小于等于

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用Jensen不等式证明(abc)^a+b+c/3小于等于a^a*b^b*c^c(a,b,c大于零,)

使用排序不等式证:由幂指数a^a易知a,b,c>0,不妨假设a>b>c>0则a^a*b^b*c^c≥(abc)^[(a+b+c)/3]<=>ln(a^a*b^b*c^c)≥[(a+b+c)/3]lnabc对不等式左右取自然对数<=>alna+blnb+clnc≥[(a+b+c)/3]lnabc<=>3(alna+blnb+clnc)≥(a+b+c)lnabc即证3(alna+blnb+clnc)≥(a+b+c)lnabc由排序不等式3(alna+blnb+clnc)≥alna+blnb+clnc顺序和+blna+clnb+alnc乱序和1+clna+alnb+blnc乱序和2=(a+b+c)lna+(a+b+c)lnb+(a+b+c)lnc=(a+b+c)(lna+lnb+lnc)=(a+b+c)lnabc即3(alna+blnb+clnc)≥(a+b+c)lnabc当且仅当a=b=c时取等易证得当a,b,c取其他关系时同有上述式子成立故a^a*b^b*c^c≥(abc)^[(a+b+c)/3]得证当且仅当a=b=c时取等*含幂代数式通常对(不)等式两侧取自然对数利于变形放缩**对形如3(a1b1+a2b2+a3b3)一类式子需要灵活处理,向目标式拼凑转化

用Jensen不等式证明(abc)^a+b+c/3小于等于a^a*b^b*c^c(a,b,c大于零,)

构造函数f(x)=xlnx,f"(x)=lnx+1,f""(x)=1/x>0所以f(x)下凸,由下凸函数的性质(即Jensen不等式)得f[(a+b+c)/3]≤[f(a)+f(b)+f(c)]/3即 [(a+b+c)/3]u2022ln[(a+b+c)/3]≤(alna+blnb+clnc)/3而 (abc)^(1/3)≤(a+b+c)/3,所以[(a+b+c)/3]u2022ln[(abc)^(1/3)]≤(alna+blnb+clnc)/3所以 ln{(abc)^[(a+b+c)/3)]}≤ln[(a^a)(b^b)(c^c)]从而 (abc)^[(a+b+c)/3)]≤(a^a)(b^b)(c^c)

在氧化还原滴定中,若Rox=Rred=1,为使误差小于等于0.1%,两电对相差应大于多少?

你是问两个电对的电极电势的差值吧?0.36V即可

在书上看到N沟道JFET的Vgs要小于等于0,如果Vgs大于0会出现什么情况,是不能导通还是管子会损坏?

指的是开启电压,最小0.6V,最大1.2V。就是这个型号的管子的开启电压(GS之间加上一定的电压刚刚好使DS之间开始导通,这个电压就是开启电压)从0.6到1.2V之间,每个管子都有所不同,这是制造时的离散性造成的。

障碍物的大小小于等于波长时会发生明显的衍射,为什么

这是理论解决和实验都验证的,由于光波其实是不连续的,是一段段的脉冲,看我对你的另外的那个问题的解答补答:首先惠更斯原理是一种比较简单易懂的解释,它在经典光学里面有很重要的作用,在以前人们用它来解释一些物理现象很成功。当然了,物理发展到现在,最好的解释就是要以量子理论为基础的。你问到:障碍物比波长长时,障碍物后面的场的光强是为什么几乎平均的,你想象一下,波长是550纳米的光波经过障碍物时,我强调过;光波其实是不连续的,是一段段的脉冲,那么这时你就要想象一下两条只有550纳米长的振动的弦,一条是从上沿传出,一条是从下沿传出,如果障碍物的尺度比波长(550纳米)大,那么那两条弦经过障碍物后,你要在障碍物后面选一个点,看它们能不能相遇或那两根那么短的弦出现一小段重合?请注意,它们是同时到达上沿和下沿的,然后它们传播速度是一样的,这会你明白了吧,产生干涉的条件是要求干涉的那两条弦的振动频率是极其接近的,如果障碍物的尺度比波长(550纳米)大,那么那两条弦经过以后没有叠加的可能,这样就没有衍射的现象了,注意衍射和干涉本质上是一样的。如果障碍物比波长大,惠更斯原理同样适用。我为了解释的更容易明白,有一些地方是不严格的,比如让你把光脉冲想象成一条振动弦了

