The futility of decision making research

We have each spent more than 50 years doing research that has had little impact. Even more lamentable is that our field, judgment and decision making (JDM), has on the whole had little impact during that span. We attribute that failure to the use of methodologies that emphasize testing models rather than looking for differences in behavior. The “cognitive revolution” led the field astray, toward the goal of studying model fit rather than comparing observable results. With modeling as the goal, experimentation was stultified. Simple tasks became dominant. Although a poor metaphor for real decision making, the gambling paradigm has lasted forever because the inputs to the decision are known to the researcher and thus easily modeled.     

New theories for new instruments: Fabrizio Mordente's proportional compass and the genesis of Giordano Bruno's atomist geometry

The aim of this article is to shed light on an understudied aspect of Giordano Bruno's intellectual biography, namely, his career as a mathematical practitioner. Early interpreters, especially, have criticized Bruno's mathematics for being “outdated” or too “concrete”. However, thanks to developments in the study of early modern mathematics and the rediscovery of Bruno's first mathematical writings (four dialogues on Fabrizio's Mordente proportional compass), we are in a position to better understand Bruno's mathematics. In particular, this article aims to reopen the question of whether Bruno anticipated the concept of infinitesimal quantity. It does so by providing an analysis of the dialogues on Mordente's compass and of the historical circumstances under which those dialogues were written.     

黎曼猜想什么时候会被证明出来?

首先从对数学猜想证明的理解得出了影响证明数学猜想的两个重要因素,即数学猜想的证明依赖于必要的数学进展和合适的数学家;接着对这两个因素进行分析;由于对黎曼猜想的证明来说,无论是所需要的数学知识和方法是否具备还是是否有合适的数学家二者都是不确定的,因而无法肯定该猜想什么时候才能被证明出来。     

Multi-model ensembles in climate science: Mathematical structures and expert judgements

Projections of future climate change cannot rely on a single model. It has become common to rely on multiple simulations generated by Multi-Model Ensembles (MMEs), especially to quantify the uncertainty about what would constitute an adequate model structure. But, as Parker points out (2018), one of the remaining philosophically interesting questions is: “How can ensemble studies be designed so that they probe uncertainty in desired ways?” This paper offers two interpretations of what General Circulation Models (GCMs) are and how MMEs made of GCMs should be designed. In the first interpretation, models are combinations of modules and parameterisations; an MME is obtained by “plugging and playing” with interchangeable modules and parameterisations. In the second interpretation, models are aggregations of expert judgements that result from a history of epistemic decisions made by scientists about the choice of representations; an MME is a sampling of expert judgements from modelling teams. We argue that, while the two interpretations involve distinct domains from philosophy of science and social epistemology, they both could be used in a complementary manner in order to explore ways of designing better MMEs.     

浅谈极限在《数学分析》课程中的作用

该文首先介绍极限定义的形成,发展和完善,在了解极限定义的基础上来进一步理解极限理论,极限理论是微积分的基础,其次主要介绍了极限在连续定义、导数定义、积分定义等方面的应用.     

库车裂缝性砂岩气藏渗透率模型研究与应用

裂缝性气藏中孔隙介质包括压裂裂缝、天然裂缝及基质孔隙。考虑裂缝与基质间的物质交换,建立了考虑压裂裂缝的多重孔隙介质渗流数学模型,研制了裂缝性气藏压裂后生产动态模拟器。根据库车天然裂缝发育程度综合量化分类,天然裂缝发育程度是影响压裂后产能的重要因素之一;裂缝系统连通差、发育差的气藏,压裂后也难以获得理想的增产效果。统计分析了裂缝参数与渗透率的关系,裂缝密度与测试渗透率相关性好,给出了裂缝密度与渗透率的关系,建立了渗透率地质模型。结合裂缝性砂岩气藏压裂井生产动态模拟器,通过拟合试采压力校正渗透率,打破了关井测试计算地层渗透率的传统做法。通过实例计算表明,所建立的多重介质渗流数学模型和渗透率地质模型是合理的,试采压力拟合精度高,校正渗透率准确且误差较小,为油田开发提供了一种新思路。     

基于Soft多结构元素形态学的TM图像边缘检测

基于传统的数学形态学边缘检测算法,改进结构元素,提出Soft多结构元素算子。针对TM图像中存在噪声多和边缘形态多样性的特点,构建多结构元素,并结合Soft形态学方法,对TM图像进行形态学的腐蚀和膨胀,实现遥感图像的边缘检测。     

在高职院校高等数学的教学中融入数学实验的探讨

21世纪教学内容和课程体系改革的趋势是朝着实践性和应用性方向发展。结合本校教学实际的改革措施:在教学过程中融入数学思想,初步探讨了融入数学实验思想的必要性。     

一种有效的车牌定位方法——数学形态学和字符边缘特征相结合的车牌定位方法

汽车车牌的定位是车牌自动识别系统中的关键环节。采用数学形态学和字符边缘特征相结合的方法对车牌进行定位,首先对车牌图像进行图像的预处理,然后利用数学形态学进行粗定位,最后利用字符边缘特征进行车牌的精确定位。从而实现了车牌图像的准确定位。     

左脑是计算的,右脑是几何的吗?——关于R·斯佩里“裂脑”研究引发的两个观点的质疑

数学认知不仅涉及认知神经科学研究,而且也关乎知识论的辨护。自R.斯佩里开展裂脑研究以来,关于人类大脑左半球是计算的(或数学的),右半球是几何的(或非数学的)的观点,似乎成为一种定论。然而,随着认知神经科学的充分发展和脑成像技术的广泛运用,人们愈来愈清楚地看到,这种划分和判断过于简单化了,同时缺乏可靠的实证材料的支撑,同时在一些概念上混淆不清。为此,依据最新的实验报告加以诠释,并从知识论的高度进行辨析,显然是十分必要的。