Comparing the value from the monotony of a function 利用函数的单调性比较大小
Monotonicity of some operator functions under the order defined by a2 2下若干算子函数的单调性
On monotonicity of function generated by two integer inequalities 两个积分不等式的构成函数的单调性
Application of monotonicity of function and limit in drenching rain model 函数的单调性和极限在淋雨模型中的应用
Secondly , some properties of reasoning function are discussed in details such as monotonicity , compatibility and satisfiablity 详细讨论了推理函数的单调性、相容性、可满足性,并给出推理方法的一般步骤。
In the higher mathematics category , routine methods to work out the proof of an inequation are a flexible use of mathematical knowledge like monotonicity of functions , extremum values , maximum and minimum values , convexity function , medium value theorem , taylor equation , holder inequation , schwarz inequation , and the analysis , formation and transformation of inequation problems as well 摘要在高等数学?畴中,灵活运用函数的单调性、极值、最值、凸性函数、以及中值定理与泰勒公式、赫尔德不等式、施瓦兹不等式等数学知识,对不等式问题进行分析、构造与转化,是解决不等式的证明问题的常用方法。
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 ( fbsde ) , 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。