1) symmetric derivative
对称导数
1.
In this paper,symmetric derivative and symmetric partial derivative are researched and some new differential mean value theorems are defined.
针对对称导数、对称偏导数,给出了一些新形式的微分中值定理。
2.
Through studying symmetric derivative , the author gives many simple properties about it .
对对称导数作了些探讨,并给出对称导数的一些简单性质。
3.
Four important conclusions of deciding functional convexity will be available by converting derivative into differential quotient, derivative and second-order derivative into symmetric derivative and second-order symmetric derivative respectively.
"改微为差",改导数和二阶导数分别为对称导数与二阶对称导数,即可得到判定函数凸性的四个重要结论。
2) symmetric partial derivative
对称偏导数
1.
In this paper,symmetric derivative and symmetric partial derivative are researched and some new differential mean value theorems are defined.
针对对称导数、对称偏导数,给出了一些新形式的微分中值定理。
2.
In this paper,the author defines the symmetric partial derivative of the binary function and discusses the interrelated property about the symmetric partial derivative.
定义了二元函数的对称偏导数,讨论了二元函数的对称偏导数及相关性质。
3) symmetric biderivation
对称双导
1.
Moreover,if R is a 2-torsion free prime ring and U a Lie ideal of R such that u2∈U for all u∈U and γ is a generalized derivation with d≠0,B∶R×R→R is a symmetric biderivation associated with the trace function g(x)=B(x,x),then U■Z(R) when one of the following conditions holds(1) γ acts as a homom.
此外,如果R是2-扭自由的素环,U是平方封闭的李理想,γ是伴随导子非零的广义导子,B:R×R→R是迹函数为g(x)=B(x,x)的对称双导,当下列条件之一成立时U为中心李理想(1)γ同态作用于U(2)2[x,y]-g(xy)+g(yx)∈Z(R)(3)2[x,y]+g(xy)-g(yx)∈Z(R)(4)2(x°y)=g(x)-g(y)(5)2(x°y)=g(y)-g(x)对所有的x,y∈U。
2.
Since Posner s well-known paper appeared in 1957, the research of derivation, generalized derivation, symmetric biderivation, and etc, in prime rings has become an important field in the theory of ring.
自从1957年Posner关于素环上导子的两个著名定理问世以来，素环上导子、广义导子、对称双导等的研究成为环论研究中的一个重要领域。
4) symmetric function
对称函数
1.
Synthesis of symmetric functions based on RM type universal logic module ULM3;
基于RM型通用门ULM3的对称函数综合
2.
New method of detecting symmetry of CRM type symmetric function in OR-coincidence algebraic system based on tabular method;
基于表格法的CRM型对称函数检测
3.
Denotation and application for d_j-Map of symmetric function.;
对称函数的d_j图表示及其应用
5) symmetric functions
对称函数
1.
This paper analyses the characteristics of the symmetric functions in the field GF (2～m),derives the relations of a class of usual determinants and the Vandermonde determi-nants.
分析了ＧＦ（２～ｍ）上对称函数的特点，并且导出了一类常用的行列式与范德蒙德行列式的关系式，对于研究编码理论有一定的参考意义。
2.
In this paper,the author gives an explicit LU factorization and 1-banded factorization of the generalized Vandermonde matrix by using symmetric functions.
主要讨论如何利用对称函数构造证明文献[1]给出的广义范德蒙矩阵显式LU分解定理。
3.
An explicit LU factorization and 1-banded factorization of the generalized Vandermonde matrix are given by using symmetric functions.
利用对称函数给出了广义Vandermonde矩阵的显示LU分解和带宽为1的分解,从而可将广义Vandermonde矩阵表示为n个带宽为1的下三角矩阵和n个带宽为1的上三角矩阵的乘积。
补充资料：对称导数
对称导数
symmetric derivative
对称导数[卿m毗州c deriVa山e;e“MMe，职e~npo-H3Bo八n即l 导数概念对n维Eueljd空间上集函数中情形的一种推广.在点x的对称导数是极限 lim龚，华业j不典二氏_。(二)， 而一乙}S(x;;)}一sym一、一’如果它存在的话，其中S(犯;)表示以x为心，r为半径的闭球.一元函数f在点x的n阶对称导数(symmetrie deriVdt1Ve ofordern)定义为极限 △忿f〔x，h) 五nl止二立止生三竺二兰二.= 万二毛h” 召/n、，‘、。，/n一Zk八 )l，-’】(一l丫f{x+竺上生hl *瞥〕、k/“一产J\’一2一/ 二五m几二二‘止二二一一一一一一一立一= 厂;b hn 一D导。f(x)·一元函数f在点x有Zr阶对称导数 D狐f(x)一刀Zr，如果 1，.，、。，、、价_矿k 言(z、x+h)+f(x一”))一*截“2止谁贡万- =o(hZr);如果l··丫.:、，，:、、币五Zk+、言‘j‘x+h，一f(一”)，一*氰“2*一拭片可- =o(h，r+’)，则f在点x有2:+1阶对称导数 D篇’f(x)=夕Zr+二 当f在点x有n阶导数f(的时，则(在两种情形)它在点x都有对称导数，且等于f(”)(x).
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