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关键词： 雨中行走   矢量合成   相对运动   行走策略   三种典型情况  

摘要： 人在雨中的行走过程,结合风速风向,是一个典型的矢量合成场景问题,在不同的外部环境下,为了使人在相同的行进路程中,被淋到的雨最少,人的行走有这不同的策略,本文从物理学相对运动的角度出发,建立相关的数学模型,以数学建模的思路对行走策略进行计算和讨论,本文讨论了三种不同的典型情况。

关键词： 数学分析   有限与无限   教学改革   教学方法  

摘要： 数学分析是数学专业重要的主干基础课,它所呈现的理论、数学思想、逻辑推理方法以及处理问题的技巧对学生后续的学习起着奠基的作用。为进一步提高教学质量,顺应信息化时代对学生的培养要求,对数学分析课程的教学内容、教学方法及考核方式等方面提出几点建议。

关键词： 高中数学   分析问题   解决问题   策略  

摘要： 高中数学新课程对于提高分析和解决问题的能力有着更深层次的要求,本文就我们教师在平时教学中应注重分析和解决问题能力的培养的方法和策略上进行研讨,得给出了一般性的结论。

关键词： magnetic particle imaging   model-based reconstruction   reconstruction operator   inverse problems   ill-posedness  

摘要： Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

关键词： Performance-based regulation market   performance score   mileage   California ISO   Mid-continent ISO  

摘要： This letter investigates the fundamental differences between how California Independent System Operator (ISO) and Midcontinent ISO calculate performance accuracy scores in their performance-based regulation markets. Both ISOs tend to follow the Federal Energy Regulatory Commission order 755 to pay regulation resources-whether conventional generators or distributed and demand side resources-based on their actual performance. The advantages and disadvantages of each method are systematically explained. First, real-world ISO data are used to show that there may exist major differences between these two methods in scoring accuracy under similar regulation performance scenarios. Next, the root causes for the observed differences are studied mathematically. Finally, some suggestions are made to improve these scoring methods;should these or other ISOs seek to refine their scoring formulas.

关键词： Bidomain model   homogenization   asymptotic analysis   two-scale convergence  

摘要： The aim of this paper is to provide a complete mathematical analysis of the periodic homogenization procedure that leads to the macroscopic bidomain model in cardiac electrophysiology. We consider space-dependent and tensorial electric conductivities as well as space-dependent physiological and phenomenological nonlinear ionic models. We provide the nondimensionalization of the bidomain equations and derive uniform estimates of the solutions. The homogenization procedure is done using 2-scale convergence theory which enables us to study the behavior of the nonlinear ionic models in the homogenization process.

关键词： Upper Texas Coast   beach erosion   remote storm   overwash   Empirical Orthogonal function  

摘要： The upper Texas coast has been severely damaged by repeated beach erosion without any landfall of tropical storm. Since the average wave height was lower than 1.5 m and the mean tide range was smaller than 0.5 m there, they were not enough to explain the extreme erosion along the coast. Many studies had been conducted to find the causes of continuous erosion and then overwash was suspected by morphological analysis. The past studies, through the analysis of the observation data, concluded that the impact of remote storm might be a major cause of coastal erosion. The Texas Land Office has developed a master plan for coastal resilience and they switched to recovery from investigation. However, beach erosion is still a complicated process and continuous erosion has not been studied until now. For that reason, we here propose an alternative way for the further examination. A mathematical approach called as Empirical Orthogonal Function (EOF) is chosen to analyze spatiotemporal variations. We here applied the EOF method to the observed beach profile data to examine the spatiotemporal characteristics of waves related to the erosion problem. During the observation, the landfall of hurricane was made in the study area and it would be an interesting analysis of affected or unaffected beach change by storm. The short and long-term variations by landfall of storm or impact of remote storm were also studied by EOF method respectively. The dominance of cross-shore process such as overwash was also analyzed in this study.

关键词： 数学分析   极限  

摘要： 数学分析可以分为两大类,分别是一元数学分析和多元数学分析,其中多元数学分析是以一元数学分析为基础的,而一元数学分析可以分为四大板块,分别是极限论、微分论,积分论和级数论,从本质上讲,微分论,积分论和级数论都可以看成是极限论在特殊情形下的表达形式。极限是数学分析中最重要也是最基本的思想,掌握了求极限的方法,可以让我们对数学分析的认识有一个质的升华。

关键词： 向量函数   微分   反函数   変量変换   克莱姆法则  

摘要： 论文首先回顾了向量函数的定义和向量函数微分的定义以及可微的条件。其次给出了向量函数微分中值不等式的一种简单证明。最后给出了向量函数在解决积分的变量变换和克莱姆法则证明中的应用。