stochastics of diagnostic and threat detection tests, in which we have an interest, has a strong bearing on indices of concentration like the Lorenz Curve, the Gini index, and the entropy. Thus the notion of excess wealth, which conveys a sense of income concentration should also be relevant to diagnostics. The second motivation is to honor Moshe Shaked, a prolific researcher and a friend of the first author, by developing a paper based on an idea that is co-attributed to him.     

Loans,ordering and shortage costs in start-ups: a dynamic stochastic decision approach

Start-up companies are a vital ingredient in the success of a globalised networked world economy. We believe that such companies are interested in maximising the chance of surviving in the long term. We present a Markov decision model to analyse survival probabilities of start-up manufacturing companies. Our model examines the implications of their operating decisions, in particular how their inventory strategy is influenced by purchasing, shortage, transportation and ordering costs, as well as loans to the firm. It is shown that although the start-up company should be more conservative in its component purchasing strategy than if it were a well-established company it should not be too conservative. Nor is its strategy monotone in the amount of capital available.     

The structure of qualitative decision-making

A system is proposed for analysing qualitative decision-making. Its structure is based on dichotomous answers to simple questions. What should be done? Has it more of a planning emphasis, or has it more to do with putting plans into effect? Where should it be done? Is it more in the place of the decision-making activity, or has it more to do with the people involved? These lead to the creation of four general kinds of activity: proposition, perception, pull and push, which are shown to be phases in a cycle. Corresponding primary feelings are identified: fear, anxiety, guilt and resentment, and, similarly, appropriate responses: faith, hope, righteousness and love. A distinction is made between the decision-possessor and the decision-participant. Guilt is seen as being imposed by a decision possessor on the decision participant as part of a pull activity. Subjective (as distinct from objective) decision-making arises when the decision possessor is subjectively involved as the participant; the pull activity does not occur and consequently guilt cannot arise. Subjective decision making is shown to be a developmental activity which has three levels: somatical, psychical and pneumatical. By contrast, objective decision making is seen to correspond more to adjustment to outside impulses. Supporting evidence from different contexts is given to show that such categorisations of activities are natural to decision-making.     

关于∑*-空间的一点注记

指出Ｄｎ真包含于∪｛Ｅｍ：ｍ∈Ｎ｝对σ－空间成立,但对∑＾＊－空间,我们给出了一个例子说明它是不成立的。因而「５」中是３．２．１３是不对的。这样「３」中的主要结论需要重新考虑。     

The Placing of Service Points to Minimize Travel

We wish to site a given number of offices or other service points in a district, so that the mean travelling distance between clients and their nearest office is as low as possible. It is shown that the density of the offices should be proportional to the two-thirds power of the population density. This theoretical result does not take account of local conditions, but it may be made the basis for a study on the ground.     

OR as Technology: Some Issues and Implications

There has been a growing acceptance of the view that OR can be more appropriately understood as a technology rather than as a science. This view has, however, not been fully developed. This paper seeks to extend this area of investigation by addressing three issues: first, to consider why it is inappropriate to see OR as a science; second, if OR is to be seen as a technology, to ask what model of a technology, the classical or the modern, should be adopted; finally, to explore what implications for understanding OR are held by the most appropriate model of OR as technology. This paper shows that valuable insights might be gained for understanding and guiding the development of OR by seeing it as a technology.