“薄利多销”的统计建模与分析

针对2019年全国大学生数学建模竞赛的E题——"薄利多销"分析问题,首先介绍了问题的背景和问题的提法;然后给出了赛题的一个可行的解法,包括部分商品的成本价补充、打折力度的度量以及营业额、利润率与打折力度的相关分析与回归分析;最后对竞赛论文进行简要评述.     

结构:数学解题的切入点

数学问题结构是指影响和决定问题本质、条件与结论相互作用方式、解决问题的策略和方法的深层特征.明晰数学问题结构的常用策略与方法有:寻找、发现问题表现形式的共性;透过问题的表现形式,发现其本质;追问条件和目标的数学意义;寻找与问题的条件或目标相关联的数学概念;分析相关数学知识的结构特征.应以问题结构为抓手,改进和优化数学解题教学.     

研究生数学公共课程中教学案例创新与建设的思考

通过对磁浮列车悬浮系统的Hopf分支的研究,提出了任课教师将科学研究中的实际问题抽象出来,按照"发现问题、分析问题、解决问题、总结验证"研究过程,"驱动的问题背景、问题的数学描述、所需数学知识、数学推导与证明、数值仿真验证、回归原始问题解释和分析"的步骤,将科研成果转化为精彩教学案例,启发学生通过实际问题的数学分析与处理,激发其活学活用数学兴趣、提高创新能力.     

中考数学平行四边形压轴题解决策略探究

平行四边形压轴题大多以"存不存在"的形式出现,需要学生根据题意结合平行四边形相关知识利用分类讨论法和数形结合思想画图与分析相关情况.在面对这种问题时,学生往往难以准确画图和分析.为此,本文先对解决这类问题的主要方法和技巧进行简要介绍,然后举例分析与说明具体解决过程,最后阐述解决该类问题时需注意的几个问题,从而帮助学生排难释疑,在解决这类问题的过程中逐步建立学好、用好、考好的信心.     

基于“问题发现”的类比学习——再认识线段和角

《义务教育数学课程标准(2011年版)》从强调“分析问题、解决问题”到“发现问题、提出问题、分析问题、解决问题”,特别增加了“发现问题、提出问题”.在课堂上如何引导学生发现问题、提出问题,对于学生自身的发展和创新意识的培养很重要.在学习完线段与角的相关知识后,基于线段与角的相似之处,利用学习的通性套路让学生领悟学习的路径与方法,从而能自主学习.通过类比学习,让学生体会数学课堂注重以“问题”为中心,以“问题”促思考,以“问题”促探究,以“问题”促创新.本文借助线段与角的通性,借助类比思想诱导学生发现问题、提出问题,进而解决问题.     

蕴含系分析法

针对决策科学中的策略集生成问题,提出蕴含系分析法.该方法基于蕴含系的概念与性质所建立,用于诊断问题形成的根本原因、发掘与问题相关的潜在与隐含因素、搜索求解问题的切入点,提供了一种分析问题和引导问题求解策略生成的形式化方法.     

指向核心素养的综合与实践教学

《义务教育数学课程标准(2022年版)》指出：综合与实践活动是小学数学学习的重要领域.学生将在实际情境中和真实问题中,运用数学和其他学科的知识与方法,经历发现问题、提出问题、分析问题、解决问题的过程,感悟数学知识之间、数学与其他学科之间、数学与科学技术和社会生活之间的联系,积累活动经验,感悟思想方法,形成和发展模型意识、创新意识,提高解决实际问题的能力,形成和发展核心素养.     

解斜三角形

本单元的重点是：正弦定理、余弦定理，求周长、面积，判断三角形的形状，与解斜三角形有关的实际应用问题．综合运用正弦定理、余弦定理和内角和定理等基础知识解决几何问题和实际问题，有助于培养和提高学生分析问题和解决问题的能力．     

函数与方程思想在三角问题中的应用

函数思想,是指用函数的概念和性质去分析问题、转化问题和解决问题.方程思想,是从问题的数量关系入手,将问题中的条件转化为数学模型:方程、不等式或方程与不等式的混合组,然后通过解方程(组)或不等式(组)来使问题获解.函数与方程犹如亲兄弟,彼此身上存在对方的影子,两者互相转化接轨,形成了函数与方程思想.本文将用函数与方程思想来解决三角函数的证明求值问题.     

