例说概率与立体几何的交汇与融合

1研究缘起 在高中数学复习中，各知识点练习题选配的优劣，对于巩固所学知识，并使所学知识信息系统化有着很重要的作用．因此，练习题的选配作为知识链的衔接应当予以足够重视。实践证明，练习题若过多过滥，教师和学生将陷入茫茫题海战，很难理出头绪；若过少，则又会出现“狗熊掰棒子”现象，所以如何在复习中针对性地把握好课本中数学命题的实质、内涵，而后在质和量上选配好练习题，值得每位老师认真对待。     

极值分布理论在计算波高多年分布中的应用

在海洋工程的设计中,正确掌握波高的多年分布规律,从而合理地确定多年一遇的设计波高数值,对于建筑物的造价和安全,都很有关系。我们对国内外现有的计算方法进行了比较和验证。归纳起来,国内外较为普遍采用的方法,不外是两种类型:一种为对年最大波高组成的系列选取一条适合的理论频率曲线(如皮尔逊三型曲线、冈贝尔曲线等),外延推求多年一遇设计波高;另一种为使用全部实测波高资料,利用某种坐标转换,再直线外延求多年一遇设计波高。第一类方法的主要问题在于波高实测资料的年限太短,由十余个经验点选配一条理论频率曲线,其任意性是比较大的。第二类方法,系经验     

复合极值分布理论及其应用

在海洋工程、水利工程、排水及铁路桥涵等建筑工程中,普遍采用皮尔逊三型、龚贝尔、克-曼型曲线推求多年一遇设计波浪、暴雨、风速等。由于一年只选用一个最大值组成系列进行计算,因此,在资料年限较短的情况下,计算误差较大,并且也难于选配一条与经验点配合较好的理论频率曲线。本文提出了一个新概念:一个离散型分布和一个连续型分布可以构成一个“复合极值分布”。在此概念基础上得到了使用泊松(Poisson)-龚贝尔(Gumbel)复合极值分布来推算台风波浪多年一遇设计波高,多年一遇设计风速,多年     

财经类中专珠算教学之我见

珠算课在财经类中专学校中属于专业性基础课，也是必修课，由于各校师资配备和对珠算课的重视程度不同，所以效果也各不尽相伺。有的学校选配年富力强，教学有方的教师，有的学校则选用年老体弱或能力较差的教师承担珠算课教学。更由于各校的招生对象、目的和教学方法上的差异，导致同类学校珠算技术水平存在着一个很大的差距。珠算是中华民族的宝贵遗产，     

正多边形控制的曲线段及其性质

本文给出了由多边形控制曲线段的方法，并依据多边长的延长量的性质，讨论了相应曲线段的性质，并给出了数值例子和对应图象，文末还给出了以曲线段为切线多边形的B－样条曲线方程和以曲线段端点为插值点的插值函数。     

基于刘徽割圆术的等距线逼近算法

给出了一种基于刘徽割圆术的平面NURBS曲线的等距线的逼近算法。利用正多边形代替圆所扫掠出的区域边界来近似等距曲线，所得到的逼近曲线是与基曲线同次的NURBS曲线，并且可以达到任意的精度。     

有理曲线的多项式逼近

利用曲线摄动的思想给出了用多项式曲线逼近有理曲线的一种新方法．其基本步骤是对有理曲线的控制顶点进行摄动，使之产生一多项式曲线，并使摄动误差在某种范数意义之下达到最小．同时，通过适当控制摄动曲线的顶点，使逼近多项式曲线与有理曲线在两端点保持一定的连续性．这一结果可以与细分（ｓｕｂｄｉｖｉｓｉｏｎ）技术结合给出有理曲线的整体光滑的分片多项式逼近．实例表明，在某些情况下本文中的方法要优于传统的Ｈｅｒｍｉｔｅ插值方法及Ｔ．Ｗ．Ｓｅｄｅｒｂｅｒｇ和Ｍ．Ｋａｋｉｍｏｔｏ（１９９１）提出的杂交曲线逼近算法．     

拟合及预测饱和增长趋势的广义逻辑（Logistic）曲线模型

本文讨论了逻辑（Ｌｏｇｉｓｔｉｃ）曲线与龚柏兹（Ｇｏｍｐｅｒｔｚ）曲线模型结构上的缺点。针对这些缺点，文中提出利用广义逻辑曲线模型拟合及预测饱和增长趋势，解释了该模型包含的实际经济意义，并给出了相应的参数估计算法，以实例说明了该模型具有高于逻辑曲线和龚柏兹曲线的预测精度。     

