1) function germs of two variables
二元函数芽
1.
A sufficient condition for the finite R-determinacy of function germs of two variables;
二元函数芽有限R-决定的一个充分条件
2) 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。
3) 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。
4) two variable function
二元函数
1.
Rolle theorem and Lagrange mean value theorem are improved in the case of two variable function, and the geometric meaning is given.
给出的两个定理是罗尔定理及拉格朗日中值定理在二元函数上的推广，并给予几何意
2.
This paper gives out a sufficient and solution of quadratic function s maximum with theory of quadratic form and gives out the define of the positive d efinite property of the following homogeneous polynomial of degree 2n two varia ble function ,based on the definite of local maximum of two variable function i s derived .
本文利用二次型理论给出了二次函数最值的一个充分条件及求法 ,定义了二元齐次多项式的正定性 ,并基于定义给出了二元函数极值的一个充分条件。
5) bivariate function
二元函数
1.
This paper is mainly devoted to provide a supplementary analysis of extreme value problem of bivariate functions,in which a new sufficient condition and its concise proof when critical case is given.
对二元函数的极值判定条件进行了新的补充分析,给出了临界情形下的又一充分条件,并做了简明的证明。
2.
In the paper,we mainly discuss the unification of the conception and the corresponding properties of bivariate functional limit improper integral with parameter,sequence of function and series of functions from the point of view of teaching,so that students can better understand the conception and corresponding properties of uniform convergence deeply.
从课堂教学的角度出发,讨论了二元函数极限、含参量广义积分、函数列、函数项级数一致收敛的概念和相关性质的统一,从而加深学生对一致收敛性的概念和相关性质的理解。
3.
The asymptotic properties of mean value in the mean value of bivariate functions are discussed,a solution is presented for related inverse problem.
讨论了二元函数中值定理中间值的渐近性质,给出了一个相关反问题的解。
6) function of 2-variables
二元函数
1.
We got at the concept that convergence in almost uniform of f(x,y) withfunction of 2-variables,discussed specificity of their limit functions and the conditionfor convergence in almost uniform of function of 2-variables.
提出了当ｘ→＋∞时二元函数ｆ（ｘ，ｙ）的次一致收敛的概念，并讨论了其极限函数的性质及次一致收敛的条件。
2.
In allusion to Funar Conjecture :"If a random triangle lies in a closed unit square,then its inscribed circle s radius,r≤(5-1)/4",an equivalent minimum problem about a function of 2-variables is studied;the stagnation point and its value,value on the boundary of the function of 2-variables are studied,the equivalent problem is proved correct,so the Funar Conjecture is proved correct.
针对Funar猜想:“设任意三角形位于闭单位正方形内,则该三角形的内切圆半径,r≤(5-1)/4”,研究了与其等价的某二元函数的最小值问题;利用对此二元函数驻点及其取值、边界取值讨论,证明了等价问题成立,进而此Funar猜想得证。
补充资料：高斯函数模拟斯莱特函数
尽管斯莱特函数作为基函数在原子和分子的自洽场（SCF）计算中表现良好，但在较大分子的SCF计算中，多中心双电子积分计算极为复杂和耗时。使用高斯函数(GTO)则可使计算大大简化,但高斯函数远不如斯莱特函数(STO)更接近原子轨道的真实图象。为了兼具两者之优点，避两者之短,考虑到高斯函数是完备函数集合,可将STO向GTO展开：
式中X(ζS,A,nS,l,m)定义为在核A上，轨道指数为ζS，量子数为nS、l、m 的STO；g是GTO：
其变量与STO有相似的定义；Ngi是归一化常数：
rA是空间点相对于核A的距离;ci是组合系数；K是用以模拟STO的GTO个数（理论上，K→∞，但实践证明K只要取几个，便有很好的精确度）。
ci和ζ在固定K值下, 通过对原子或分子的 SCF能量计算加以优化。先优化出 ζS＝1 时固定K值的ci和(i＝1,2,...,K)，然后利用标度关系式便可得出ζS的STO展开式中每一个GTO的轨道指数，而且，ci不依赖于ζS,因而ζS＝1时的展开系数就是具有任意ζS的STO的展开系数。对不同展开长度下的展开系数和 GTO轨道指数已有表可查。
式中X(ζS,A,nS,l,m)定义为在核A上，轨道指数为ζS，量子数为nS、l、m 的STO；g是GTO：
其变量与STO有相似的定义；Ngi是归一化常数：
rA是空间点相对于核A的距离;ci是组合系数；K是用以模拟STO的GTO个数（理论上，K→∞，但实践证明K只要取几个，便有很好的精确度）。
ci和ζ在固定K值下, 通过对原子或分子的 SCF能量计算加以优化。先优化出 ζS＝1 时固定K值的ci和(i＝1,2,...,K)，然后利用标度关系式便可得出ζS的STO展开式中每一个GTO的轨道指数，而且，ci不依赖于ζS,因而ζS＝1时的展开系数就是具有任意ζS的STO的展开系数。对不同展开长度下的展开系数和 GTO轨道指数已有表可查。
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