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关键词： 三叉树模型   资产期权定价   Black-Scholes期权定价方程   风险中性概率   随机微分方程   金融数学   数学分析   数值计算  

摘要： 讨论了一般三叉树模型期权定价公式 ,它是二叉树模型的推广。证明了三叉树模型下期权价格所满足的方程是Black

关键词： 债券价格   到期期限   到期收益率   数学分析方法   票息率   实证方法  

摘要： 对债券市场价格与票息率、到期收益率以及到期期限等参数之间关系的研究通常采用实证方法 ,这种用个别推出一般的方法不甚严密。本文中采用数学分析的方法 ,利用计算机进行数据处理 ,对以上各参数之间的关系进行了严格的论证。通过对量化结果的讨论 ,提出了分析各参数对债券价格影响的有效方法 ,得出了一些有意义的结果。

关键词： 粉末注射成型   二维充模流动   控制方程   数学分析   非牛顿流体   扁平模腔  

摘要： 注射成形二维充模流动属于具有自由流动移动世界、非牛顿、非等温的流动问题.将扁平型腔内流动视为Hele Shaw流,由于模腔的复杂性及控制方程的非线性,采用数值计算得到腔内流体的压力场、温度场、速度场,得到压力和速度2个控制方程;引入2个相应的变换,将压力控制方程及速度控制方程化为拉普拉斯方程,并得到压力流函数可由拉普拉斯解表示的一个解析式,简化了计算过程,提高了计算精度,在此基础上进行计算机模拟,可检验Hele Shaw近似的精确程度.

关键词： 可积性   充分条件   充要条件   有界  

摘要： 纠正《数学分析讲义》(刘玉链、傅沛仁编 )中的一个错误 .

关键词： 泰勒公式   不定式   极限   求解方法   马克劳林公式   洛比达法则   数学分析  

摘要： 文章论述了应用泰勒公式求解不定式的极限的方法。

关键词： 数学分析   研究性学习   义务教育   课程改革   中学教育   科学精神   思维品质   数学教学   教学改革  

摘要： 随着《国家九年义务教育课程计划(实验稿)》的推出,“研究性学习”课程将正式成为我国教育课程体系的有机构成,这已是当前我国课程改革的一大亮点,当然也是数学教学改革的一大举措。本人认为:“研究性学习”虽然作为一门课程安排在中学,但它作为一种教学思想和方法则不应限于中学,而应更广泛地实施。

关键词： 极限公式   证明   非可导函数   不定式   可导函数   数学分析  

摘要： 证明了一个极限公式 。

关键词： skeletal muscle   transport   microcirculation  

摘要： An approach is presented for modeling transport and exchange in skeletal muscle that can be used to analyze vascular beds consisting of a large number of interacting capillaries. First the oxygen concentration is determined in a functional unit consisting of a single capillary surrounded by a region of tissue in which a flux is prescribed on the outer boundary of the region. This flux, which is a result of the interaction among all of the capillaries comprising the vascular bed, is then found by matching the concentration along the borders between adjacent units. This leads to a system of ordinary differential equations for the oxygen concentration in the capillaries coupled with a system of algebraic equations for the fluxes. The method is illustrated by obtaining the oxygen concentration within an array of capillaries for the case when each capillary has a different initial concentration and for the case when each capillary has a different flow rate.

关键词： capillary viscometers   differential capillary viscometer   forced flow viscometer   perturbation methods   Taylor dispersion  

摘要： A general formulation for capillary flow of two miscible fluids - one a dilute plug of polymer fluid inserted into a fully developed Poiseuille flow of the other, a Newtonian stream - is examined for its long time behavior. Phenomenologically, the system evolves from an initial state, that of a plug within the boundaries of sharp, well defined fronts inside a Newtonian stream, to a more homogenized state in the very long time scale. This problem was addressed by G. I. Taylor but with regard to a system of two Newtonian fluids, leading to the well-known results commonly described as 'Taylor axial dispersion'. In this paper, a general and systematic perturbation analysis is presented from which Taylor's result is recovered as a special case of a more general solution which applies to fluids incorporating elastic properties. In particular, the influence of viscoelasticity and (polymer) diffusivity on the observed pressure profile in the capillary conduit is examined. This effect is clearly separated out for small Peclet number flows using asymptotic and numerical analysis. The results identify the influence of fluid viscosity, elasticity, and diffusivity on the observed pressure profile and form the basis for the improved characterization of polymeric elasticity using capillaries - a finding that is of significant scientific and commercial interest. These results were obtained by the authors as a class of observations resulting from the perturbation analysis of forced-flow capillary devices in viscoelastic fluid property investigation.

关键词： atelectasis   diffusion   mathematical model   ventilating tube  

摘要： Aim: A mathematical model was developed to identify time periods of atelectasis induction in middle ear (ME) ventilated via ventilating tubes (VT). Atelectatic ears are characterized by a total gas pressure lower than 760 mmHg. Methods: Ventilating tubes were deliberately sealed and ME gas content changed in the presence of a preset blood gas pressure. Once sealed, CO2 rapidly diffuses out of the blood via lining tissues into the ME cleft. This results in initially a total ME pressure rise followed by a decrease in subatmospheric pressures. Time periods for atelectasis reformation was determined once ME pressure crossed the 760 mmHg value and continued to decline as the atelectasis reached higher grades. Results: Time periods calculated by the model varied from 18 to 125 min in ME cavities ranging in volume from 0.5 to 3.5 mL, respectively. These results were calculated for conditions of venous blood in the lining mucosa blood and are consistent with prior clinical tests that measured an induced return to previous atelectasis state following the closure of the VT in 33 tested ears within 25-120 min (43 min on average). Conclusions: The model demonstrates that under the above conditions, diffusive gas transfer in relation to blood gas content is the leading mechanism to alterations in ME pressure and volume. It may be used as a tool to determine ME physiological cavity volume of ears with VT.