求轨迹方程时要注意“去伪”与“补漏”

我们知道，求曲线方程可分为两类：（1）已知曲线类型，求曲线方程；（2）不知曲线类型，求曲线方程．对于第（1）类，通常可用待定系数法解决．对于第（2）类，需要在适当的直角坐标系中，将动点满足的几何关系转化为动点坐标的方程后，经化简得出轨迹方程．教学中发现，学生在解决第（2）类问题时，常常在求出方程后就以为大功告成，不再去考虑方程的曲线是否与已知轨迹相符．根据曲线与方程的关系，只有当所求方程的曲线与已知轨迹恰好一致，即方程的曲线上的点恰好与已知轨迹上的点一样多，才能称所求方程是已知轨迹的方程，如若不然，…     

重心坐标系下平面上三次Bezier曲线奇拐点的分布

本文利用重心坐标，研究Bezier曲线奇拐点的分布，绘出了奇拐点存在的区域和充要条件，简化了判别Bezier曲线奇拐点的充要条件。并给出了Bezier曲线的重心坐标表示方法．     

A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem

In this paper, a new fuzzy multiple attribute decision-making (FMADM) method, which is suitable for multiple attributive group decision making (GDM) problems in fuzzy environment, is proposed to deal with the problem of ranking and selection of alternatives. Since the subjectivity, imprecision and vagueness in the estimates of a performance rating enter into multiple attribute decision-making (MADM) problems, fuzzy set theory provides a mathematical framework for modelling vagueness and imprecision. In the proposed approach, an attribute based aggregation technique for heterogeneous group of experts is employed and used for dealing with fuzzy opinion aggregation for the subjective attributes of the decision problem. The propulsion/manoeuvring system selection as a real case study is used to demonstrate the versatility and potential of the proposed method for solving fuzzy multiple attributive group decision-making problems. The proposed method is a generalised model, which can be applied to great variety of practical problems encountered in the naval architecture from propulsion/manoeuvring system selection to warship requirements definition.     

Decision making in industrial production planning using fuzzy linear programming

Any modern industrial manufacturing unit inevitably faces problemsof vagueness in various aspects such as raw material availability,human resource availability, processing capability and constraintsand limitations imposed by the marketing department. Such acomplex problem of vagueness and uncertainty can be handledby the theory of fuzzy logic. In this paper, a new fuzzy logicbased methodology using a S-curve membership function is usedto solve a fuzzy mix product selection problem in industrialengineering. Profits and satisfaction levels have been computedusing a fuzzy linear programming approach. Since there are severaldecisions to be taken, a performance measure has been definedto identify the decision that achieves a high level of profitwith a high degree of satisfaction.     

Metaphysical Vagueness and Metaphysical Indeterminacy

The topic of this paper is whether there is metaphysical vagueness. It is shown that it is important to distinguish between the general phenomenon of indeterminacy and the more narrow phenomenon of vagueness (the phenomenon that paradigmatically rears its head in sorites reasoning). Relatedly, it is important to distinguish between metaphysical indeterminacy and metaphysical vagueness. One can wish to allow metaphysical indeterminacy but rule out metaphysical vagueness. As is discussed in the paper, central argument against metaphysical vagueness, like those of Gareth Evans and Mark Sainsbury, would if successful rule out metaphysical indeterminacy. One way to argue specifically against the possibility of metaphysical vagueness might be thought to be to argue for a specific theory of the nature of vagueness according to which vagueness is a semantic phenomenon. But it is shown that there are complications also pertaining to arguments with that structure. Toward the end of the paper, I discuss Trenton Merricks’ well-known argument against a semantic view on vagueness and for a metaphysical view.     

Exact and heuristic procedures for solving the fuzzy portfolio selection problem

We propose a fuzzy model for the portfolio selection problem which takes into account the vagueness of the investor’s preferences regarding the assumed risk. We also describe an exact method for solving it as well as a hybrid meta-heuristic procedure which is more adequate for medium and large-sized problems or in cases in which a quick solution is needed. As an application, we solve several problems based on data from the IBEX35 index and the Spanish Stock Exchange Interconnection System.     

