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多项式函数在无理点的函数值 被引量:2
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作者 刘宏 张西恩 +1 位作者 杨建宇 刘向南 《大学数学》 2012年第2期142-144,共3页
在高等数学的教学过程中,经常会遇到求多项式函数在无理点的函数值这类问题.如果这个无理点仅仅是2^(1/2),3^(1/2)之类,往往还是很容易解决的.但是遇到象2±(13)^(1/2)3这类无理点时,如果采用直接把无理数带入多项式来求多项式函数... 在高等数学的教学过程中,经常会遇到求多项式函数在无理点的函数值这类问题.如果这个无理点仅仅是2^(1/2),3^(1/2)之类,往往还是很容易解决的.但是遇到象2±(13)^(1/2)3这类无理点时,如果采用直接把无理数带入多项式来求多项式函数的值,那么这项工作会很复杂且容易出差错.本文给出一个十分有效的解决此类问题的方法,可以把这一类的求值问题转化为一次多项式函数的求值问题,从而大大降低了求解此类问题的难度. 展开更多
关键词 多项式 无理点 函数值 高等数学
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“无理”的点——“正弦函数、余弦函数图像”的教学实录与感悟
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作者 蔡文慧 戚有建 《上海中学数学》 2023年第5期17-18,27,共3页
通过对“正弦函数、余弦函数的图像”教学实录的分析,阐述如何突破本节课的重点、难点,说明数学实验在数学教学中的重要作用,从而实现数学培养学生思维能力的功能.
关键词 无理”的 正弦函数图像 余弦函数图像
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Physical layer design of wireless sensor network nodes 被引量:5
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作者 钟子果 胡爱群 王丹 《Journal of Southeast University(English Edition)》 EI CAS 2006年第1期21-25,共5页
Major consideration dimensions for the physical layer design of wireless sensor network (WSN) nodes is analyzed by comparing different wireless communication approaches, diverse mature standards, important radio fre... Major consideration dimensions for the physical layer design of wireless sensor network (WSN) nodes is analyzed by comparing different wireless communication approaches, diverse mature standards, important radio frequency (RF) parameters and various microcontroller unit (MCU) solutions. An implementation of the WSN node is presented with experimental results and a novel "one processor working at two frequencies" energy saving strategy. The lifetime estimation issue is analyzed with consideration to the periodical listen required by common WSN media access control (MAC) algorithms. It can be concluded that the startup time of the RF which determines the best sleep time ratio and the shortest backoff slot time of MAC, the RF frequency and modulation methods which determinate the RX and TX current, and the overall energy consumption of the dual frequency MCU SOC ( system on chip) are the most essential factors for the WSN node physical layer design. 展开更多
关键词 wireless sensor network node physical layer radio frequency energy consumption node lifetime
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PIR-based data integrity verification method in sensor network
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作者 Yong-Ki Kim Kwangnam Choi +1 位作者 Jaesoo Kim JungHo Seok 《Journal of Central South University》 SCIE EI CAS 2014年第10期3883-3888,共6页
Since a sensor node handles wireless communication in data transmission and reception and is installed in poor environment, it is easily exposed to certain attacks such as data transformation and sniffing. Therefore, ... Since a sensor node handles wireless communication in data transmission and reception and is installed in poor environment, it is easily exposed to certain attacks such as data transformation and sniffing. Therefore, it is necessary to verify data integrity to properly respond to an adversary's ill-intentioned data modification. In sensor network environment, the data integrity verification method verifies the final data only, requesting multiple communications. An energy-efficient private information retrieval(PIR)-based data integrity verification method is proposed. Because the proposed method verifies the integrity of data between parent and child nodes, it is more efficient than the existing method which verifies data integrity after receiving data from the entire network or in a cluster. Since the number of messages for verification is reduced, in addition, energy could be used more efficiently. Lastly, the excellence of the proposed method is verified through performance evaluation. 展开更多
关键词 data integrity VERIFICATION private information retrieval sensor network
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凭初等数学常识发现中学数学有一系列重大错误——让5千年无人能识的自然数一下子暴露出来 被引量:1
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作者 黄小宁 《学周刊》 2018年第9期180-185,共6页
数列最起码常识让5千年都无人能识的标准无穷大自然数及其倒数一下子暴露出来,从而揭示有首项的无穷数列必有末项。数集相等概念以及几何起码常识和区间概念凸显中学几百年解析几何有一系列将两异点集误为同一点集的错误。从而产生出病... 数列最起码常识让5千年都无人能识的标准无穷大自然数及其倒数一下子暴露出来,从而揭示有首项的无穷数列必有末项。数集相等概念以及几何起码常识和区间概念凸显中学几百年解析几何有一系列将两异点集误为同一点集的错误。从而产生出病态的"高深"理论:直线段的部分点可与全部点一样多;射线S沿S正向平移变为射线S′≌S是S的真子集;巴拿赫-塔尔斯基分球定理。证明存在:几千年都无人能识的等长却不"等势"从而不合同的直线段;2500年都无人能识的R外标准实数。不识这类"更无理"的数和直线段使数学一直不知直线A沿本身伸缩或平移后就≠A了,所以"直线公理(定理)"和"R轴完备、封闭"论其实是将无穷多各异直线误为同一线的"以井代天"的"井底"误区。 展开更多
关键词 N内、外标准无穷大自然数及N最大元 貌似重合的伪二重直线段 用而不知的“更无理”数推翻“R轴各与各标准实数——对应定理” 推翻百年集论和百年自然数公理 推翻巴拿赫-塔尔斯基分球定理 保距及非保距变换
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Existence of Positive Periodic Solutions of Competitor-Competitor-Mutualist Lotka-Volterra Systems with Infinite Delays 被引量:9
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作者 ZHANG Daoxiang DING Weiwei ZHU Min 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2015年第2期316-326,共11页
In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of pos... In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of positive periodic solutions of the model by using the Krasnoselskii's fixed point theorem,and then present an example to illustrate the main results. 展开更多
关键词 Competitor-competitor-mutualist Lotka-Volterra systems with infinite delays Krasnoselskii's fixed point theorem positive periodic solutions.
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Existence and Incomparability of Positive Solutions for Singular Boundary Value Problems of First Order Differential Equation on Unbounded Domains
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作者 ZHANG Xing Qiu 《Journal of Mathematical Research and Exposition》 CSCD 2009年第3期491-499,共9页
By constructing a special cone and applying the fixed point theorem of cone compression and expansion,this paper investigates the existence of positive solutions for a class of first order singular boundary value prob... By constructing a special cone and applying the fixed point theorem of cone compression and expansion,this paper investigates the existence of positive solutions for a class of first order singular boundary value problem(BVP,for short) on unbounded domains.Moreover,an incomparable result about two positive solutions for the BVP is also obtained and an example is given to illustrate the application of the main results. 展开更多
关键词 singular equation unbounded domain positive solution incomparability
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