可微的

This article is mainly discussed the relation between some important concepts and conclusions about the Limit of Sequence, the Limit, Continuity ,Differentiability, Integrability of Function, the Infinite Series , and the Limit, Continuity, Derivativeness,Differentiability of Multivariable Function ,as well as the Multiple Integral, and Integral with parameter .

本文对数列极限，一元函数的极限、连续性、可微性、可积性，无穷级数，多元函数的极限、连续性、可导性、可微性以及重积分，参变量积分中的一些重要概念和结论之间的关系进行了一些探讨，每一个问题都作了适当说明或举出反例，并对一些相关的内容进行了讨论，得到若干结果。

If all of the partial derivations exist and only one of them is not continuous,the multivariate function is differentiable.

最后结合实例进行了讨论，结果表明，所有偏导数存在并不蕴含可微，函数可微时可以没有连续的偏导数。

Optimal algorithm of combined nonlinear Hopfield network appears powerful validity in solving nonlinear planning, which includes nonlinear objective function, linear constrains and high-demension of decision-making variants, for its ability of nonlinear parallel computation. It is prominent among optimal algorithms because of its function of simply implement with electrocircuit hardware. Genetic algorithm is expressly suitable for optimal calculation regarding the planning of massive, highly nonlinear, inconsecutively differentiable and multiobjective function as well as objective function without analytical expression. However, it inclines to prematurity, as well as its limitation in ability of partial optimal search. Introducing the optimal algorithm of niche genetic simulated annealing to standard Genetic algorithm, can therefore improve the full-scale or partial search ability of Genetic algorithm effectively. It has a far-flung perspective in the field of systemic planning of water pollution control.

组合式非线性Hopfield网络优化算法所具有的非线性大规模并行计算能力在求解具有非线性目标函数、线性约束条件及高维决策变量的非线性规划问题方面显示出了强大的生命力，它易于电路硬件实现的功能更是在优化算法中独树一帜；遗传算法采用概率搜索技术，不受目标函数与约束条件的限制，特别适合大规模、高度非线性的不连续可微的多峰目标函数及无解析表达式的目标函数的规划问题的优化计算，但其存在容易早熟、局部寻优能力较差等缺点，本文在标准遗传算法中引入小生境技术及模拟退火算法有效地改善遗传算法的全局和局部搜索性能，提高了全局最优解的寻优质量，小生境遗传退火模拟优化算法在水污染控制系统规划中的应用前景极为广阔。

The existence theorem of generalized weak efficient solutions with respect to variable, cone for a linear G〓teaux differentiable mapping is proved with set valued mapping fixed-point theorem and the relation between a vector optimization and a variational inequality problem. The existence of weak efficient solutions for multi-objective convex vector optimization is characterized.

建立映射在线性G〓teaux可微条件下关于可变锥的广义弱有效解的存在性及多目标凸向量优化问题在G〓teaux可微条件下弱有效解的特征，利用集值映射不动点定理及向量优化与变分不等式的关系证明线性G〓teaux可微锥凸映射关于可变锥的广义弱有效解的存在性定理。

The Lewy equation is locally solvable and globally solvable,and we have got the analytic expressions of the local solution and the global solution.So we obtain the conclution "when ,Lewy's equation (5) has solution ".

Lewy方程是局部可解与整体可解的，我们已经获得了其局部可微解与整体可微解的解析表达式，获得了"Lewy方程（5）当，则有解"的结论。

First,The properties of the spherical Bezier Curvesproposed by Ken Shoemake(Spherical Bezier curve of first kind)are listed,such asEndpoint property,Symmetry property,Invariant property under solid motion,Spherical convex hull property,etc.,and the fact that this kind of spherical BezierCurve is devoid of subdivision property is pointed out;Based on subdivision,theconcept of a new kind of spherical Bezier curve(Spherical Bezier curve of secondkind)is proposed.This kind of spherical Bezier curve is continuous differentiable.Furthermore,generalization of Bezier curve on more comprehensive manifolds isdiscussed.2Spherical Chaikin algorithm and general spherical corner-cuttingalgorithm.

