查询词典 existence theorem of implicit function

In order to study vector-valued optimization problem, in chapter 5, a class of vector -valued function, that is, uniformly same-order set-valued function is introduced , which includes the separated functions as its proper subset; without hypothesis of convexity, new minimax theorem and saddle point theorem for uniformly same-order set-valued function are established. Next, by employing Ky Fan\'s lemma and H-KKM mapping , several existence results for generalized vector equilibrium problem established.

为了研究向量优化问题，作为可分函数的推广，第五章引入了一致同阶集值函数类，在没有凸性条件的假设下，对一致同阶集值函数建立了新的极小极大定理与鞍点存在定理；利用H-KKM映射，对一般向量均衡问题建立了(来源：A73BcbC论文网www.abclunwen.com)几个存在性定理；最后讨论了集值向量均衡问题系统，利用集值映射的拟凸性，在较弱的条件下证明了解的存在性。

By getting Lebesgue characteristic of integrable function of Riemann from the definition of Gather zero measure, discussing the relation between almost continuous everywhere and existent of limit, it gets the theory which is from the function integrability to the consecution and from consecution to the limit existence .i.e. the almost limit existence is equal to the almost continuous everywhere in the integrable function of Riemann. It also gets a unified condition which has a wider range than regulated function and comes to the conclusion that the function of bounded variation is the integrable function of Riemann.

通过定义零测度集给出了可积函数的特征，讨论了其几乎处处连续与极限存在的关系，从而得到了从函数可积性到连续性，从连续性到极限存在性的函数特性理论，即可积函数中极限的几乎处处存在与几乎处处连续是等价的，得出比正规函数更加宽泛的统一条件，得出了有界变差函数是可积函数的结论。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational, basic, differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式，给出了这几个不等式的一些应用实例，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational ,basic , differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality and Minkowski inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式和闵可夫斯基不等式以及这几个不等式的应用，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

On the basis of extending the concepts of the derived function, primitive function and integration of interval-valued function to complex interval-valued function and using the descomposition theorem of complex fuzzy set, the derived function, primitive function and integration of complex fuzzy set-valued function and some properties of them are proved.

2在国际上最先引入了复模糊集合与复模糊数的基本概念，证明了它们的基本代数运算的封闭性，并且其运算可通过α水平复集合的相应运算来进行

We prove the existence theorem of rationed with Borel points for meromorphic functions in the unit circle, discuss the operations of algebroid functions and the existence theorem of Nevanlinna direction of algebroid function dealing with mutiple values, and obtain some uniqueness theorems dealing with mutiple values of algebroid functions.

证明了单位圆内限定Borel点的亚纯函数的存在性定理，讨论了代数体函数的运算性质以及涉及重值的Nevanlinna方向的存在性定理，得到了一些涉及重值的代数体函数的唯一性定理； 2。

Theorem 1 constructs a set of universal measure zero using continuous extension; Theorem 2 verifies absolutely continuous function being of good property under some condition; Theorem 3 reveals some relation between real function and meager.

定理1 主要运用了连续延拓构造了一个泛测度零集；定理2 证明绝对连续函数在一定条件下具有良好的性质；定理3 揭示了实函数与第一纲集的某种关系。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

Theorem, Implicit Function Theorem and its Applications.

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

By using implicit function theorem, Taylor's formula and mean theorem, the form of the non-affine nonlinear systems is transformed into the form of affine nonlinear systems.

利用隐函数定理和泰勒公式及中值定理，将非仿射非线性系统转变为仿射型非线性系统。

For the head-teacher of the class said that I had seriously broken the school rules,which led me to a three-day suspend class.

为什么呢？因为我的班主任说我严重的违反了校规，于是让我停课三天。

Many of them believe that the conversion of thousands of working-class folk in England spared that nation from the mass carnage and the tyranny that came with the revolution in France.

他们之中有许多人相信，在英国数以千计的劳工阶级之悔改信主使英国免於遭受如法国大革命所造成的大屠杀和专制暴政。