空间向量的几种常见问题解析

空间向量的概念及其运算与平面向量类似,向量加、减法的平行四边形法则以及相关的运算规律仍然成立.空间向量的数量积运算、共线向量定理、共面向量定理都是平面向量在空间中的推广.通过研究方向向量与法向向量之间的关系,可以确定直线与直线、直线与平面、平面与平面等的位置关系以及有关的计算问题.     

A comparison of different entransy flow definitions and entropy generation in thermal radiation optimization

In thermal radiation, taking heat flow as an extensive quantity and defining the potential as temperature T or the black body emissive power U will lead to two different definitions of radiation entransy flow and the corresponding principles for thermal radiation optimization. The two definitions of radiation entransy flow and the corresponding optimization prin ciples are compared in this paper. When the total heat flow is given, the optimization objectives of the extremum entransy dissipation principles （EEDPs） developed based on potentials T and U correspond to the minimum equivalent temperature difference and the minimum equivalent blackbody emissive power difference respectively. The physical meaning of the definition based on potential U is clearer than that based on potential T, but the latter one can be used for the coupled heat transfer optimization problem while the former one cannot. The extremum entropy generation principle （EEGP） for thermal radiation is also derived, which includes the minimum entropy generation principle for thermal radiation. When the radiation heat flow is prescribed, the EEGP reveals that the minimum entropy generation leads to the minimum equivalent thermodynamic potential difference, which is not the expected objective in heat transfer. Therefore, the minimum entropy generation is not always appropriate for thermal radiation optimization. Finally, three thermal radiation optimization examples are discussed, and the results show that the difference in optimization objective between the EEDPs and the EEGP leads to the difference between the optimization results. The EEDP based on potential T is more useful in practical application since its optimization objective is usually consistent with the expected one.     

对两道平面向量最值题的探究

本文以2020年高考中的两道平面向量最值题为例,分析试题的解法,并对背后隐藏的本质进行思考、探究,总结出一般性规律.     

球上Dirichlet空间的生成核与复合算子

本文的记号沿用〔1〕中的.令B”CC“是单位球,:、。于户,:·匆=习二叭. ‘.1Vf=(f二,,…,了:。),其中介‘=af丽’d。(:)为C“=RZ”上不一测度,且使v(B“)二1 .B”上Diriehlet空间的定义如下〔2〕: D“=={f{l在B,上全纯,f(0)=o,}ljl}’==J,.v了·示。(2)之下成为一个H*lbe·t空间.},.vj.初·相似文献   

煤粉起动速度与粒径及湿度的关系

在煤码头和车站的煤堆积场上,煤粉的扬起是污染环境的主要原因之一.作者根据力学的基本原理,考虑颗粒和液滴重力、煤粉颗粒尺寸和湿度的影响,利用煤粉颗粒起动时的力平衡条件,推导出在风的作用下,具有一定湿度的煤粉颗粒开始扬起的起动风速的理论表达式.最后.根据煤粉起动速度与煤粉颗粒粒径及湿度的关系,将理论公式和风洞实验结果进行了比较,理论和实验结果符合得相当好.     

基于DCGAN的拉曼光谱样本扩充及应用研究

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巧解一个速算密诀

我们班是一个藏龙卧虎的地方,有许多数学高手,其中最富传奇色彩的当属小A.小A有一招秘诀,能够速算九十几乘以九十几,如93×95=8835,94×97=9118,95×99=9405等等,小A都能够脱口而出,直接秒杀,真叫人瞠目结舌.小玲和小青仰慕已久,多次诚心请教,小A总是笑而不答.小A是怎样进行速算的呢?这里面到底蕴藏着什么奥秘,小玲和小青决定合作一探究竟.     

基于伪模态转换的红外目标融合检测算法

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利用规律巧解分式方程

解可化为一元一次方程的分式方程,除了依据课本中介绍的"在方程的两边同乘以各分式的最简公分母,约去分母,化成整式方程"外,还应因题制宜,灵活运用一些数学规律,使     

Moderate deviation for the single point catalytic super-Brownian motion

We establish the moderate deviation for the density process of the single point catalytic super-Brownian motion. The main tools are the abstract Grtner-Ellis theorem, Dawson-Grtner theorem and the contraction principle. The rate function is expressed by the Fenchel-Legendre transform of log-exponential moment generation function.