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1)  binary in analytic function
二元整函数
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:整函数
整函数
integral function
    在整个复平面上处处解析的函数。整函数总可以在原点
展开成泰勒级数:!!!Z0698_1,它在全平面收敛,整函数以∞点为唯一的孤立奇点,它在∞点的罗朗展式与它在原点的泰勒展式有一样的形式。当∞点是整函数的可去奇点时,这个整函数只能是常数,这就是著名的刘维尔定理,通常表述为“有界整函数必为常数”。利用这一定理可以得到代数基本定理的简单证明。当∞点是整函数的n阶极点时,这个整函数是一个n次多项式  ,也就是它的泰勒展式(或罗朗展式)只有有限多项。当∞点是整函数的本性奇点时,这个整函数的泰勒展式一定有无限多项,这类整函数称为超越整函数。由代数基本定理知道n次多项式一定有n个零点(也就是根),它总可以分解为n个一次因式的积,对于超越整函数,它可能有无限多个零点  ,比如sinπz就以全体整数为其零点集,也有的超越整函数没有零点,如ez就处处不为零,一般来说,没有零点的超越整函数总可以表成eg(z)的形式,此处gz)也是一个整函数,而有无限多个零点的超越整函数fz)也有一个因子分解式 ;形如!!!Z0698_2 ,其中gz)是整函数,0是m阶零点,zk是非零零点集,gk(!!!Z0698_3)是!!!Z0698_4的多项式,这是魏尔斯托拉斯因子分解定理。超越整函数还有一个重要性质:若fz)是超越整函数,则对任意复数A(包括A=∞),存在点列{zk },使zk !!!Z0698_5∞(k!!!Z0698_6∞)而有fzk!!!Z0698_7A。这一结果有一个更精确的发展:对超越整函数f(z),最多除去一个值(称为例外值)外,对所有其他的复数v值(v≠∞),fz)-v都有无穷多个零点(毕卡定理)。
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