1EXCEL中如何实现两个日期之间的时间差,并且显示的时间差在1天之内(小于等于1)显示1,1-2天显示2,2-3天

beqbq850

坡度小于等于5%是怎么解释

利于雨水排水

rab小于等于ra怎么理解

rab等于ra说明:R(A)是矩阵A的秩,R(AB),AB是A与B两个矩阵的积,也是一个矩阵,R(AB)就是这个积矩阵的秩。秩是线性代数术语。在线性代数中,一个矩阵的秩是其非零子式的最高阶数,一个向量组的秩则是其最大无关组所含的向量个数。在解析几何中,矩阵的秩可用来判断空间中两直线、两平面及直线和平面之间的关系。

c级点验钞机的漏辨率应小于等于

c级点验钞机的漏辨率应小于等于0.03%。漏辨率是指未辨出的假币张数与实际清点假币张数的比率,简而言之就是,漏辨率过高,不是说完全验不出假币,而是验出率不够。国标对于C级验钞仪的漏辨率规定是不超过0.03%。点验钞机是一种自动清点钞票数目的机电一体化装置,一般带有伪钞识别功能,集计数和辨伪钞票的机器。由于现金流通规模庞大,银行出纳柜台现金处理工作繁重,点钞机已成为不可缺少的设备。随着印刷技术、复印技术和电子扫描技术的发展,伪钞制造水平越来越高,必须不断提高点钞机的辨伪性能。点验钞机的工作原理——验钞机的核心部件就是传感器,每一类型的传感器对应着一种鉴别技术,比如荧光鉴别、磁性鉴别等。传感器类型越多,意味着鉴别技术越全面,同时也代表着成本会更高。点验钞机辨伪原理包括荧光检测、磁性检测、红外穿透、激光检测、多光谱检测、分析检测等,其中磁性检测的工作原理是利用大面额真钞(20、50、100元)的某些部位是用磁性油墨印刷,通过一组磁头对运动钞票的磁性进行检测。

大于小于等于号儿歌

记忆儿歌:小小两条鱼,长得真稀奇。长着大嘴巴,名叫大小于。嘴巴向左边,名字叫大于。嘴巴向右边,名字叫小于。记忆口诀:大于号,小于号,两个兄弟一起到。尖头在前是小于,开口在前是大于。两个数字中间站,谁大冲谁开口笑。总结:大于号和小于号都是一头尖,一头张开大口,像一只鳄鱼张开大嘴巴。不一样的是,前面开口,后面尖尖的是大于号,它表示前面的物品或数字比后面的要多、要大;前面尖尖,后面开口的是小于号,它表示前面的物品或数字比后面的要少,要小。

at least 是什么符号 是大于等于 还是小于等于

至少,大于等于

数学问题请教高手 已知二次函数f(x)=ax的平方+x,若X属于【0 1】时有f(x)的绝对值小于等于1恒成立,则实数a

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less than,代表的是小于等于还是小于

这里不受重用

f(x)g(x)的积分小于等于f(x)²的积分与g(x)²的积分的1/2怎么证明

看来你对变上限积分求导概念没有建立,一般地,对形如:F(x)=∫(0,g(x))f(t)φ(t)dt,若f(x),φ(x)在g(x)的值域范围内连续,可导,那么:F"(x)=f[g(x)]·φ[g(x)]·g(x)该定理可用积分和导数的定义来证明,这里略根据题意,令h(t)=f.

受拉钢筋的最小锚固长度d小于等于25时为39d大于25时为42d中的d代表什么?

级配是集料各级粒径颗粒的分配情况,可通过筛析试验确定. 建筑中的级配一般是指:砂,石的级配.在土木工程中,粒径大于5mm的骨料为粗骨料,又称为“石子”;粒径小于5mm的骨料为细骨料,又称为“砂”.我们可以通过筛分析,计算砂子的大小搭配状况,判断砂子的级配和细度模数.

受拉钢筋的最小锚固长度d小于等于25时为39d大于25时为42d中的d代表什么?

受腊钢筋直径(mm)

三正数abc平均数的三次方小于等于他们三次方的平均数有没有会证明的啊

因[(a+b+c)/3]^3 =(1/27)(a+b+c)(a+b+c)^2 =(1/27)(a+b+c)[(a^2+b^2+c^2)+2(ab+bc+ca)] 而由基本不等式或排序不等式有 2(ab+bc+ca)≤2(a^2+b^2+c^2)(a=b=c时取等) 则[(a+b+c)/3]^3 ≤(1/9)(a+b+c))(a^2+b^2+c^2)(a=b=c时取等) =(1/9)[(a^3+b^3+c^3)+(ab^2+bc^2+ca^2)+(a^2b+b^2c+c^2a)] 又由排序不等式有 ab^2+bc^2+ca^2≤a^3+b^3+c^3(a=b=c时取等) a^2b+b^2c+c^2a≤a^3+b^3+c^3(a=b=c时取等) 所以[(a+b+c)/3]^3≤(a^3+b^3+c^3)/3(a=b=c时取等) 即原命题成立 说明: 令a≤b≤c 则a^2≤b^2≤c^2 依据排序不等式,以上两组数的同序积和不小于乱序积和 这里a^3+b^3+c^3为同序积和 而ab^2+bc^2+ca^2、a^2b+b^2c+c^2a都是乱序积和