逻辑演算与形式化方法

逻辑演算对推理形式有效性的研究 ,比传统逻辑更抽象、更严格 ,其原因是形式化方法的运用。形式化方法包括构造形式系统 (语法的 )和对该系统进行解释 (语义的 )两个阶段。以一阶逻辑演算KL 系统为例 ,形式化方法的前期阶段 ,又包括符号化和系统化两个步骤 :符号化是用特制的人工语言符号将推理形式或演绎关系公式化 ;系统化是在符号化基础上构造形式系统 ,即用系统给定的公理和变形规则推导出一系列定理的形式证明系统 ,这是逻辑演算的主要内容。形式化方法的后期阶段或第三步骤是对系统的解释 ,也称模型化。经过解释 ,该系统的符号、公式有了内涵 ,从而就有了更普遍的适用价值。纯形式的逻辑演算的性质、意义和作用也因此变得十分清晰     

LAN property for an ergodic Ornstein–Uhlenbeck process with Poisson jumps

In this article, we consider an ergodic Ornstein–Uhlenbeck process with jumps driven by a Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients as well as its jump intensity depend on unknown parameters. Considering the process discretely observed at high frequency, we derive the local asymptotic normality property. To obtain this result, Malliavin calculus and Girsanov’s theorem are applied to write the log-likelihood ratio in terms of sums of conditional expectations, for which a central limit theorem for triangular arrays can be applied.     

大学数学基础课教学中融入数学建模思想的实践

数学建模不仅限于解决实际问题,也可以是数学发展过程中提出的理论问题。基于近年来在大学数学基础课教学中融入数学建模思想的教学实践,论述了其主要思路与做法。介绍了将数学建模思想融入数学基础课教学的两个教学案例,即微积分方法的本质和从方程组出发引入线性相关与线性无关概念。     

LAN property for an ergodic diffusion with jumps

In this paper, we consider a multidimensional ergodic diffusion with jumps driven by a Brownian motion and a Poisson random measure associated with a compound Poisson process, whose drift coefficient depends on an unknown parameter. Considering the process discretely observed at high frequency, we derive the local asymptotic normality (LAN) property.     

关于非数学专业的微积分教学改革

本文认为,当前非数学专业的微积分教学改革,应特别强调微积分的数学建模方法和计算功能,强调对数学原理和背景的介绍.为此,作者以"启发应用意识,提高应用能力"为宗旨,提出从教材到教学法直至成绩考核方法的一整套教学改革方案.     

Risk minimization for an insurer with investment and reinsurance via g-expectation

Abstract

This paper is devoted to the study of a risk-based optimal investment and proportional reinsurance problem. The surplus process of the insurer and the risky asset process in the financial market are assumed to be general jump-diffusion processes. We use a convex risk measure generated by g-expectation to describe the risk of the terminal wealth with investment and reinsurance. Under the aim of minimizing the risk, the problem is solved by using techniques of stochastic maximum principles. Two interesting special cases are studied and the explicit expressions for optimal strategies and corresponding minimal risks are derived.     

独立学院微积分教材改革探析

文章介绍了独立学院微积分改革的背景和现状,根据独立学院的实际和微积分的特点,着重对微积分改革的指导思想、理论体系、微积分应用以及改革中的主要问题作了大胆地探索和实践,最后对微积分改革提出了一些对策建议。     

Rejoinder to 'Ahmed, M.S. (1998). A note on regression-type estimators using multiple auxiliary information.'

In the estimators t ₃ , t ₄ , t ₅ of Mukerjee, Rao & Vijayan (1987), b _{y x} and b _{y z} are partial regression coefficients of y on x and z , respectively, based on the smaller sample. With the above interpretation of b _{y x} and b _{y z} in t ₃ , t ₄ , t ₅ , all the calculations in Mukerjee at al. (1987) are correct. In this connection, we also wish to make it explicit that b _{x z} in t ₅ is an ordinary and not a partial regression coefficient. The 'corrected' MSEs of t ₃ , t ₄ , t ₅ , as given in Ahmed (1998 Section 3) are computed assuming that our b _{y x} and b _{y z} are ordinary and not partial regression coefficients. Indeed, we had no intention of giving estimators using the corresponding ordinary regression coefficients which would lead to estimators inferior to those given by Kiregyera (1984). We accept responsibility for any notational confusion created by us and express regret to readers who have been confused by our notation. Finally, in consideration of the above, it may be noted that Tripathi & Ahmed's (1995) estimator t ₀ , quoted also in Ahmed (1998), is no better than t ₅ of Mukerjee at al. (1987).     

类型--逻辑语法的句法特色

论述类型—逻辑语法的句法特色———兰贝克演算。兰贝克演算是对由爱裘凯维茨和巴—希勒尔所创立的经典范畴语法的改进和发展,其表述有多种形式,重点论述在实践中应用广泛的根岑风格的兰贝克演算。