对数学分析教科书中一些例题和练习的商榷

对数学分析教科书中的一些周期函数、极限的证明、近似式的应用提出商榷的意见．补充、修正了其中不完善之处．     

Bounds on Normal Approximations for the number of Descents and Inversions

In this article, we use Stein’s method to give non uniform bounds for normal approximation for the number of descents and inversions. Moreover, we also improve a constant on uniform bounds for normal approximation of those random variables in Fulman’s work in 2004. Our constants are 13.42 and 14.24, respectively.     

Quadratic reflected BSDEs and related obstacle problems for PDEs

Abstract

In this paper, we study a kind of reflected backward stochastic differential equations (BSDEs) whose generators are of quadratic growth in z and linear growth in y. We first give an estimate of solutions to such reflected BSDEs. Then under the condition that the generators are convex with respect to z, we can obtain a comparison theorem, which implies the uniqueness of solutions for this kind of reflected BSDEs. Besides, the assumption of convexity also leads to a stability property in the spirit of above estimate. We further establish the nonlinear Feynman-Kac formula of the related obstacle problems for partial differential equations (PDEs) in our framework. At last, a numerical example is given to illustrate the applications of our theoretical results, as well as its connection with an optimal stopping time problem.     

The Multi-scale Marked Area-interaction Point Process: A Model for the Spatial Pattern of Trees

Abstract.  The spatial pattern of trees in forests often combines different types of structure (regularity, clustering or randomness) at different scales. Taking species or size into account leads to marked patterns. The question addressed is to model such multi-scale marked patterns using a single process. Within the category of Markov processes, the area-interaction process has the advantage of being locally stable, whether it is attractive or repulsive. This process was originally defined as a one-scale non-marked process. We propose an extension as a multi-scale marked process. Three examples are presented to show the adequacy of this process to model tree patterns: 1. A pine pattern showing anisotropic regularity and clustering at different scales. 2. A bivariate (adult/juvenile) kimboto pattern in French Guiana, showing regularity for one type, clustering for the other and repulsion between the two. 3. A marked pattern in Gabon where the mark is tree diameter.     

MP3法律争议对数字化音乐版权的冲击--从法经济学的视角审视

数字音乐与网络的结合对现行的版权制度提出了挑战 ,而在数字化的语境下人们仍是囿于传统法律框架去寻求数字音乐版权的支撑点。殊不知 ,音乐版权制度在时下的功能变异导致了利益的失衡 ,本是对作者利益保护的音乐版权制度却偏向了作为中间人的发行人。因此文章从法经济学的视角出发对数字音乐版权的存废做一剖析 ,并试图对合理使用制度作一建设性的扩张 ,以期给从网上免费下载音乐找一个合法的理由。     

一个新有心力公式的建立和应用

从动能定理出发 ,建立起计算有心力的一个新公式F =12 mh2 ddr ( drdθ) 2 +r2 /r4,并应用于求多种曲线运动的有心力     

对经济增加值指标构建及其应用的思考

经济增加值(EVA)源于剩余收益(RI)模型。EVA公式中资本成本,尤其是股东投入资金的机会成本的测度可采用比CAPM更一般的定价模型,并加入物价变动因素。资本成本的考虑,对上市公司改变股权融资偏好有重要作用。EVA实际上是资本效率(ROI-r)与资本额之积,也是投资、购并的决策依据。市场增加值MVA可弥补EVA的不足。MVA的分解使总市值可表示为当前营运价值COV与未来增长价值之和。COV与FGV之间存在比例优化问题。本文首次将财务杠杆系数(D/E)明确嵌入EVA中,并将杜邦分析法与D/E、r结合起来,构造了全新的EVA算式。EVA的缺陷在于“结果决定一切”,可用相对指标弥补。EVA在国企改革与管理中具有特别意义。     

探讨第二类换元法积分

第二类换元法是一种既重要又不易掌握的积分方法。经过多年探索,发现第二类换元法也并非无规律可循,它也存在一定的规律性。一般可以用三角代换法、根式代换法、繁式代换法等三种代换法求出积分。     

Inventory Models with Continuous and Poisson Demands and Discounted and Average Costs

We develop a new, unified approach to treating continuous‐time stochastic inventory problems with both the average and discounted cost criteria. The approach involves the development of an adjusted discounted cycle cost formula, which has an appealing intuitive interpretation. We show for the first time that an (s, S) policy is optimal in the case of demand having a compound Poisson component as well as a constant rate component. Our demand structure simultaneously generalizes the classical EOQ model and the inventory models with Poisson demand, and we indicate the reasons why this task has been a difficult one. We do not require the surplus cost function to be convex or quasi‐convex as has been assumed in the literature. Finally, we show that the optimal s is unique, but we do not know if optimal S is unique.