A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection

This paper presents a new procedure that extends genetic algorithms from their traditional domain of optimization to fuzzy ranking strategy for selecting efficient portfolios of restricted cardinality. The uncertainty of the returns on a given portfolio is modeled using fuzzy quantities and a downside risk function is used to describe the investor's aversion to risk. The fitness functions are based both on the value and the ambiguity of the trapezoidal fuzzy number which represents the uncertainty on the return. The soft-computing approach allows us to consider uncertainty and vagueness in databases and also to incorporate subjective characteristics into the portfolio selection problem. We use a data set from the Spanish stock market to illustrate the performance of our approach to the portfolio selection problem.     

采购量分配决策模糊规划模型

供应商对形成企业的竞争力起着关键性的作用。采购决策中,采购商需要决策两方面的问题:应该选择哪些供应商以及在每一供应商应该采购多少。本文考虑了多目标性和目标的模糊性,同时为供应商选择和采购量分配提出了一个集成的决策模型。最后,通过一个算例阐释了该模型。     

Introduction: Vagueness and Ontology

The article introduces a special issue of the journal Metaphysica on vagueness and ontology. The conventional view has it that all vagueness is semantic or representational. Russell, Dummett, Evans and Lewis, inter alia, have argued that the notion of “ontic” or “metaphysical” vagueness is not even intelligible. In recent years, a growing minority of philosophers have tried to make sense of the notion and have spelled it out in various ways. The article gives an overview and relates the idea of ontic vagueness to the unquestioned phenomenon of fuzzy spatiotemporal boundaries and to the associated “problem of the many”. It briefly discusses the question of whether ontic vagueness can be spelled out in terms of “vague identity”, emphasizes the often neglected role of the difference between sortal and non-sortal ontologies and suggests a deflationary answer to the ill-conceived question of whether the “ultimate source” of vagueness lies either in language or in the world.     

可重构制造系统重组过程中设备选择模型的研究

根据生产任务选择加工设备进行制造资源重组是实现可重构制造系统的关键问题之一，由于设备的选择涉及到多种因素，既有定量指标，又有定性指标，传统的依靠人工经验的方法显得力不从心。本文首先结合实际情况，提出了一套设备选择评价体系，通过对模糊判断矩阵采用最小对数二乘法确定各评价因素的权重系数，针对定性指标和定量指标采用不同的方法确定其性能指标值，通过模糊积分对评判指标进行综合评判，最后进行了实例研究。所提出的方法有效地简化了决策过程，为可重构制造系统设备选择提供了一套行之有效的方法。     

Moral Dilemmas and Vagueness

In this paper we point out some interesting structural similarities between vagueness and moral dilemmas as well as between some of the proposed solutions to both problems. Moral dilemma involves a situation with opposed obligations that cannot all be satisfied. Transvaluationism as an approach to vagueness makes three claims concerning the nature of vagueness: (1) it involves incompatibility between mutually unsatisfiable requirements, (2) the underlying requirements retain their normative power even when they happen to be overruled, and (3) this incompatibility turns out to be rather benign in practice. Given that transvaluationism is inspired by moral dilemmas, these claims are assessed in respect to them. Transvaluationism provides a smooth account of the mentioned claims concerning vagueness. Following a brief discussion of Sorensen’s views on moral dilemmas and conflict vagueness, we offer a model of moral pluralism accommodating structurally similar claims about the nature of moral conflict and moral dilemmas.     

Ten questions and one problem on fuzzy logic

Recently, I had a very interesting friendly e-mail discussion with Professor Parikh on vagueness and fuzzy logic. Parikh published several papers concerning the notion of vagueness. They contain critical remarks on fuzzy logic and its ability to formalize reasoning under vagueness [10,11]. On the other hand, for some years I have tried to advocate fuzzy logic (in the narrow sense, as Zadeh says, i.e. as formal logical systems formalizing reasoning under vagueness) and in particular, to show that such systems (of many-valued logic of a certain kind) offer a fully fledged and extremely interesting logic [4, 5]. But this leaves open the question of intuitive adequacy of many-valued logic as a logic of vagueness. Below I shall try to isolate eight questions Parikh asks, add two more and to comment on all of them. Finally, I formulate a problem on truth (in)definability in Łukasiewicz logic which shows, in my opinion, that fuzzy logic is not just “applied logic” but rather belongs to systems commonly called “philosophical logic” like modal logics, etc.