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关键词： 课程思政   数学分析   BOPPPS教学模式  

摘要： 当代教育,其根本是立德树人,因此,要用好课堂教学这个主渠道。本文以知识点“曲率”为例,分析了如何在课程思政视角下,基于BOPPPS教学模式进行课程设计。最后,针对现有的教学问题提出相应的对策。

关键词： 课程思政   数学分析   教学方法  

摘要： 为了将思想政治教育理论知识、价值理念以及精神追求融入到数学分析课程中,坚持数学分析课程思政元素的融入是非常必要的。但由于数学分析课程自身的特点,导致课程思政的融入必须讲究方式方法及遵循一定的原则。本文结合自己在教学实践中的体会和数学分析课程特点,总结了课程思政在数学分析课程教学中的融入原则,包括内容与多元思政元素相结合,自然合理的融入方式,贴近学生的生活实践,教学设计与随机应变相结合,并且每个原则都配有相应的教学案例。

关键词： Capacitive pressure sensor   Touch mode   Touch point   Concave well substrate   Circular diaphragm  

摘要： Touch mode capacitive pressure sensor (TMCPS) is focused due to its advantages of good linearity, mechanical robust and large overload protection for harsh industrial environment. This paper proposes a concave well-shaped substrate bottom electrode for further improvement of capacitance response of TMCPS. Small deflection model is utilized for mathematical analysis of proposed design and ANSYS and MATLAB software are utilized for simulation. The simulation result is compared with analysis and the excellent agreements predict the accuracy of analytical modeling. The sensitivity of proposed TMCPS is increased as 1.36 times as in operating pressure range from 0.25 to 2 MPa and the linear region of it is expanded as 2.60 times as the normal (flat substrate) one in touch mode, respectively. The analysis and simulation results indicate a significant improvement of sensitivity and linearity in touch mode. The analytical modeling and overall results will be helpful to design TMCPS for performance improvement and predict the behavior of it.

关键词： Hypothalamic-pituitary-adrenal (HPA) axis   Ultradian rhythms   Mathematical model   Delayed differential equation  

摘要： The hypothalamic-pituitary-adrenal (HPA) axis is a biological system in the human body that plays an important role in controlling stress and regulating various physiological elements, including the immune system, emotions, and moods in tense situations. Over the past two decades, several ordinary or delay differential equations models of the HPA axis have been proposed. In the majority of studies presented so far, corticotropin-releasing hormone (CRH), adrenocorticotropic hormone (ACTH), and cortisol are among the main variables employed to build the HPA axis models. In the present study, based on a previously introduced hypothesis which asserts that ultradian rhythms in the HPA axis are produced by the pituitary-adrenal network alone and these rhythms can endure in the absence of CRH secretion, a simple two-dimensional delayed dynamical model of the HPA axis based on only ACTH and cortisol is introduced. The model is shown to be able to capture the ultradian (low frequency) rhythms of ACTH and cortisol released into the bloodstream. By mathematical analysis of the model using the Hopf bifurcation theorem, it is also demonstrated how oscillating solutions can emerge. Also, the model employs physiologically reasonable parameter values to exhibit how in the absence of CRH secretion, a simple model of the pituitary-adrenal interaction can be used to produce ultradian rhythms of both cortisol and ACTH hormones.

关键词： Chlamydia trachomatis (CT)   Gonorrhea   Codynamics   Stability   Optimal Control  

摘要： A model for Chlamydia trachomatis (CT) and Gonorrhea codynamics, with optimal control analysis is studied and analyzed to assess the impact of targetted treatment for each of the diseases on their co-infections in a population. Analysis of the gonorrhea-only sub-model shows the existence of a stable disease free equilibrium (DFE) and a stable endemic equilibrium (EE) when the associated reproduction number is less than one. In the absence of re-infection, the DFE of the gonorrhea-only sub-model is shown to be globally asymptotically stable when the respective reproduction number is below one. The endemic equilibrium of the gonorrhea-only submodel is also shown to be globally asymptotically stable when reproduction is greater than one. Applying the Centre Manifold Theory, the complete model is shown to undergo backward bifurcation when the associated reproduction number is less than unity. The optimality system for the co-infection model is established using the Pontryagin's Maximum Principle. Implementing male CT treatment and male gonorrhea treatment cause a reduction in the total number of females and males co-infected with CT and gonorrhea. Also, implementing male CT treatment and female gonorrhea treatment leads to a decrease in the total number of females and males co-infected with CT and gonorrhea. Moreover, implementing female CT treatment and male gonorrhea treatment averts the highest co-infected cases, in comparison with all the intervention strategies.

