查询词典 monotone function

Firstly, on the base of the strictly monotone map, we provide the definition of strictly invariant quasi-monotone map, it is the extent of the strictly monotone mapping, at the same time, it is the especial case of the invariant quasi-monotone map, too. It is supported by some examples.

在理论部分做了三方面的工作：首先，在严格拟单调映射的基础上，提出了严格不变拟单调映射，它是严格拟单调映射的推广，同时也是不变拟单调映射的特殊情况，举例加以说明。

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。

Through the research of binomial probability distribution function,it has been proved that the PDF is a monotone increasing function of probability p and allowable failure time r in test,and is a monotone decreasing function of test time n.

通过对二项分布函数的研究，证明它是关于概率p和试验中允许失败次数r的单调增函数，是关于试验次数n的单调减函数。

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。

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。

In part 3, utilizing the existing Lipschitz results and the property of Yosida approximation of monotone and continuous function, we prove the existence and uniqueness theorem of a general backward stochastic differential equation with monotone and continuous coefficient.

第三部分在系数仅满足单调连续这样一个新条件下，我们综合运用单调连续函数的Yosida逼近的性质以及Lipschitz条件下的已有结果，证明了一般形式的倒向随机微分方程解的存在唯一性。

By calculating the sub-cluster parameters and the total antioxidant capability parameter of some kinds of fresh vegetable with diet therapy function, we found that there is clear linear correlation between distribution parameters of biopolymer active center elements (1-x)1/3ln(r1r2/k)、(1-x)1/3ln(k2r1/r2) and antioxidant capability parameter ln[F(1-x)3], and which show monotone decreasing and monotone increasing respectively.

同时对更大范围内的9大类蔬菜和5大类水果的生物高分子活性中心元素分布及其维生素C及维生素E含量进行了考察，结果发现群子统计参数(1-x)1/3ln(r1r2/k)、(1-x)1/3ln(k2r1/r2)与维生素C、E含量参数lnVc(1-x)3、lnVe(1-x)3均分别呈单减和单增的线性关系。

Based on two newly - defined monotone restrictions for heuristic function h, the characteristic of monotone restrictions for algorithm BHAO is also investigated, and the comparison between two BHAO algorithms is also discussed.

本文还提出了两类新的启发式函数的单调限制概念，并据此研究了算法BHAO的单调限制性质，研究了两个BHAO算法间的比较性质。关键词广义

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

The work of this paper is as follows: 1. Looking back the progressing history of the linear motor, introducing the features of the elevator driven by linear induction motor, radicating the topic of this paper "the digital frequency variable control of the elevator bi-side direct driven by linear induction motor". The research of this paper covers the conventional VVVF control, space vector based VVVF control, vector control and DTC.

本文主要开展了以下几个方面的工作： 1 回顾了直线电机发展历史，电机的驱动技术演变，特别是针对直线电机的驱动，简要介绍了直线感应电机驱动电梯的优点和不同结构类型，对传统的v／f控制，基于空间矢量法的v／f控制，矢量控制，和基于电压空间矢量的直接转矩控制进行了比较，确立了本课题的研究主题：直线感应电机双边直推式驱动电梯的全数字变频控制。

The article combines with the treatment of a superficial civil air defense work to introduce how the grouting method to improve the performance of the backfill soil.

文章从治理漂浮人防工事的角度提出了注浆技术在改善回填土性质方面的应用，并详细阐述了注浆技术的施工流程。