用琴生不等式证明一类含“abc=1”条件的不等式

在诸多证明不等式的问题中,笔者发现一些含"abc=1"条件的不等式用琴生不等式来证明很简     

谁来登基

下面是一道有关继子立的简单动脑筋题.有一天,老皇帝突然一命呜呼,他留下了外号叫象、狮、虎、豹……的18个儿子,但没有遗嘱,而这18个儿子又互不相让.那么,究竟由谁来登基做皇帝呢?三朝元老某公忽然想出了一个好办法:他叫这些王子们排成一圆圈     

一道三角函数题的复数解法

我们先看下面这道题及其常规解法.题目:已知cosA+cosB+cosC=0,sinA+sinB+sinC=0,求证:cos3A+cos3B+cos3C=3cos(A+B+C),sin3A+sin3B+sin3C=3sin(A+B+C).解法一:由条件可得cosA+cosB=-cosC,sinA+sinB=-sinC,则(cosA+cosB)2+(sinA+sinB)2=1.     

两道课外练习题的另解

下面给出《中学生数学》2011年12月(下)期课外练习(初二年级)的两道题的另外解法,供大家参阅.题1(初二年级第1题)已知实数a,b,c,k(k≠0)满足(ka-c)2/((a-b)(kb-c))=4k,求2kb-c的值.     

意大利新型隔声卷材和隔振板材

意大利艾索格玛公司（ＩＳＯＬＧＯＭＭＡ）在中国的独家代理上海得善贸易有限公司,于２０００年９月２２日在上海召开了新型隔声卷材和隔振板材介绍会．意大利工程师讲解了该种材料的性能、规格、用途、特点等． 新型隔声卷材和隔振板材的基料是被打碎的废橡胶轮胎,添加软木、树脂、乳液聚脂化合物等,制成Ｒ型和Ｓ型毡状卷材以及Ｍ型和ＭＡＶ型权状材,广泛应用于建筑物、工业、道路、铁路等领域的隔声、隔振． Ｒ型隔声卷材可以铺放在结构层地面上,不需要钉子和胶水粘结,它可降低噪声２４－２６ｄＢ．Ｓ型隔声卷材可简单地铺装于地面…     

如何比较两数大小

比较两个数的大小,常通过作差、作商进行比较,或利用特珠不等式进行比较,较复杂些的,需通过放缩,拆项等进行比较,请看下面的例子.     

再谈美丽的数字三角形

文[1]介绍了四个美丽的数字三角形,但这些美丽的数字三角形只能是有限项,下面十个数字三角形除两个外都可以无限延伸.1.以下九个用数字"堆"出来的美丽的数字三角形算式,上小下大,像宝塔一样,又叫数字金字塔.     

Influence of resonator shape on nonlinear acoustic field in a thermoacoustic engine

The influence of the resonator shape on nonlinear acoustic field in a thermoacoustic engine is studied.The resonator of themoacoustic engine is boundary driving by a piston at one end,and the other end of it is rigid closed.A one-dimensional wave equation that accounts for gas dynamic nonlinearities and viscous dissipation in the resonator is established based on the governing equations of viscous hydromechanics.The nonlinear wave equation is solved using approximate Galerkin method.The nonlinear acoustic field in four different types of shaped resonators including hyperbolical,exponential,conical and sinusoidal are obtained and compared with that of a cylindrical resonator.It is found that the amplitude and waveform of the pressure are strongly affected by the resonator shape,the driving amplitude and the oscillation frequency of the piston.Waveform distortion,resonance frequency shift and hysteresis are observed,when the piston oscillation amplitude is large enough.The advantages of shaped resonator for thermoacoustic engine lie in inhibition of higher order harmonics and improvement of pressure ratio,etc.