融数学思想和应用的高等数学课程教学改革

在分析当前高等数学课程教学现状和存在问题的基础上,提出了更新教学理念、优化教学内容、改革教学方法的思路与举措,通过实行“案例教学法、找错误教学法、可视化教学法、实验教学法以及讨论教学法”,提高学生学习兴趣和分析问题、解决问题的能力。     

伪抛物线回归函数模型的建立与参数估计

在大量的实际问题中，变量与变量间的相关关系都呈现出伪抛物线状的变化规律，尤其在以投入报酬递减率为事物本质的研究中更是如此．本文通过对伪抛物线函数性质的深入分析，建立了伪抛物线回归函数模型，并根据该模型的特点，运用数值计算和解析计算相结合的方法，建立了该模型的参数估计方法，同时给出了显著性检验方法．     

Some properties of minimal solutions for a fuzzy relation equation

Some properties of the solution set and minimal solutions of a fuzzy relation equation are considered. In this paper, we show the necessary and sufficient condition for existence of a minimal solution of a finite fuzzy relation equation defined on infinite index sets.     

Granger因果检验用法探讨

在经济分析中,常常要对经济变量之间的因果关系作出判断,Granger因果性检验因为其简单实用而得到了广泛运用.但目前国内一些实证研究存在着对该方法的不正确运用.本文从Granger的因果性定义出发,对目前国内文献应用中存在的问题进行了讨论,并对该方法在应用中存在的问题作进一步探讨.     

Extended rough set model based on known same probability dominant valued tolerance relation

Classical rough set theory is based on the conventional indiscernibility relation. It is not suitable for analyzing incomplete information. Some successful extended rough set models based on different non-equivalence relations have been proposed. The data-driven valued tolerance relation is such a non-equivalence relation. However, the calculation method of tolerance degree has some limitations. In this paper, known same probability dominant valued tolerance relation is proposed to solve this problem. On this basis, an extended rough set model based on known same probability dominant valued tolerance relation is presented. Some properties of the new model are analyzed. In order to compare the classification performance of different generalized indiscernibility relations, based on the category utility function in cluster analysis, an incomplete category utility function is proposed, which can measure the classification performance of different generalized indiscernibility relations effectively. Experimental results show that the known same probability dominant valued tolerance relation can get better classification results than other generalized indiscernibility relations.     

Graph dismantling problems

Problems involving the dismantling of a digraph (graph) by removal of arcs (edges) are investigated. Some of these problems have good characterizations related to the familiar results about Euler trails, others are NP-complete.     

Hypergraphs and Hypergroups Based on a Special Relation

The purpose of this paper is the study of hypergroups associated with hypergraphs. In this regards, we construct a ρ-hypergroup by means a given hypergraph by defining a special relation ρ, and then we investigate some related properties. Further, we introduce a special product of ρ-hypergroups. Also, we bridge between subhypergraphs and subhypergroups. Finally, the fundamental relation of a ρ-hypergroup is studied.     

Some models for deriving the priority weights from interval fuzzy preference relations

Interval fuzzy preference relation is a useful tool to express decision maker’s uncertain preference information. How to derive the priority weights from an interval fuzzy preference relation is an interesting and important issue in decision making with interval fuzzy preference relation(s). In this paper, some new concepts such as additive consistent interval fuzzy preference relation, multiplicative consistent interval fuzzy preference relation, etc., are defined. Some simple and practical linear programming models for deriving the priority weights from various interval fuzzy preference relations are established, and two numerical examples are provided to illustrate the developed models.     

Functions of finite logarithmic order in the unit disc,Part I

The concept of logarithmic order in the unit disc forms a bridge between meromorphic functions of unbounded Nevanlinna characteristic and meromorphic functions of (usual) zero order of growth. A collection of fundamental results for meromorphic functions of finite logarithmic order is given. Some of these results are reminiscent from the finite order case. Part I of this paper culminates in solving the inverse problem related to the famous defect relation in the case of finite logarithmic order. Part II deals with the analytic case.     

The Initial-Boundary-Value Problems for the Hirota Equation on the Half-Line

An initial boundary-value problem for the Hirota equation on the half-line,00, is analysed by expressing the solution q(x, t) in terms of the solution of a matrix Riemann-Hilbert(RH) problem in the complex k-plane. This RH problem has explicit(x, t) dependence and it involves certain functions of k referred to as the spectral functions. Some of these functions are defined in terms of the initial condition q(x,0) = q₀(x), while the remaining spectral functions are defi...     

一个特殊可重复排列数的算法

研究一类特殊的可重复排列性质,建立了一般情形下求这类排列数的递推公式,导出了一些特殊情形下的具体计算公式.