GRADIENT ESTIMATES AND ENTROPY FORMULAE FOR WEIGHTED p-HEAT EQUATIONS ON SMOOTH METRIC MEASURE SPACES

Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].     

应用数学方法 深化化学认知——以高中阶段速率平衡的常见结论的证明为例

选取了在高中课堂教学中出现的关于速率平衡的几个常见的结论,以阿伦尼乌斯公式为模型讨论了温度对反应速率的影响;推导并梳理了反应物转化率随投料量的变化关系;基于浓度商的单调性证明了平衡状态的"殊途同归"结论在数学上的合理性.在加深对常见结论认识的同时,通过对证明过程中应用的数学方法的总结,实现对几个相似化学问题证明方法的统...     

Ordinary differential inequalities and quasimonotonicity in ordered topological vector spaces

A well known comparison theorem on ordinary differential inequalities with quasimonotone right-hand side was carried over by
Volkmann (1972) to (pre)ordered topological vector spaces. We prove that the quasimonotonicity of is a necessary condition here if is continuous. Then it is shown that quasimonotonicity can be verified by considering only a few positive continuous linear functionals in the definition (for instance in by taking coordinate functionals).

     

Inequalities for the gamma function

Some inequalities for the gamma function are given. These results refine the classical Stirling approximation and its many recent improvements. Received: 2 May 2008, Revised: 2 September 2008     

一类函数的对数完全单调性

通过对参数λ,μ的讨论,主要利用函数的单调性理论,已有对数完全单调函数的性质以及幂函数的积分表达式研究了函数Gλ,μ(x)及函数[Gλ,μ(x)]-1的对数完全单调性,并在此基础上得到了一定条件下函数Gλ,μ(x)及[Gλ,μ(x)]-1对数完全单调的充要条件.