首先，文中列举了Ken Shoemake提出的点点生成的球面Bezier曲线(第一类球面Bezier曲线)的性质，如端点性质、对称性质、运动不变性质、球面凸包性质等，并指出这种球面Bezier曲线没有剖分性质；基于细分，文中给出了一种新的球面Bezier曲线(第二类球面Bezier曲线)的构造方法，指出这种曲线是连续可微的；作为这些理论的应用，文中改进了Ken Shoemake提出的球面插值曲线构造方法；进一步，文中探讨了Bezier曲线在更广泛的流形上的推广方法。2球面Chaikin算法和一般的球面割角算法。

In this dissertation, InGaAs/InGaAsP/InP MQW microdisk laser and its characterization were presented. Some conclusions are as following: the characteristics of lasing threshold was discussed by using rate equation. The dependent relations between threshold and cavity volume, spontaneous emission coupling efficiency β were investigated. The whispering gallery mode and spontaneous emission in a microdisk geometry were then studied. Almost all spontaneous emission was coupled into the lowest order TE mode when the normalized thickness of photonics well was between 0.15 and 0.5. The design principle and device process of InGaAs/InGaAsP/InP MQW microdisk laser were presented. The microdisk lasers with the diameter of 8μm, 4. 5μm and 2μm were succesfully fabricated by using etching techniques. The pulse lasing thresholds for the microdisk with the diameter of 8μm and 4. 5μm were 170μW and 15μW, a record results compared with the published in the literature. The cw lasing threshold for a 2-μm-diameter microdisk was only a few μW. We haven't found similar report up to now. To solve the problem of directional output in a microdisk laser, the power coupling efficiency in a double disk geometry was investigated with the theory of waveguide mode couple. A new structure of electrically pumped microdisk laser with output waveguide was designed, making a foundation for the practical use of microdisk laser.

本文主要研究InGaAs/InGaAsP/InP多量子阱半导体碟型激光器的研制和特性表征，并取得如下结果：利用速率方程理论讨论了激光器激射阈值的特性，分析了阈值与腔体积和自发发射耦合系数β之间的关系；讨论了微碟光子阱结构中的自发发射特性和微碟中WGM模式特性；光子阱结构在其归一化厚度在0.15-0.5之间时，几乎全部自发发射进入到最低阶TE模式中；研究了InGaAs/InGaAsP/InP多量子阱微碟激光器的结构设计原理和器件的制备工艺；利用刻蚀方法成功制备出直径分别为8μm、4.5μm、2μm的碟型微腔激光器；直径8μm和4.5μm的微碟脉冲光泵浦激射阈值分别为170μW、15μW，是目前所见文献报导中比较低的；直径2μm的微碟连续光泵浦激射阈值仅几μW，目前尚未见到达到类似结果的研究报导；为解决微碟激光器激射光定向引出的问题，通过波导耦合模理论分析了双层碟之间功率耦合效率；据此设计了新型带耦合输出波导的电泵浦微腔激光器，为进一步研制可实用的电泵浦微腔激光器打下基础。

Nevertheless, induced bilevel programming models for the former category usually belong to a subject of nondifferentiable optimization problems, whereas that for the latter category becomes the continuously differentiable optimization problems.

此文首先从模型和算法的角度总结了有关这类问题已有的研究成果，接着介绍有关这方面的最新的研究进展，即如何把用户基于平衡原则下的交通网络优化问题的双层规划模型统一地转换为一个连续可微的单层最优化问题，并设计统一的算法。

In this study, nonionic surfactant sorbitan trioleate (Span 85) was modified with Cibacron Blue F-3GA to become an affinity surfactant (CB-Span 85) and to form affinity-based reversed micelles while dissolved in hexane. Since the CB molecule possesses a specific conformation that mimics nicotinamide adenine dinucleotide, it can bind strongly and specifically to a wide range of nucleotide-dependent enzymes such as dehydrogenases and kinases. Moreover, high protein transfer efficiency in the reverse micelles can be easily achieved by controlling the ionic strength of the aqueous phase.

本实验使用非离子型界面活性剂Span 85与蓝色染料分子Cibacron Blue F-3GA结合，形成具有亲和性的界面活性剂 CB-Span 85，由於CB染料分子具有与NAD+相似的结构，可与含核苷酸部位的蛋白质具有亲和力，将CB-Span 85溶於有机溶剂形成反微胞相，可有效的提高反微胞的选择率，可以只控制离子强度来调节蛋白质进出反微胞的效率。

Daubechies'wavelet frame theorem is extended from one dimension to n dimensions. According to this framework, an example of n-dimensional radial wavelet is given. Differing from tensor product multidimensional wavelet, the radial wavelet is inseparable, locally supported and infinitely differentiable. The family, obtained by dilations and translations from this radial wavelet, constitutes a special type of radial wavelet frame in L〓.

Daubechies的框架定理推广到了n维情形，同时，也按照这一理论框架，给出了高维二进径向小波的具体例子，具有下列性质：ψ是无穷次连续可微的；ψ是局部支撑的，支集为‖x‖≤1；ψ含有分式因子，因此对&奇异点&更为敏感；ψ是不可分的，不同于张量积形式的高维小波；ψ是各向同性的。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。