与Dedekind函数ψ(n)倒数有关的误差项的新研究

Ψ (n)是Dedekind函数 ,以E(x)表示和式 ∑n xnΨ(n) 的渐近公式中的误差项 ,研究了E(x)的加权平方积分均值     

Unnatural Disasters: Two Calculus Projects for Instructors Teaching Mathematics for Social Justice

Abstract

We provide context and motivation for an instructor to use real-life examples in the calculus classroom. To this end we describe two specific project ideas, one related to the devastating impact of methylmercury fungicide in a grain seed supply and the other to a catastrophic methane leak. By using calculus in contexts that have social justice implications, we hope to empower students to reason for themselves, to use mathematics as a powerful tool to deepen their understanding of the world, and ultimately, to effectively confront the challenges society faces.     

形如∑anbn级数收敛判定的一个命题

比较判定形如∑anbn级数收敛的Abel．N．H判别法和Dirichlet．P．G．L判别法，套用“分而治之”的思路，给出一个新的级数收敛判别法。     

Mathematics in ancient India

In this series of articles, we intend to have a glimpse of some of the landmarks in ancient Indian mathematics with special emphasis on number theory. This issue features a brief overview of some of the high peaks of mathematics in ancient India. In the next part we shall describe Aryabhata’s general solution in integers of the equationax -by =c. In subsequent instalments we shall discuss in some detail two of the major contributions by Indians in number theory. The climax of the Indian achievements in algebra and number theory was their development of the ingeniouschakravala method for solving, in integers, the equation x² -Dy² = 1, erroneously known as the Pell equation. We shall later describe the partial solution of Brahmagupta and then the complete solution due to Jayadeva and Bhaskaracharya.     

戴煦《外切密率》对级数的认识

本文从级数除法、级数收敛速度、两级数收敛快慢之比较、级数的确定等方面探讨清代数学家戴煦在《外切密率》中对级数的认识程度,借以窥见清代数学的理论性与深度.     

CDMA技术在数据通信系统中的应用

人类对更高质量无线通信的需求推动了CDMA技术的出现．CDMA是按照码型结构的差别来分割信号的．在CDMA系统中，用户数的增加相当于背景噪声的增加．在保持高质量通话的同时，CDMA可以容纳更多的用户，CDMA手机的用户每次通话时，系统编码有4．4万亿种可能的排列，具有天然的保密性，其消息在空中信道上被截获的概率几乎为零．CDMA技术的标准化，推进了这项技术在世界范围内的应用．     

谈谈一类递推数列极限的求法

通过几个实例,说明一类递推数列极限的求法。     

微积分在证明不等式方面的应用

初等教学中证明不等式的常用方法一般来说比较讲究解题技巧.用微积分证明不等式,有时可大大降低对解题技巧的需要,简化解题过程.     

RLC串/并联谐振回路的谐振特性与典型参数分析

RLC串/并联回路是各种复杂网络的基础,也是各种具有频率特性的电路网络的基本组成部份;全面了解RLC串/并联谐振回路各方面的特性对理解、学习及实践电路尤为重要,同时也是一个难点。     

"三项基本假设"的缺陷和负反馈放大电路优化定律

文章分析了米尔曼"三项基本假设"的缺陷,提出了负反馈放大电路优化定律,从而实现了使假设向科学理论的过渡.