1) elementary symmetric mean
初等对称平均
1.
The second elementary symmetric mean and power mean of three positive numbers x,y,zare defined byP2Mrespectively.
Ｐ２（ｘ）是三元二次初等对称平均，Ｍｓ（ｘ）是ｓ次幂平均。
2) Symmetric mean
对称平均
1.
A symmetric mean and its basic property;
一类对称平均及其基本性质
2.
In this paper,the authors established a chain of inequalities involving first symmertic mean of k degree ∑~k_n(a)=nk~(-1)∑1≤i_1<…<i_k≤n∏kj=1a_(i_j)~(1/k),and second symmetric mean of k degree σ~k_n(a)=nk~(-1)∑1≤i_1<…<i_k≤n(a_(i_1)a_(i_2)…a_(i_k))~(1/k) and third symmetric mean of k degree ∏~k_n(a)=∏1≤i_1<…<i_k≤na_(i_1)+a_(i_2)+…+a_(i_k)k~(nk~(-1)) as follows.
用降维法建立了含n个正实数a1,a2,…,an的第一k次对称平均∑kn(a)=nnk-1∑1≤i1<…
3.
A condition of equivalence for the convex sequence is established by means of the theory of majorizotion, moreover a class of inequality for weighted symmetric mean is generalized by the above condition of equivalence.
利用控制不等式理论建立了凸数列的一个等价条件 ,并应用其推广了一类加权对称平均不等
3) elementary symmetric expression
初等对称式
4) elementary symmetric function
初等对称函数
1.
By using the theory of majorization and combining with the analysis methods,three known extensions of the classic Bernoulli s inequality are proved,and a new extension of this inequality is established by the Schur-concatity of the elementary symmetric functions and simple majoricotions.
此外,利用初等对称函数的Schur凹性和简单的控制关系建立了该不等式的一种新推广。
2.
The main result is:for I=(0,1),g(t)=1t-t,(x-1,…,x-n)∈I+n,E-m(x-1,…,x-n) is elementary symmetric function,denote s=∑ni=1x-i,m∈N,n≥m and n≥3,if 0<s≤1,then E-n[g(x-1),…,g(x-n)]≥C+m-n[g(s/n)]+m.
主要结果是 :对于I=(0 ,1) ,g(t) =1t-t,(x1 ,… ,xn)∈In,Em(x1 ,… ,xn)是初等对称函数 ,记s =∑ni=1xi, m∈N , n≥m且n≥ 3,若 0
5) elementary symmetric polynomial
初等对称多项式
1.
Taking the 5th,7th,and 11th harmonics eliminated for instance,the results show that the elementary symmetric polynomials can be exploited to reduce the degrees of the polynomials and the resultant theory can be utilized to eliminate variables.
文中以消除5、7、11次谐波为例,说明了在求开关角过程中如何应用初等对称多项式降幂和结式理论消元,并总结出应用多项式理论求解消谐方程的一般性步骤。
6) non-elementary symmetric function
非初等对称函数
补充资料：对称与非对称
反映客观事物在结构、功能、时空上的特殊联系的范畴。对称指事物以一定的中介进行某种变化时出现的不变性，非对称指事物以一定的中介进行某种变化时出现的可变性。在自然界中普遍存在，形式多样。对称有空间对称(包括形象对称和结构对称)、时间对称、概念对称等。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条