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关键词： 函数的奇偶性   解题过程   认真观察   数学分析   纽带作用   直观图   函数奇偶性   巧妙应用  

摘要： 函数的奇偶性从直观图象角度反映了其相应的对称性,充分体现了“数”与“形”之间的有机联系,是进行数学分析和数学研究的有力工具之一,对函数的知识体系和综合应用具有重要的纽带作用,是历年高考中比较常见的考点之一.在具体解题过程中,要从问题的条件或结论出发,通过认真观察、分析与思考,巧妙应用函数的奇偶性,将会收到意想不到的功效.

关键词： 分析问题   数形结合   化繁为简  

摘要： 在数学中,分析问题是解决问题的前提,本文从教学实际出发,结合教学过程中出现的问题,提出了借助图形直观、化繁为简来分析问题,通过提升学生的逻辑思维能力,达到提升学生分析问题、解决问题并将数学应用于日常生活中的能力的目的。

关键词： 职工互助保障   微观视角   数学分析   工会  

摘要： 近年来,职工互助保障在各级工会的大力支持下得到长足发展。其以低成本、低风险,自愿参加、不以盈利为目的的特点,受到越来越多的职工群众的关注和欢迎。职工互助保障与社会保险、商业保险既有相通之处,又存在巨大差异,是我国综合社会保障体系的重要一环。通过从微观视角细致分析某个单位或单个职工群众个体在参加职工互助保障后所带来的变化,有效推动最终达到职工互助保障增强职工保证功能、覆盖全社会职工保障网络体系的目标。

关键词： Fokker‐   Planck equation   modified theta model   nonlinear dynamics  

摘要： Information processing in the brain is performed by the interactions of numerous number of neurons. However, much remains unknown about complex behaviors of a network composed of numerous number of neurons. Especially, in what case cross frequency coupling emerges and how it alters timings of individual firing are open questions. Therefore, in order to quantitatively evaluate the dynamics of the nervous group, we reproduced phenomena such as cross frequency coupling observed in the brain on a mathematical model and analyzed. The analyses of Fokker-Planck equation provide the region of gamma/theta oscillations as well as their cross-frequency couplings. In addition, we demonstrated that the populational oscillation synchronizes sequences of spike trains, which is supposed to be a possible mechanism of memory coding in hippocampus by theta-gamma neural code.

ISBN: (纸本)9787512434837

关键词： coronavirus   fractional calculus   SEIR model   q-Homotopy analysis transform method  

摘要： Throughout the globe, mankind is in vastly infected situations due to a cruel and destructive virus called coronavirus (COVID-19). The pivotal aim of the present investigation is to analyze and examine the evolution of COVID-19 in India with the available data in two cases first from the beginning to 31st March and beginning to 23rd April in order to show its exponential growth in the crucial period. The present situation in India with respect to confirmed, active, recovered and deaths cases have been illustrated with the aid of available data. The species of novel virus and its stages of growth with respect some essential points are presented. The exponential growth of projected virus by the day-to-day base is captured in two-dimensional plots to predict its developments and identify the needs to control its spread on mankind. Moreover, the SEIR model is considered to present some interesting consequences about COVID-19 within the frame of fractional calculus. A newly proposed technique called q-Homotopy analysis transform method (q-HATM) is hired to find the solution for the nonlinear system portraying projected model and also presented the existence and uniqueness of the obtained results with help of fixed point theory. The behavior has been captured with respect to fractional order and time. The present study exemplifies the importance of fractional operator and efficiency of the projected algorithm.

关键词： flattening   rolling   carbon-fiber-reinforced plastic   technological parameters   ultrathin prepregs  

摘要： A mathematical model and a technique for evaluating the technological process parameters to obtain superthin prepregs by flattening carbon tows impregnated with an epoxy binder have been developed. It is recommended to simultaneously roll 25-50 carbon tows containing 400-600 monofilaments by rolls 50-100 mm in diameter, which is conceptually and technically consistent with possibilities of the existing equipment. The preferred viscosity range of the binder within which superthin prepregs with a thickness of 1-10 monofilament diameters are obtained has been identified. The results found significantly expand the design and technological potentialities of creating superthin skins made of carbon-fiber-reinforced plastics in comparison with the existing ones

关键词： compressible unsteady flows   finite volume formulation   hybrid time integration   local time stepping   space–   time stability analysis  

摘要： The Reynolds-averaged Navier-Stokes equations and the large eddy simulation equations can be coupled using a transition function to switch from a set of equations applied in some areas of a domain to the other set in the other part of the domain. Following this idea, different time integration schemes can be coupled. In this context, we developed a hybrid time integration scheme that spatially couples the explicit scheme of Heun and Crank-Nicolson's implicit scheme using a dedicated transition function. This scheme is linearly stable and second-order accurate. In this article, an extension of this hybrid scheme is introduced to deal with a temporal adaptive procedure. The idea is to treat the time integration procedure with unstructured grids as it is performed with Cartesian grids and local mesh refinement. Depending on its characteristic size, each mesh cell is assigned to a rank. And for two cells from two consecutive ranks, the ratio of the associated time steps for time marching the solutions is 2. As a consequence, the cells with the lowest rank iterate more than the other ones to reach the same physical time. In a finite-volume context, a key ingredient is to keep the conservation property for the interfaces that separate two cells of different ranks. After introducing the different schemes, the article recalls briefly the coupling procedure, and details the extension to the temporal adaptive procedure. The new time integrator is validated with the propagation of 1D wave packet, the Sod's tube, and the advection of 2D vortex.

关键词： bacterial contamination   bacterial culture   optimization   platelets   transfusion  

摘要： Background: The US Food and Drug Administration (FDA) issued a guidance for bacterial risk control strategies for platelet components in September 2019 that includes strategies using secondary bacterial culture (SBC). While an SBC likely increases safety, the optimal timing of the SBC is unknown. Our aim was to develop a model to provide insight into the best time for SBC sampling. Study Design and Methods: We developed a mathematical model based on the conditional probability of a bacterial contamination event. The model evaluates the impact of secondary culture sampling time over a range of bacterial contamination scenarios (lag and doubling times), with the primary outcome being the optimal secondary sampling time and the associated risk. Results: Residual risk of exposure decreased with increasing inoculum size, later sampling times for primary culture, and using higher thresholds of exposure (in colony-forming units per milliliter). Given a level of exposure, the optimal sampling time for secondary culture depended on the timing of primary culture and on the expiration time. In general, the optimal sampling time for secondary culture was approximately halfway between the time of primary culture and the expiration time. Conclusion: Our model supports that the FDA guidance is quite reasonable and that sampling earlier in the specified secondary culture windows may be most optimal for safety.

关键词： 数学  

ISBN: (纸本)9787030656292

摘要： 本书主要解决数学分析中的收敛与发散及相关的一些问题,内容包括数列的收敛与发散、反常积分的收敛与发散、数项级数的收敛与发散等.本书深入浅出,表达清楚,可读性和系统性强.书中主要通过一些疑难解析和大量的典型例题来解析数学分析的内容和解题方法,并提供了一定数量的习题,便于教师在习题课中使用和学生在学习数学分析时练习使用.本书通过二维码配有一些概念、定理和方法的应用的视频讲解,内容呈现方式更加生动直观.