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关键词： 逻辑思维   实变函数   数学分析  

摘要： 实变函数是高师院校数学系开设的课程中的一门重要课程,它起着承上启下的关键作用,它既是先前各类分析课程的深化和继续,同时又为其他后续课程打下必要的基础。

关键词： 课程   教学探讨   计算   常微分方程   数学分析   高等代数   泛函分析   连贯性  

摘要： 计算方法是一门应用性很强的课程，包含了数学分析、高等代数、常微分方程、泛函分析诸多内容，各部分内容自成体系，知识连贯性不强，要求记忆的定理和公式较多，不便学生掌握。因此，教师在教授课程的过程中，要努力做到使各章之间保持一种紧密的联系，使学生能从整体上把握这门课程，

关键词： 反证法   直接证法   极限   有界性定理   区间套定理  

摘要： 数学分析中宜于用反证法证明总的原则是:对于所要论证的论题(若A则B),没有直接证明的正面根据,此时运用反证法证明,只要证明其反论题(若A则不B)的谬误即可。运用反证法证明的习题类型及规律是:1.证明“函数某个特定常数”;2.在已知极限存在或易证出极限存在的前提下,证明“极限等于零”或“极限等于某个特定常数”;3.证明有关“不存在”的题目;4.证明“至少有一点”的题目,对于题设中函数不具连续条件者,有时宜于用实数理论找点,再用反证法证明为所求;5.证明集合个数为“有限个”;6.证明“函数有界性”;7.证明“最多只有”的题目;8.证明“唯一性”。

关键词： free-boundary problem   travelling waves   diffusive instability   branching morphogenesis  

摘要： Lung branching morphogenesis has been widely studied in the field of developmental biology. Lung airway trees consist of relatively regular-sized distal branches, but how this regular branched pattern is formed is not well understood. In the present study, we undertake a detailed mathematical analysis of the model proposed in Hartmann & Miura (2006), which numerically captures branching morphogenesis of the simplest possible experimental system in vitro. We investigate analytically the stability of ID travelling waves with respect to periodic perturbations in two dimensions. This linear stability analysis leads to the so-called dispersion relations, predicting that a certain representative length dominates in this model. As the analytical analysis is restricted to travelling waves, we generalize the linear analysis to any I D solution by numerical simulations. Both results predict how the representative lengths will change by experimentally changing specific parameters. Finally, we discuss the importance of the analytical results from a biological point of view and propose an experimental scheme for a quantitative comparison between experiments and theory.

关键词： monod biodegradation kinetics   sorption   undisturbed sediment   pseudo-homogenous   aged contaminant  

摘要： Rates of C-14-phenanthrene mineralization in contaminated, undisturbed marine sediments were measured using the whole core injection method to assess microbial natural attenuation activity as a function of sediment depth. Submerged sediments were sampled from Eagle Harbor, a marine superfund site in Puget Sound. Experiments show significant biodegradation activities (0.0012-0.0036 day(-1) in the sediment horizons from 0 to 10 cm. The purpose and scope of this paper is to evaluate the range of experimental conditions giving valid results;a mathematical simulation described competing contaminant C-14-phenanthrene diffusion and simultaneous biodegradation (Monod kinetics), both retarded by sorption. The effect of aging was examined with two sorption models in presumed pseudo-homogenous sediments having effective properties. The simulation predictions provide quantitative guidelines for the successful use of the whole core injection method. (1) The effective Monod constant K-S' in sediment is increased by a large partition coefficient K-P between sediment and water and makes the apparent C-14-phenanthrene biodegradation approach first-order kinetics. (2) When K-S' > 1 mg(-1) l(-1) the measured C-14-phenanthrene biodegradation extent is biased by inadequately distributed injected tracer only when less than 7% of the sediment horizon is initially probed and mixed with injected tracer. (3) A short incubation time (< 20 days) is necessary when a mobile indicator, e.g., gaseous (CO2)-C-14, is used. For longer incubation times, predictions show that a (CO2)-C-14 indicator diffuses to adjacent horizons, thus smearing the depth profile of biodegradation. (4) This method employing a radiolabeled tracer provides accurate biodegradation rates for freshly contaminated sediments, and represents an upper limit to the natural phenanthrene biodegradation extents if the contaminant is aged over 50 days. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： 随机分析   第二版   应用   大学教材   数学分析   分析理论   分析基   概率  

摘要： 本书是随机分析理论大学教材，作者在大学数学分析和基础概率的前提下用简明严格的方式给出随机分析基本理论和重要应用。初版问世后得到好评，美国和德国的“数学评论”杂志认为该书取材范围广泛，论述方式现代，例题习题配备适当，特别适宜自学。现版本（第二版）是原书增订版，

关键词： 房地产   房产地产   不动产   灰色关联分析   数学分析   房价  

摘要： 一、我国房地产价格现状房地产业是我国现阶段国民经济发展中的一个重要支柱产业,房地产业的持续、稳定、健康发展不仅有利于人们的安居乐业,还有利于城市和国家经济的平稳、快速增长。但目前我国的房地产业中还存在着一些问题。

关键词： 课程设置   专业基础课   教学改革  

摘要： 重点课程建设是提高高等师范院校办学水平的重要手段,《数学分析》是数学系的核心课程之一。本文从教材与教材内容的选择,教学方法和教学手段的改革,师资队伍的建设和考试制度的改革等方面提出几点设想和建议。

关键词： 数学分析   现状   教学改革  

摘要： 数学分析是高等院校数学与应用数学专业最重要的基础课程之一。文章针对数学分析教学现状提出了一些改革的方法。

关键词： 数学分析   微分中值定理  

摘要： 从二元实函数与复数间的联系出发,将一元微分中值定理推广到二元实函数上,然后利用二元实函数的微分中值定理,将实数域上的微分中值定理推广到复数域上,得到解析函数的微分中值定理。