关键词： Small cells   mMIMO   Cell-free networks   MMSE   MRC   Spectral efficiency   Energy efficiency   BER   Cognitive radio  

摘要： One of the motivations towards the 5G cellular networks and beyond is the large increase in the supported data rate in both uplink and downlink. Deployment of small size cells, massive MIMO, wherein a large number of antennas are deployed at transmitters and receiver, are effective tools in these networks. Users under cell massive MIMO networks "mMIMO" can provide high data rate. However, the cell-edge user and users, under shadowing, can have a poor performance. Cell-Free networks can provide a satisfied data rate even for shadowed and cell-edge users. In this paper, cell-Free mMIMO networks are mathematically analyzed applying different cooperation mechanisms among the access points APs. Moreover, a new mathematical formula for the throughput, based on BER, is derived. Furthermore, closed formulas for the throughput-BER as well as energy efficiency (EE) performance are derived. Finally, the cognitive radio concept is proposed in order to limit the interference among users accessing the same resources in uplink. Simulation results show that the fully centralized cell-Free mMIMO network has a higher spectral efficiency and energy efficiency than the cellular mMIMO networks at different BER values especially when MMSE is applied. Furthermore, the cognitive radio theory can increase the SE and EE performance of the cell-Free networks when all cooperation mechanisms are applied.

关键词： HIV   Age-structured model   Spatial diffusion   HAART   Global stability   Permanence  

摘要： Compared with the existing HIV/AIDS host model that considers only age-since-infection or only spacial diffusion, we propose a new age-space structured model that incorporating both two infection ages, spacial diffusion, and HAART (highly active antiretroviral therapy) to analyze the global dynamics of HIV/AIDS epidemic and study the incident of its transmission among MSM (men who have sex with men) group. We first obtain the well-posedness and positivity of the solution for the model. The generation operator R is obtained by the process of renewal, followed by the basic reproduction number R-0. Then we prove that the disease-free equilibrium is globally asymptotically stable (g.a.s) when R-0 < 1, the space-independent steady state is g.a.s, and the disease will be present when R-0 > 1. Numerical simulations are conducted to reinforce these analytical results. Finally, numerical results show that key model parameters influence the value of R0 effectively, and indicate that the spatial factor plays a crucial role as a control measure and cannot be ignored during the intervention for HIV transmission among MSM group. Moreover, our work suggests that treatment adherence should be improved during the HAART for HIV infected individuals among MSM. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： 翻转课堂   大学数学   线性代数   应用策略  

摘要： 本文深入分析了翻转课堂教学模式在大学特别是地方大学数学课程教学中的利弊,提出了解决问题的方法和方法,并以线性代数教学为例给出了策略用于翻转教室的教学实践,以提升自身的教学能力。

摘要： 数学教师在对初中生开展课程教育过程中应该摒弃陈旧的授课思维,重视结合实际情况制定科学的教学方案,围绕实际情况开展多样化的知识讲解与学科能力的培养,有助于收获更高水准的课程教育质量。数学分析是初中生应该具备的一项学科能力,通过多种教学活动的开展提高班级学生的主体性,同时也能引导学生们结合生活实际对问题进行分析,利于强化初中生的分析能力。所以在后续课堂教学中应该立足多种教学活动的开展有效培养班级学生的数学分析能力。

关键词： Transmission-blocking antimalarial drug   Mathematical modeling   Data fitting   Treatment coverage   Drug efficacy   Bifurcation analysis   Numeral simulation  

摘要： Recently, promising clinical advances have been made in the development of antimalarial drugs that block the parasite transmission and also cures the disease and has prophylactic effects, called transmission-blocking drugs (TBDs). The aim of this paper is to develop and analyze a population level compartmental model of human-mosquito interactions that takes into account an intervention using TBDs. We do this by extending the SEIRS-SEI type model to include a class of humans who are undergoing the treatment with TBDs and a class of those who are protected because of successful treatment. Before we proceed with an analysis of the model's stability and bifurcation behaviours, we start by ensuring that the model is well-posed in a biologically feasible domain. Mathematical analysis indicates that the model exhibits a forward and backward bifurcation under certain conditions. Results from our analysis shows that the effect of treatment rate on reducing reproduction number depends on other key parameters such as the efficacy of the drug. The projections of the validated model show the benefits of using TBDs in malaria control in preventing new cases and reducing mortality. In particular, we find that treating 35% of the population of Sub-Saharan Africa with a 95% efficacious TBD from 2021 will result in approximately 82% reduction on the number of malaria deaths by 2035. (C) 2021 Elsevier Inc. All rights reserved.