教学课程资源库 更多>>

关键词： Meridian system   Pumping power   Fluid mechanics   Human physiology   Work of breathing  

摘要： Energy expenditure of the meridian system in traditional Chinese medicine(TCM)for living human bodies is one of the fundamental questions regarding the physical properties of the meridian *** a first attempt to address this,24 hand/foot meridians were modeled as a continuous channel with the sustainable movement of Qi and blood ***,the fluid mechanics energy equation for steady and incompressible flow was applied to estimate the pumping power of meridian circulation,based on the meridian length,blood viscosity and circulation *** findings based on the pumping power estimation results include:(1)new information to corroborate the determination of the production era of Yellow Emperor’s Inner Classics(Huang Di Nei Jing,《黄帝内经》);(2)a new definition for work of breathing(WOB)from a TCM *** paper could lead to future research aimed at modernizing the understanding of the meridian system,Qi and TCM using quantitative methods.

关键词： 教师资格考试   数学分析   实践教学  

摘要： 在国考教师资格证的《数学学科知识与教学能力》中,主要考查学科知识、课程知识、教学知识和教学技能,其中学科知识占比41%,且数学分析是其中分值最大的部分。这对高校数学专业的教学提出了更高的要求,主要措施是以教师资格证考试为导向建立数学分析知识题库,采用问题导向的教学方法,并贯穿于整个理论和实践教学过程,做到课证融合,提高教师资格证考试的通过率。

关键词： Riemann可积   变上限积分   Newton-Leibniz公式  

摘要： 本文分别从f(x)的Riemann可积性和连续性出发,厘清了f(x)与其相对应变上限积分函数Φ(x)的连续性和可导性之间的局部内在联系,并首次给出了许多数学分析教材中常见的一个典型例题的新证明方法,最后讨论了上述理论的若干应用。

关键词： Heart  

摘要： This article reviews contemporary methods for analysis of heart rate variability. Along with classical processing methods using spectral and statistical assessments, novel approaches based on analysis of the nonlinear heart rate dynamics are also discussed.

关键词： Nonlinear optimization   Stochastic demand   Heterogeneous clouds   Resource placement  

摘要： In the large-scale online services built upon data centers from heterogeneous clouds, user requests come from all over the world and will create stochastic demands for various resources in these data centers. It is an impending need to optimally schedule resource while considering the heterogeneity of different data centers. The corresponding general scheduling problem is a highly complex non-linear programming problem, which can hardly be solved efficiently using existing algorithms. We establish a differential evolution oriented mathematical model that can help reduce the search space significantly, and then propose an improved differential evolution algorithm to handle the problem efficiently. Experiments using the emulated and realistic data show that the algorithm outperforms the existing algorithms by increasing the revenue by up to 35%.

关键词： analytic solutions   lubrication theory   non-Newtonian material   roll coating  

摘要： This article describes the development of a mathematical model of forward roll coating of a thin film of a non-Newtonian material when it passes through a small gap between the two counter-rotating rolls. The conservation equations of mass, momentum, and energy in the light of LAT (lubrication approximation theory) are non-dimensionalized and solutions for the velocity profile, flow rate, pressure distribution, pressure, forces, stresses, power input to the roller, and temperature distribution are calculated analytically. It is found that by changing (increasing/decreasing) the value of material parameters, one can really control the engineering parameters like, stress and the most important the coating thickness and is a quick reference for the engineer working in coating industries. Some results are shown graphically. From the present study, it has been established that the material parameter is a device to control flow rate, coating thickness, separation points, and pressure distribution.

关键词： 3D-models   Filtration   MSCT   GFR   Split renal function assessment   Renal scintigraphy  

摘要： Purpose: whilst renal scintigraphy (RS) can be associated with interobserver variability, it remains the standard method of evaluating split renal function. Aim: to compare the efficacy of the novel technique of kidney function assessment and renal scintigraphy. Method: for this prospective single-arm study we recruited patients who were recommended dynamic renal scintigraphy with 99mTc-DTPA (diethylenetriaminepentacetate). After scintigraphy, mathematical analysis of computed tomography (MACT) was done in all patients, by a single person (SK) blinded to RS results. Results: the study included a total of 97 patients with mean age of 50.9 (range, 23-78) years. From this sample, 65 were females and 32 males. All patients underwent both RS and contrast-enhanced computed tomography for further MACT in 2016-2018. CT results were found to be similar to renal scintigraphy results with Pearson correlation coefficient of 0.945 (.< 0.001). Substantial similarities in renal plasma flow for both kidneys were also observed (0.815,.< 0.001). Conclusion: MACT proved feasible, effective and safe in estimating renal function. Its results are closely correlated with RS findings and could be easily integrated into surgical practice.

关键词： 数学分析  

ISBN: (纸本)9787030658661

摘要： 数学优化是研究优化问题的数学理论和方法的一门学科,是数学的一个重要学科方向, 是应用数学的重要组成部分,是数学在其他领域应用的重要工具,也是当前机器学习、人工智能的基础之一.优化理论与方法在科学和技术的各个领域以及国防、经济、金融、工程、管理等许多重要实际部门都有直接的应用.《中国学科发展战略·数学优化》系统分析了目前数学优化的主要分支、核心前沿方向、当前进展及发展态势,包括当前热门研究课题、主要的思想、方法与技巧、主要的难题,以及近年来的主要成果与前沿人物;提出对学科发展态势的观点与看法;提炼出学科的基本思想、核心方法与关键技巧;根据我国学科发展和国家重大需求,提炼与该学科密切相关的重要问题,建议、组织攻关和研发队伍,解决重大理论或实际问题;为我国优化学科发展和人才培养提出整体建议.

关键词： adjoint problem   epidemic model   optimal control  

摘要： This article deals with an optimal control problem governed by a system that models the dynamics of predator-prey interactions. We study the minimization of the infective prey density. Furthermore, our purpose is here to establish the existence of weak solutions and derive some optimality conditions. Finally, the impact of the control terms are studied to get an insight of the predator-prey model adopting various numerical simulations.

摘要： The moving contact line paradox discussed in the famous paper by Huh and Scriven has lead to an extensive scientific discussion about singularities in continuum mechanical models of dynamic wetting in the framework of the two-phase Navier-Stokes equations. Since the no-slip condition introduces a non-integrable and therefore unphysical singularity into the model, various models to relax the singularity have been proposed. Many of the relaxation mechanisms still retain a weak (integrable) singularity, while other approaches look for completely regular solutions with finite curvature and pressure at the moving contact line. In particular, the model introduced recently in [A.V. Lukyanov, T. Pryer, Langmuir33, 8582 (2017)] aims for regular solutions through modified boundary conditions. The present work applies the mathematical tool of compatibility analysis to continuum models of dynamic wetting. The basic idea is that the boundary conditions have to be compatible at the contact line in order to allow for regular solutions. Remarkably, the method allows to compute explicit expressions for the pressure and the curvature locally at the moving contact line for regular solutions to the model of Lukyanov and Pryer. It is found that solutions may still be singular for the latter model.