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关键词： 柯西不等式   应用   证明   高中数学   数学分析   数学家   高考  

摘要： 柯西不等式是由法国数学家柯西在研究数学分析中的流数问题时得到的.它是高中数学中重要的不等式,也是推证其他许多复杂不等式的基础,在高中数学中有着广泛的应用.近年来,柯西不等式在高考中出现得比较活跃,是高考的一个新亮点.

关键词： 奖牌榜排名   影响因素   多元线性回归   灰色预测  

摘要： 利用第26~31届夏季奥运会奖牌榜排名前10位国家的相关数据,使用多元线性回归法建立了奥运会奖牌榜排名在影响因素:国家综合实力、人口数量、国家体制和东道主效应作用下的线性回归方程。运用基于GM(1,1)模型的灰色预测,利用前6届国家影响奖牌榜排名相关数据,预测出了2020年相应影响因素对应的数值,采用加权求和和定量计算的方式预测了2020年东京奥运会的奖牌榜前10名的排名。

关键词： 名言名语   定理   性质  

摘要： 本文主要用哈萨克族名言名语来修饰数学分析中的一些部分定理和性质,从而改善学生对学习死记硬背的现象,比较抽象的数学概念改为谚语来理解.

关键词： 表面等离子激光器   损耗-补偿   有机染料分子   系统不稳定性  

摘要： 设计了有机染料分子的球形波导结构,采用最内层金属金(Au)、外层Si介质的多层球形结构,在环形介质中植入有机染料分子作为增益耦合介质。理论上分析了模型的的受激辐射磁场能量、辐射谱以及有机染料分子增益效果。特性分析结果表明:光波在有机染料分子增益区能够与内层金属实现耦合,发生了多层电场局域化现象,增益对金属-介质间的表面等离子有一定的补偿效果,从增益的高折射区与低折射率区间发生了全反射,实行了表面等离子传播的增益补偿效果。能够通过调节波导参数实现损耗-补偿控制,高折射区能够实现SPP补偿,有机染料分子距离核区越近补偿效果更好,损耗更小。

关键词： 粗糙集   无限度量   粗糙函数   粗糙分析  

摘要： 一元粗糙函数及其数学分析性质具有意义,但当前研究主要局限于有限度量.基于无限度量研究一元粗糙函数及其数学分析性质.将度量从有限集扩展到无限集,讨论粗糙函数分类;基于无限度量研究粗糙函数的粗糙连续、粗糙极限、粗糙导数.采用无限度量,推进了一元粗糙函数及其分析性质.

关键词： 数学分析思想   教学   问题   方法  

摘要： 数学是高中教学中的一门基础学科,其具体性、实用性、逻辑性非常强,所以对于学生来讲学习数学存在一定的难度,而如果继续采用老式的教学方法很难提高数学课堂教学效率与质量,教师需要及时更新自身的教学方式和理念,能够与时俱进,把学生作为课堂教学的主体对象,而自己就要起到一个合理的、正确的引导作用,让学生能够自主、积极的去思考数学题,从而培养出学生较为优秀的发散性、逻辑性思维能力。数学分析思想在高中数学教学中有着重要的作用,要想提高培养学生的数学分析思想,需要教师不断采取新的教学模式,从而促进高中数学课堂教学达到质的提高。

关键词： Combined convection   Rotating cone   Heat transfer   Mass transfer   Jeffrey fluid  

摘要： In the present study we have explored the time dependent combined convectional flow on a rotating cone in a rotating Jeffrey fluid with the combined effects of heat and mass *** governing equations of motion,energy and mass transfer for unsteady flow are presented and simplified using similar *** reduced coupled nonlinear differential equations are solved analytically with the help of strong analytical technique homotopy analysis *** heat transfer analysis for prescribed wall temperature is *** results for Nusselt number and Sherwood number have computed and *** physical features of pertinent parameters are discussed by plotting the graphs of velocity,heat transfer,concentration,skin friction,Nusselt number and Sherwood number.

关键词： Heterogeneous sensor networks   3D coverage   Coverage hole   Hole healing   Connectivity  

摘要： The coverage and connectivity are the two imperative performance metrics for the growth of wireless sensor networks (WSNs) with sprouting technologies. In order to maintain these metrics, the issue of finding and healing of coverage hole is closely related to these two facts and plays a vital role in the performance improvement of the network. Many works in the past explored for 2D-WSNs, but now the time has come to investigate this matter for 3D-WSNs to reach the new heights of research and technology. In this paper, different scenarios with respect to the deployment of sensor nodes or network topology with the presence of different shaped coverage holes are discussed. Not only this, to heal these perceived holes introduction of sensor nodes having sensing radius different from initial deployed sensors has been suggested which in turn outlines the development of heterogeneous sensor networks, a keen issue with respect to technology development. This deployment of sensors to constitute heterogeneous sensor networks also influences the overall network cost in terms of cost reduction with an optimum coverage level. A mathematical analysis to give a relationship between the radii of former and later deployed sensor nodes is presented in the form of theorem. At the end, the results and discussion in order to achieve a specified level of coverage with respect to different packing patterns based on the mathematical analysis are provided. Also, some future directions to guide the researchers are discussed in this paper.