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关键词： 数学分析   考试改革   阶段考试  

摘要： 分析了《数学分析》课程的特点与传统考核机制的弊端,阐述了进行考试改革的必要性.以实施阶段化考试为改革思路,提出了一套以督促教与学为目的,评价结果更为全面、客观、科学的考试方法与具体实施方案,并通过试点实例分析,证明了考试改革方案的可行性与有效性.

关键词： 数学分析   分层辅导   教学改革  

摘要： 数学分析是现代数学的重要分支之一,在物理、金融、工程等领域都有广泛的应用。本文分析了目前我校在数学分析教学中存在的问题,基于以生为本和因材施教的原则,探讨了分层辅导在该门课程的具体实施方法,从而得出分层辅导是数学分析课堂教学的重要补充。

关键词： 理想化思维   新冠疫情研究   传染病预测   数学分析   防控策略  

摘要： 作为近年来影响最大的突发公共卫生事件,新冠疫情的后续走势备受国人乃至世界人民的关注。在理想状态下,感染数量受且仅受感染力、死亡力和治愈力的作用,将三力合成并进行回归分析之后,可以得出国内疫情的第一个阶段性节点:3月4日前后将明显感受到胜利的曙光。将回归函数进行不定积分之后,可以得出疫情的第二个阶段性节点:3月29日疫情将得到全面而有效的控制。将回归函数进行二次不定积分之后,可以得出疫情的终点:4月23日前后基本结束。除了后续预测外,还根据模型的影响因子提出了应对传染病普遍适用的措施和建议。由于这些措施和建议现在都已逐步成为现实,我们有理由对打赢新冠疫情战役充满信心。

关键词： 中学数学   函数概念   近代数学   解析几何   数学分析   起源和发展  

摘要： 函数是中学数学中的一个十分重要的概念,是数学分析研究的主要对象.可以说,"函数概念是近代数学思想之花".中学数学可以说是以函数为中心的一门科学.那么,函数概念是怎样起源和发展呢?1函数概念的产生在历史上,函数概念的出现与解析几何的产生有着密切的关系.

关键词： 医疗机器人   服务机器人   康复机器人   计算机视觉   手术机器人   机械学   生物力学   数学分析  

摘要： 医疗机器人是指用于医院、诊所的医疗或辅助医疗的机器人,是一种智能型服务机器人,它能独自编写操作计划,依据实际情况确定动作程序,然后把动作变为操作机构的运动。医疗机器人主要涉及医学、生物力学、机械学、材料学、计算机视觉、数学分析等诸多学科,主要用于伤病员的手术、救援、转运和康复,分为手术机器人、康复机器人、辅助机器人、服务机器人四大类。

关键词： 矿物加工   矿产资源   数学建模   新兴交叉学科   数学分析   数学模型   制造成本   输入和输出  

摘要： 矿物加工作为矿产资源生产过程中重要的生产环节,在国民经济发展中有着重要作用。传统矿物加工很多都依靠工程师的经验来解决设计和生产过程中的问题,往往容易走弯路,造成不必要投入。在工业技术领域使用数学模型研究对象输入和输出的关系,探索工业技术的客观规律,通过数学分析得到最佳生产效率和最低制造成本,已经成为一种新兴交叉学科研究领域。

关键词： Convection   Convective parameterization  

摘要： Arakawa and Schubert proposed convective quasi equilibrium as a guiding principle for the closure of convection parameterization. However, empirical experiences from operational implementation efforts suggest that its strict application does not work well. The purpose of the present paper is to explain mathematically why this closure does not work in practice, and to suggest that problems stem from physically unrealistic assumptions. For this purpose, the closure hypothesis is examined in its original form, and without imposing a condition of a positiveness to the convective mass fluxes. The Jordan sounding with idealized large-scale forcing is used for diagnosis purposes. The question is addressed from several perspectives including the completeness of the entraining-plume spectrum, and a singular vector decomposition of the interaction kernel matrix. The main problems with the quasi-equilibrium closure are traced to (i) the relatively slow response of shallower convective modes to large-scale forcing and (ii) detrainment at convection top producing strong cooling and moistening. A strict application of the convective quasi-equilibrium principle leads to a singular response of shallow convection. An explicit coupling of convection with stratiform clouds would be crucial for preventing this unrealistic behavior, recognizing that the reevaporation of detrained cloudy air is a relatively slow process.

关键词： quantum random number generation   lasers   single-photon detection   probability  

摘要： A quantum random number generation method based on measuring the time differences between photon detections is analyzed mathematically in terms of bit generation efficiency and bit generation rate. It was found that these two values cannot be maximized simultaneously by altering the incident photon rate of a light source with Poisson statistics, but the generation rate can be increased at the expense of efficiency. Analytical results are presented for both an idealized and a practical case. The detector's dead time has been taken into consideration in the latter case, implying that, for certain combinations of the dead time and the measurement clock period, the generation rate becomes a two-peaked function of the incident photon rate. The theoretical results are confirmed by simulations, showing excellent agreement between the two. (C) 2020 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： Anopheles mosquito   Basic offspring number   Fluctuation method   Global Stability   Nonstandard method   Spatial heterogeneity  

摘要： We propose a novel model for the population dynamics of mosquitoes by considering the dispersal states of female mosquitoes of oviposition's cycle and spatial variations. From the modeling perspective, a general functional form of eggs oviposition rate is used including the Malthusian, the Verhlust-Pearl logistic, the Hassell, and the Maynard-Smith-Slatkin functions. From the theoretical and numerical perspectives, the study is done in two steps using the more realistic birth Maynard-Smith-Slatkin function. First, we consider an ordinary differential equations model and show that the mosquito-free equilibrium (MFE) is globally asymptotically stable, whenever the basic offspring number R-0(ode) is less than unity. Using a fluctuation argument, we prove that the unique mosquito-persistent equilibrium (MPE) is globally attractive, whenever R-0(ode) exceeds the unity. Moreover, the temporal model undergoes a Hopf bifurcation in the absence of density-dependentmortality in the aquatic stage ofmosquitoes. Second, the temporal model is extended into an advection-reaction-diffusion model in order to account for the movement of mosquitoes and their spatial source of heterogeneity. We establish the uniform persistence and the existence of at least one positive steady state whenever the spatial basic offspring number R-0(pde) is greater than unity. Finally, for the case study of malaria vector agent (Anopheles mosquito), we construct a nonstandard finite difference scheme that is dynamically consistent with the features of the continuousmodel to illustrate our results, including the spatial heterogeneity of mosquito resources.

关键词： Hill equation   hysteresis   maraging steel   minor loops   Rayleigh model  

摘要： Minor loops of solubilized and aged samples of maraging-400 steel were measured and mathematically analyzed. The descending and ascending parts of the hysteresis curves obtained for this soft ferromagnetic material were fit with polynomials of varying degree. The fits were successful and the obtained polynomial coefficients revealed that a symmetry operation (S2) transforms the ascending part into the descending part (or vice versa). Based on the particular mathematical relation between the polynomials, an analytical expression for the minor loop area was obtained as a function of the specific maximum applied field. The curves of the minor loop area versus the maximum applied field for every aged sample were shown to be typical for a cumulative distribution function (CDF). The experimental curves were fit using the complementary function of the Hill equation. The fit Hill parameters revealed a systematic dependence on the sample aging conditions.