查询词典 monotone decreasing

In this paper, we use the coupled fixed point theorem for mixed monotone condensing operators to obtain an existence, uniqueness and iterative approximation theorem of solutions of initial value problems for second order mixed monotone type of impulsive differential equations.

利用混合单调凝聚算子的耦合不动点定理，给出了二阶混合单调型脉冲微分方程的初值问题的解的存在唯一性及迭代逼近定理。

We prove the equivalent conditions of completely monotone function, we also discuss the relationship of positive definite function, semi-positive definite function and completely monotone function when the function take values in a commutitive von Neumann algebras.

我们证明了完全单调函数的几个等价条件，并且讨论了取值于交换von Neumann代数的正定函数，半正定函数及完全单调函数之间的关系。

Firstly, we combine the theories of monotone operator and maximal monotone operator's Yosida approaching with domain method to prove the solution's existence of single input-output equation in R n in the similar economical backgrounds in present articles and then gain the solution's continuity by exterior approaching method,at last we give the responding economical meaning about the solution's existence and continuity.

就R n空间中消耗为单调单值型的投入产出方程，在现有文献类似的经济背景之下，利用单调算子的理论以及极大单调算子的Yosida逼近结合邻域逼近法给出了投入产出方程的解的存在性的证明，然后利用外部逼近法结合方程截断技巧证明了投入产出方程的解的连续性，最后给出了相对应于存在性和连续性的经济解释。

Secondly, we combine the theories of monotone operator and maximal monotone operator's Yosida approaching with domain method to prove the solution's existence of set-valued input-output equation in R n in the similar economical backgrounds in present articles too and then gain the solution's continuity by interior approaching method,at last we give the responding economical meaning about the solution's existence and continuity.

对于R n空间中消耗为单调集值型的投入产出方程，也在现有文献类似的经济背景之下，利用单调算子的理论以及极大单调算子的Yosida逼近结合邻域逼近法给出了投入产出方程的解的存在性的证明，接着利用内部逼近法结合方程截断技巧对投入产出方程的解的连续性给予了证明，然后顺便简单的介绍了运用外部逼近法来得到方程的解的连续性的思路，最后也给出了相对应于存在性和连续性的经济意义。

With the cone theory and monotone iterative technique,the existence and uniqueness of the solution for the ordering symmetric contraction mixed monotone operator equations are studied,and the error estimations for the convergent iterative sequence are also given.

摘 要 利用锥理论和单调迭代技巧，研究序对称压缩的混合单调算子方程解的存在唯一性，并给出迭代序列收敛于解的误差估计。

The monotone class theorem of multiple dimension functional format.This is the generalization from the one dimension monotone class theorem.

给出了多维函数形式的单调类定理，它是一维函数形式单调类定理的推广，也是处理多维可测函数、多维随机过程的有力工具。

Owing to the monotonic mapping of fuzzy structured element established the homeomorphic property between fuzzy number space and the family of standard bounded monotone function, so, we can transform the study of any properties in fuzzy number space to the corresponding one in the family of standard bounded monotone function, e.g.

本项目针对矿井下采空区岩石陷落形成的多孔隙介质空间的极度不规则性，建立一种以模糊值函数分析学为基础的、更接近于刻划采空区内气体流动实际状况的模糊微分方程及各种边值问题，进而得出解算复杂采场气体模糊渗流问题的数学方法。

According to the linear search technique, the Quasi-Newton algorithm can be divided into monotone algorithm and non-monotone algorithm.

根据所采用的搜索准则，拟牛顿算法可以分为单调的算法和非单调的算法。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

Firstly, the generalization of Fan-Ha section theorem and a general vector variational inequality without convexity assumption and minimax theorem of vector-valued function are obtained. Then, the quasi-montone vector variational inequality problem is concerned. Cx-quasi-monotone operator is defined in topological vector space, inner point of a closed convex set K is introduced, the relation between inner point and relative algebraic interior point is given, an existence result for quasi-monotone vector variational inequality is obtained.

第三章主要研究了向量变分不等式和极小极大定理(来源：3282AB83C论文网www.abclunwen.com)，建立了广义的Fan-Ha截口定理、新的向量变分不等式与极小极大定理，并在拓扑向量空间中定义了C_x-拟单调算子，引入了闭凸集K的inner点，给出了inner点与相对代数内点的关系，利用innK_c代替K的拓扑内部，建立了新的拟单调向量变分不等式。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。