1) binary convex function
二元凸函数
1.
This article presents the definition of binary convex function,proves that the binary convex function in open and convex region must be continuous,popularizes Jensen s inequality and establishes the decision theorem of binary convex function.
该文给出了二元凸函数的定义,证明了开凸区域上的二元凸函数必连续,推广了Jensen不等式,建立了二元凸函数的判定定理。
2) concave-convex function
凹凸[二元]函数
3) convex function of many variables
多元凸函数
1.
From the definition of convex function of many variables and the conclusion in reference,we can get some necessary and sufficient conditions for judging the convexity of function of many variables by directional derivative and limit.
从多元凸函数的定义及文献中已有的性质出发,利用方向导数和极限等数学工具,给出了一个判别多元函数凸性的充分必要条件,进一步利用函数f(x)的Hesse矩阵Hf(x)的半正定性来判定函数的凸性。
4) covex quadratic function
凸二次函数
5) binary function
二元函数
1.
Distingnishing again on the extreme point of binary function;
二元函数极值点的再判别
2.
A Talk of The Relation of Certain Concepts In Binary Function Differential Calculus;
浅谈二元函数微分学某些概念间的关系
3.
This paper defines a binary function related to Schwarz inequation,investigates its properties and gives some refinements for Schwarz inequation.
定义一个与Schwarz不等式相关的二元函数,研究了它的性质,并由这些性质对Schwarz不等式进行了若干加细。
6) dualistic function
二元函数
1.
Experimental result shows that the non-uniform flux of open channel is single-valued corresponding to the opening angle of the plate and water depth in front of the plate,and satisfies the dualistic function.
通过试验可知:细长板开启角度、明渠非均匀流流量与板前水深三者单值对应,并满足二元函数的变化关系。
2.
The concept of partial derivative & directional derivative of multivariate function is presented for deducing the directional derivative & geometric meaning of Dualistic function.
利用多元函数的偏导数与方向导数的概念给出二元函数f(x,y)的方向导数及其几何意义,然后进一步给出了二元函数沿任意方向L的二阶方向导数2f/l2。
补充资料：凸函数
Image:11559688111252300.jpg
凸函数
凸函数是一个定义在某个向量空间的凸子集c（区间）上的实值函数f
设f为定义在区间ｉ上的函数，若对ｉ上的任意两点ｘ１，ｘ２和任意的实数λ∈（０，１），总有
f(λx1+(1-λ)x2)≤λf(x1)+(1-λ)f(x2),
则f称为ｉ上的凸函数.
判定方法可利用定义法、已知结论法以及函数的二阶导数
说明：补充资料仅用于学习参考，请勿用于其它任何用途。