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关键词： 小学数学   分析能力   解决问题能力   构成与培养  

摘要： 数学是一门高度抽闲、逻辑缜密的基础学科,若要学号数学需有扎实的基础,而小学阶段作为稳固根基的关键时期,分数不应是此阶段评价学生的唯一指标,应淡化分数对策引导教师在教学中注重分析和探究能力的培养,摒弃纸上谈兵。文章紧紧围绕小学数学能力各组成部分,对小学数学分析及解决能力的培养策略进行全面规划,充分体现数学知识自身价值。

关键词： backward bifurcation   control strategies   equilibria   HIV   reproduction number   stability   TV  

摘要： A deterministic model for the transmission dynamics of HIV and Trichomonas vaginalis (TV) in a human population is designed and rigorously analysed. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. This phenomenon can be removed by assuming that the coinfection of individuals with HIV and TV is negligible. Furthermore, in the absence of coinfection, the disease-free equilibrium of the model is shown to be globally asymptotically stable whenever the associated reproduction number is less than unity. Numerical simulation of the model, using initial and demographic data, shows that increased incidence of TV in a population increases HIV incidence in the population. It is further shown that control strategies, such as the treatment, condom use, and counselling of individuals with TV symptoms, can lead to the effective control or elimination of the HIV in the population if their effectiveness level is high enough. The time to disease elimination is reduced if more than one strategy (hybrid strategy) is considered.

关键词： Jet grouting   Shadow effect   Mathematical analysis  

摘要： Jet grouting is a ground improvement technique that involves the injection of binder (with or without air) in soil at high pressure. One aspect of this technique that has not been investigated until now is the risk of failure due to the shadow effect, defined as the interruption of continuity during jetting produced by obstructions, such as boulders. This can represent a very serious problem because boulders do not allow the jet to reach and erode the soil, thus reducing the diameter or preventing the complete formation of the columns. This paper presents a mathematical theoretical discussion considering boulders as spheres. Three conditions possibly causing a failure of the jet-grouted continuous system are identified. A statistical risk analysis related to the probability of an unidentified spherical boulder causing a failure of the watertightness requirement of a jet-grouting wall is assessed. The goal of this research is to provide a tool by which engineers can estimate the risk related to the shadow effect. (C) 2018 American Society of Civil Engineers.

关键词： Solidification  

摘要： An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions (e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman’s solution are consistent in the low carbon range. A conventional numerical heat analysis (i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.

关键词： basic reproduction number   ectoparasites   equilibria   Lyapunov   stability  

摘要： A new deterministic model for ectoparasite-borne diseases (which comprises four nonlinear coupled differential equations) is designed and analyzed. A full stability analysis of thismodel is investigated. First, the basic reproduction numbers (R-1, R-2, and R-3) of the model are determined. The model has a locally and globally asymptotically stable disease-free equilibrium point when R-0 = max{R-1, R-2} <= 1. A unique infestation-only boundary equilibrium point is shown to be globally asymptotically stable whenever R-2 < 1 < R-1 by using a nonlinear Lyapunov function of Goh-Volterra type, in conjunction with the LaSalle's invariance principle. On the other hand, the model has a unique globally asymptotically stable infected-only boundary equilibrium point whenever R-1 < 1 < R-2. Moreover, the model has a unique endemic equilibrium point that is globally asymptotically stable provided that R-1 > R-2 > 1 and R-3 > 1. Finally, it is shown that replacing themass incidence function with the standard incidence function in the ectoparasite-borne diseases model with mass action incidence does not alter the qualitative dynamics of the model.

