函数

It is proved that when all the ratios of the generic term of a subaddtive sequence to its ordinal number form a lower bounded sequence,the ratio sequence must have limitation .

从这一结果出发证明了，当定义在(0，+∞)上的次可加函数与其自变量之比为有界函数时，次可加函数必存在上下确界函数，并证明了其上下确界函数均为齐次线性函数。

The decreasing conditions of an energy function are investigated by the use of convex function. By utilization of the primal convex function, the conditions are analyzed under which its conjugate function minus a quadratic function is also convex.

利用凸函数的定义研究了能量函数下降的条件，根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件。

This paper discusses the continuity of elementary function and some special non-elementary function and how to decide the interval point by the conception of function' continuity.

本文利用函数的连续性定义，详细讨论了初等函数的连续性，以及几个特殊非初等函数的连续性和间断点的类型判断，展示了一些复杂的非初等函数连续性的讨论方法，这不仅说明了分段函数的多样性，而且对于研究函数的丰富性具有重要的指导意义。

The decreasing conditions of an energy function are investigated by the use of convex function.

利用凸函数的定义研究了能量函数下降的条件，根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件。

A necessary and sufficient condition for a fx + t(y + g to be a bent function is disscussed,on which basis a necessary and sufficient condition for a function F = fix + tq + g to be a bent function is given when q is not a balanced-function by use of cyclic walsh spectrum and decomposition formula of walsh spectrum.

讨论了形如fx+τ(y+g的布尔函数是Bent函数的充分必要条件，在此基础上利用Bent函数的循环Walsh谱及谱分解式，进一步给出了当q不是平衡函数时，形如F=fx+τ(yq+g布尔函数是Bent函数的充分必要条件。

Real Number System, Euclidean Space and Metric Spaces, Sequences in R and R^n, Differentiability on R and Rn, Integration on R and Rn, Infinite Series of Functions, Fourier Series, Fundamental Theorems of Vector Calculus, Inverse Function Theorem, Implicit Function Theorem and its Applications.

课程内容：实数系，Euclidean空间与距离空间，函数数列，函数级数，连续函数，可微分函数，可积分函数，反函数，隐函数定理及其应用，向量微积分基本定理，富氏级数。

Baernstein[2] gave the conclusion by using Koebe function as the extremal function , Glenn Schober[6] studied the classes such as S, P, K, S* of H and represented these functions with integral formulations. Wang Jian[3] and others investigated the integral mean values. Our work is continuation of their work.

Baernstein首先在单位圆上讨论给出了以Koebe函数作为极值函数的结论，Glenn Schober对H中一些函数子类如S、P、K、S~*等作了研究，将这些子类上的函数用积分表达出来，王键结合Baernstein~*函数的定义及Glenn Schober的结论，定义了对称集的概念并得出了一些函数类在其上的积分平均。

Using the method of approximating the Lipschitz functions by the convex functions, we give a sufficient condition for the set where Lipschitz functions on a Hilbert space are Frechet differentiable is a residual set.

我们利用Lipschitz函数空间中凸函数的逼近性质来分析Lipschitz函数的微分性质，得到Hilbert空间上Lipschitz函数的Frechet可微点集是剩余集的一个充分条件，以标题"Lipschitz函数与凸函数之间的一些联系"在中国科学杂志上发表。

Derivations of Green's functions, Green's function for the Laplacian operator, Green's function for the diffusion operator, Green's function for the wave operator.

格林函数：格林函数推导，广义格林函数，拉普拉斯运算子的格林函数，扩散运算子的格林函数，波运算子的格林函数。

Then, have stressed kinds of technology cubic Hermite function and cubic spline function, step by step, expand dual-cubic Hermite and dual-cubic spline function to progressively, sum up in the point that trinary cubic Hermite and trinary cublic spline finally.

讨论时重点突出了三次埃尔米特函数和三次样条函数，表达方式由浅入深，逐步扩展到双三次埃尔米特函数和双三次样条函数，最后归结到三三次埃尔米特函数和三三次样条函数。

On closer examination, though, this is not a vote for multilateralism but just the opposite.

仔细审视后我们发现，这并非是对多边主义投出的赞成票，而是恰好相反。

Uncovering their weak spots, so I can defeat them.

揭露出他们的弱点，这样我就可以打败他们了。