“疯狂”创富的理性密码

某种程度上讲,本次创业板IPO市盈率如此之高,正反映了市场对这些企业所在行业的产业溢价、盈利能力和未来成长预期的看好和追捧。问题在于：这种高成长是否具有可持续性？     

谈数学理性之美

"天上下雨地上湿,今天下雨今天湿"这个在生活中看似再简单不过的道理,细细想来却蕴涵着一种严密的逻辑人的思维总是结合了理性与感性,当曹孟德对酒当歌,吟诵"人生几何"之时,我们钦佩那豪放洒脱之美,然而当我们面对陈景润为证明哥德巴赫猜想所写下的密密麻麻的数字和符号时,却难以发现那种朴素严谨之美.有时我们难以理解数学家坐在书桌前为解一道题列出几米长的竖式和用掉无数张草稿纸的那种执着和狂热,但我们明白那些数字和符号、那种理性的思想就像魔法一样让他们深深地迷恋.     

Reissner厚板弹性弯曲的理性有限元法

本文在非协调元的修正泛函中引入满足系统微分方程的单元变形模式,提出了一种将解析方法与数值方法有机结合的理性有限元法。这种新的计算方案合乎单元的力学要求和结构的几何复杂性要求。据此所得的厚板弯曲四边形单元具有计算精度高、可对刚度矩阵精确积分等优点。     

有限理性双寡头博弈模型的复杂性分析

以Bowley博弈模型为核心,将寡头的调整速度作为企业的竞争策略,并对该模型Nash均衡点的稳定域进行分析;通过数值仿真把双寡头的策略区域分为均衡区、周期区和混沌区。研究发现双寡头博弈市场中,寡头为了获得更大的利润而不断改变自身产量策略,这是市场出现周期波动、甚至陷入混沌的根本内因.     

数学体验:理性思维培育的重要基点——以“弦长公式”的教学为例

理性思维的培育是发展学生核心素养的关键,也是数学育人的重要内容.本文以“弦长公式”的教学为例进行分析,指出了以数学体验为基点,培育学生理性思维的意义:数学体验是形成数学理性的经验基础,是探寻数学本质的必要历程,是理清解题逻辑的活动主线.     

有限理性下参数最优化问题解的稳定性

主要研究有限理性下参数最优化问题解的稳定性. 即在两类扰动即目标函数及可行集二者, 目标函数、可行集及参数三者分别同时发生扰动的情形下, 对参数最优化问题引入一个抽象的理性函数, 分别建立了参数最优化问题的有限理性模型M, 运用``通有'的方法, 得到了上述两种扰动情形下相应的有限理性模型M的结构稳定性及对\varepsilon-平衡(解)的鲁棒性, 即有限理性下绝大多数的参数最优化问题的解都 是稳定的, 并以一个例子说明所得的稳定性结果均是正确的.     

美元“跳水”不易

无论从市场杠杆还是政治因素来看,美元在中短期都会走出一波上升行情,但从长期来看,无论跳水还是飙升,似乎都不太可能。     

基于Agent仿真的个体有限理性与众包绩效的关系研究

如何筛选有限理性参与者是企业实施众包的关键问题。通过引入个体有限理性,扩展了经典的NK模型,构建了模拟竞赛式众包问题解决过程的多主体仿真模型,研究了个体有限理性水平、个体有限理性系统化程度以及个体有限理性水平标准差对众包绩效的影响。仿真结果显示,个体有限理性水平对提高众包绩效有显著的正向影响,尤其是在任务复杂性较高的情况下;个体有限理性系统化程度和个体有限理性水平标准差对众包绩效也有正向影响,但依赖于个体有限理性水平。当企业有一个复杂性较高的任务时,如果追求所有方案的整体改善,企业需要招募有限理性水平较高的个体,并组成有限理性系统化程度较高且有限理性水平标准差较大的群体;如果追求少数优质方案,企业需要招募有限理性水平较高的个体,并组成有限理性系统化程度较低且有限理性水平标准差较大的群体。     

群体理想偏爱映射的若干理性条件

本文研究求解群体多目标最优化问题的理想偏爱法的性质,证明了对应的理想偏爱映射满足基数型群体决策规则的匿名性,中立性,正响应性,非负响应性,强Pareto原则以及局部非独裁性等理性条件.     

感性认识走向理性思维 让空间观念的培养落地生根——以苏科版“图形的平移”为例

“空间观念”是初中阶段核心素养的主要表现之一,培养空间观念是发展空间想象力的奠基石.本文对比了“空间观念”在不同版本课标(大纲)的发展与演变过程,描述了2022版课标中“空间观念”的内涵及表征;以苏科版“图形的平移”为例,课堂上引领学生在感性认识逐渐过渡到理性思维中发展空间观念,让空间观念的培养落实到常规教学中.     

Learning to See: Making Sense of the Mathematics of Change in Middle School

In this article, we will describe the results of a study of 6th grade students learning about the mathematics of change. The students in this study worked with software environments for the computer and the graphing calculator that included a simulation of a moving elevator, linked to a graph of its velocity vs. time. We will describe how the students and their teacher negotiated the mathematical meanings of these representations, in interaction with the software and other representational tools available in the classroom. The class developed ways of selectively attending to specific features of stacks of centimeter cubes, hand-drawn graphs, and graphs (labeled velocity vs. time) on the computer screen. In addition, the class became adept at imagining the motions that corresponded to various velocity vs. time graphs. In this article, we describe this development as a process of learning to see mathematical representations of motion. The main question this article addresses is: How do students learn to see mathematical representations in ways that are consistent with the discipline of mathematics? This revised version was published online in July 2006 with corrections to the Cover Date.     

Topological Hypergroups in the Sense of Marty

In this paper, we introduce the concept of topological hypergroups as a generalization of topological groups. A topological hypergroup is a nonempty set endowed with two structures, that of a topological space and that of a hypergroup. Let (H, ○) be a hypergroup and (H, τ) be a topological space such that the mappings (x, y) → x ○ y and (x, y) → x/y from H × H to 𝒫*(H) are continuous. The main tool to obtain basic properties of hypergroups is the fundamental relation β*. So, by considering the quotient topology induced by the fundamental relation on a hypergroup (H, ○) we show that if every open subset of H is a complete part, then the fundamental group of H is a topological group.

It is important to mention that in this paper the topological hypergroups are different from topological hypergroups which was initiated by Dunkl and Jewett.     

集值映射下的粗糙集

粗糙集是一种在信息系统中处理粗糙性和颗粒性的数据挖掘工具.本文从集值映射的角度研究并推广粗糙模型,使其能解决在论域和分类信息变化下对集合的近似问题.最后,讨论了集值映射下的粗糙集的性质.     

Stability in the Sense of Bounded Average Power

An R^m-valued sequence (x_k): = (x_k : k = 1, 2, ...), e.g. generatedrecursively by x_k = f_k (x_k–_k, U_k), is called ‘averagepth power bounded’ if (1/K) is bounded uniformly in K= 1, 2,.... (The case p = 2 may correspond to ‘power’in the physical sense.) This is a notion of stability. Givenestimates of the form: f_k (x, u) < a x + ¶ _k conditionsare obtained on the coefficient sequence (a_k) and the inputestimates e_k:=¶_k (u_k) which ensure this form of stabilityfor the output (x_k). In particular, a condition (utilized inan application to adaptive control) is obtained which imposes(i) a bound b on (a_k) and a ‘sparsity measure’ m(K) on #{kK: a_k>} as K ( >1) (ii) average pth power boundednesson (e_k), and (iii) a growth condition on (e_k) related to b andm (•). This condition is sharp.