1) conformal mapping method
保形映照法
1.
The present paper provide a comprehensive retrospect and review on the applications of the macro fracture mechanics and complex variable function method,especially on conformal mapping method,including the introduction of the works of the author and the group of the author study at.
对宏观断裂力学的应用以及复变函数法特别是其中的保形映照法的作用做了一个较全面的回顾和评述 ,介绍了近来作者及其所在的研究课题小组在这方面所做的一些工作 。
2) conformal mapping
保形映照
1.
Firstly, by continuation technology and conformal mapping, the periodic collinear crack problems are studied in the two cases of permeable and impermeable boundary conditions, and solutions in closed form are obtained, then the formulae for the stress intensity factors and electric displacement inten.
首先研究了周期分布的共线反平面裂纹问题,借助于Riemann-Schwarz延拓技术和保形映照方法,分别就电学渗透性和非渗透性边界条件的两种情况做了探讨,获得了封闭形式的解,得到了裂纹尖端的应力和电位移强度因子,并数值化了周期裂纹间的干涉效应和尺度效应。
3) conformal mapping
共形映照
1.
Identifying the Bloch sphere representation of qubit with the extended complex plane by means of stereographic projection and considering the gate operations of single qubit,we obtain equivalance relation between unitary operations and one special kind of conformal mappings.
考虑一位量子比特的门操作,将幺正变换与复平面上一类特殊的共形映照相联系。
2.
It is proved that the inverse mapping Z = f-1(W) is also harmonic if and only if f is any one of the following three kinds of fUnctions: (i) one-to-one conformal mapping; (ii) affine transformation; (iii) function of the form where A, B, α and βare constants with the later two subject to the condition R(az+β) > 0, z ∈ D.
设是在一个单连通区域上的单叶调和映照，我们证明了反函数ｚ＝ｆ－１（）也是调和映照的充要条件是ｆ为下面三类函数之一：（ｉ）单叶共形映照；（ｉｉ）仿射交换映照；（ｉｉｉ）具有形式ｆ（ｚ）＝Ａ［ａｚ＋β＋ｌｏｇ（１－ｅ－ａｚ－β）－ｌｏｇ（１－ｅ－ａｚ－β）］＋Ｂ的调和映照，其中Ａ，Ｂ，α和β是常数且满足条件Ｒ（ａｚ＋β）＞０，Ｚ∈Ｄ。
4) spirallike mappings
螺形映照
1.
This paper using complex analyis and functional analysis,studies spirallike mappings on unit ball in several complex variables,and obtains the growth and covering theorems about a kind of spirallike mappings with zero of higher order.
以复分析与泛函分析为工具,研究多复变数单位球上的螺形映照,给出了一类螺形映照的高阶零点形式的增长和掩盖定理。
2.
Geometry quality for these mappings can be obtained from these inqualities, and some sufficiency conditions for starlike mappings and spirallike mappings are given.
由此导出全纯映照本身的一些几何性质,并得到星形映照和螺形映照的充分判别条件。
3.
Geometry quality for these mappings can be obtained from these inqualities,and some sufficiency conditions for starlike mappings and spirallike mappings are given.
本文建立了多复变数单位球上全纯映照的一些偏微分不等式 ,由此可映照本身的一些几何性质 ,并得到星形映照和螺形映照的充分判别条件 。
5) starlike mappings
星形映照
1.
Geometry quality for these mappings can be obtained from these inqualities, and some sufficiency conditions for starlike mappings and spirallike mappings are given.
由此导出全纯映照本身的一些几何性质,并得到星形映照和螺形映照的充分判别条件。
2.
In this paper, the authors obtain the parametric representation of starlike mappings on the unit ball Bn in Banach spaces; As a direct application, the growth theorem for starlike mappings is set up, which generalizes the corresponding results for starlike mappings on the unit ball in Cn .
本文给出Banach空间单位球B上星形映照的参数表达式;作为应用,给出B上的星形映照的增长定理;推广了Cn中单位球上已知的关于星形映照的结果。
3.
As its application, we obtain some sufficient conditions for starlike mappings and close-to-starlike mappings on bounded balanced domains in Cn.
作为应用，给出 有界平衡域上星形映照以及近似星形映照的一些充分判别条件。
6) Normal Gauss map
法Gauss映照
补充资料：超改进控制加权形心单纯形法
分子式：
CAS号：
性质：结合了超改进单纯形法与控制形心单纯形法两者的优点而产生的一种单纯形优化方法。由除响应值最差的顶点w以外的其余各单纯形顶点的响应值计算加权形心点pw，引入控制参数γ调节加权形心点的位置，确定w的反射点pγ，以保证单纯形沿逼近梯度的方向推移。在确定的推移方向上，根据顶点w、加权形心点pw。和反射点pγ的响应值用二次曲线拟合求导，决定单纯形的新顶点，以保证新顶点在该推移方向上是最优的，从而加快了优化速度。
CAS号：
性质：结合了超改进单纯形法与控制形心单纯形法两者的优点而产生的一种单纯形优化方法。由除响应值最差的顶点w以外的其余各单纯形顶点的响应值计算加权形心点pw，引入控制参数γ调节加权形心点的位置，确定w的反射点pγ，以保证单纯形沿逼近梯度的方向推移。在确定的推移方向上，根据顶点w、加权形心点pw。和反射点pγ的响应值用二次曲线拟合求导，决定单纯形的新顶点，以保证新顶点在该推移方向上是最优的，从而加快了优化速度。
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