关键词： Ciliary movement   Seminal fluid   Herschel-Bulkley fluid   Vas deferens   Metachronal wave  

摘要： In the present paper, the ciliary flow of seminal fluid (non-Newtonian fluid) in the vas deferens (ductus efferentes) of the male reproductive tract is examined through a mathematical model. The rheological behavior of seminal fluid is described as a Hershel-Bulkley fluid. The momentum equations governing the flow of Herschel-Bulkley model are simplified by considering long wave-length and low Reynolds number approximations. The analytical solutions are obtained for velocity profile, flow rate, pressure gradient and flow impedance. The variation of plug core radius with respect to the cilia length (epsilon), the measure of the eccentricity of the elliptical motion (alpha), the wave number (beta) and the time-mean flow rate (Q(av)) is reported for the first time. The time-mean flow rates obtained from the present study are compared with their experimental values of the transport of seminal fluid through the rhesus monkey reproductive track and the ductus efferentes of the male reproductive tract, respectively. It is observed that the theoretical values of time-mean flow rates for seminal fluid (Herschel-Bulkley fluid) have been found to be in good agreement with the experimental results. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Brinkman flows   cross-diffusion   finite volume method   kinetic theory   Schauder fixed-point theory  

摘要： In this paper, we propose a new nonlinear model describing the dynamical interaction of two species within a viscous flow. The proposed model is a cross-diffusion system coupled with the Brinkman problem written in terms of velocity fluid, vorticity, and pressure and describing the flow patterns driven by an external source depending on the distribution of species. In the first part, we derive macroscopic models from the kinetic-fluid equations by using the micro-macro decomposition method. On the basis of the Schauder fixed-point theory, we prove the existence of weak solutions for the derived model in the second part. The last part is devoted to developing a one-dimensional finite volume approximation for the kinetic-fluid model, which is uniformly stable along the transition from kinetic to macroscopic regimes. Our computation method is validated with various numerical tests.

关键词： 高中数学   数学分析   意义   思想  

摘要： 高中阶段的数学有着很强的逻辑性和严谨性,在学习的过程中渗透数学分析的思想对拓展我们的思维方式、丰富我们的学习方式有着很大的帮助。作为一名高中生,在高中数学的学习过程中也曾遭遇过瓶颈期,随后,我就对一些数学分析思想进行研究,再研究的过程中我发现,在这些思想方式的帮助下解题过程更加的高效,自身的数学能力也得到了一定的提升。

关键词： 中成药   毒性   乌头碱   合理用药   数学分析   处方点评  

摘要： 目的对含乌头碱中成药理论中毒风险进行数学分析。方法以2015版《中国药典》含乌头碱中成药的限量检查信息为基础,结合乌头碱一般中毒量和致死量下限,定义在用药剂量D时,含乌头碱中成药的理论中毒风险系数(TR)和理论致死风险系数(LR),并计算按说明书足量用药、超量用药、两两足量联用、两两减量联用等不同情形下的风险系数,分析规律。同时通过文献案例数据予以佐证,最后提出临床用药和处方点评的原则。结果得到61个含乌头碱中成药品种的乌头碱理论最高含有量。除去2个特殊品种,按说明书足量用药时,处于安全剂量范围(TR≤1)的品种有29个;处于理论中毒剂量范围(TR> 1且LR≤1)的品种有30个。超说明书50%或100%用量用药时,理论中毒风险系数大幅上升,并出现理论致死风险。含乌头碱中成药两两足量联用时,处于安全剂量范围的情形只占7. 1%,但均减量50%后这一比例增加为35. 6%。同时,13例临床真实药害案例信息也在一定程度上佐证了数学分析的有效性。结论该理论中毒风险系数能够对不同用药情形下含乌头碱中成药的安全性进行量化评价与预警,界定了严禁超剂量用药和足量联用的高风险品种范围。

关键词： 级数求和   无穷级数   应用   数学分析   数值计算   近似计算   积分计算   求极限  

摘要： 无穷级数是数学分析中的一个重要内容,它是表示函数、研究其性质以及进行数值计算的一种工具。作为一种研究数学的工具和思想,无穷级数的诞生推进了世界数学的发展,而级数求和则是研究级数的主要方向。所以如何将无穷级数求和应用到实际问题中就成了非常有意义的事情,本文试图通过具体问题的例举来说明无穷级数求和在实际问题中的应用,如在近似计算中的应用、在求极限中的应用、在积分计算中的应用、在经济中的应用等等。