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关键词： Existence   Special solutions   Caputo   Basic reproduction number   Numerical simulations  

摘要： In connection with issues pertinent with humans’ health, it is highly significant to comprehend the complex dynamics of the related infectious disease since the non-Markovian effects play a vital role in its spread. This research analysis investigates an epidemiological model related with diarrhea transmission dynamics that occurred in Ghana during 2008–2018. The real data of 11 years have been obtained from Ministry of Health-Ghana and used to validate the proposed model. The epidemiological model is designed for the very first time with newly devised fractal fractional Caputo type operator having the fractional order α and the fractal dimension τ. The working parameters of the model are estimated and fitted with the real data using nonlinear least-squares fitting method and the basic reproduction number is found to be R0≈2.09665. Existence and uniqueness of the special solution of the proposed model are investigated. The disease free and the endemic equilibria are also computed. Finally, numerical simulations of the model are carried out via proposed numerical method and results in the graphical illustrations based upon effects of the estimated and fitted parameters show that the disease can either be substantially controlled or eradicated if the transmission rate of the epidemic is reduced and the rate of treatment is increased.

关键词： Prostate cancer   computational oncology   phase field   semilinear parabolic equations   well posedness   isogeometric analysis  

摘要： Chemotherapy is a common treatment for advanced prostate cancer. The standard approach relies on cytotoxic drugs, which aim at inhibiting proliferation and promoting cell death. Advanced prostatic tumors are known to rely on angiogenesis, i.e. the growth of local microvasculature via chemical signaling produced by the tumor. Thus, several clinical studies have been investigating antiangiogenic therapy for advanced prostate cancer, either as monotherapy or in combination with standard cytotoxic protocols. However, the complex genetic alterations that originate and sustain prostate cancer growth complicate the selection of the best chemotherapeutic approach for each patient's tumor. Here, we present a mathematical model of prostate cancer growth and chemotherapy that may enable physicians to test and design personalized chemotherapeutic protocols in silico. We use the phase-field method to describe tumor growth, which we assume to be driven by a generic nutrient following reaction-diffusion dynamics. Tumor proliferation and apoptosis (i.e. programmed cell death) can be parameterized with experimentally-determined values. Cytotoxic chemotherapy is included as a term downregulating tumor net proliferation, while antiangiogenic therapy is modeled as a reduction in intratumoral nutrient supply. An additional equation couples the tumor phase field with the production of prostate-specific antigen, which is a prostate cancer biomarker that is extensively used in the clinical management of the disease. We prove the well posedness of our model and we run a series of representative simulations leveraging an isogeometric method to explore untreated tumor growth as well as the effects of cytotoxic chemotherapy and antiangiogenic therapy, both alone and combined. Our simulations show that our model captures the growth morphologies of prostate cancer as well as common outcomes of cytotoxic and antiangiogenic mono therapy and combined therapy. Additionally, our model also reproduces

关键词： 数学分析思想   高中数学   解题   应用  

摘要： 在各类基础学科中,作为一门源于实际生活需要又超越直接使用界限的学科——数学,在人类知识体系中有着举足轻重的地位,它既具有基础性又具有工具性,还是提升、发展这些学科的动力。近年来,随着信息技术的发展,数学与其他学科的深入交流,人们越来越发觉数学学科在各个方面的重要作用。文章以高中视角,就数学分析思想在高中数学解题中的应用谈谈个人的一些看法。

关键词： 数学教育专业   数学分析   教学策略   思考  

摘要： 专业基础课程的学习是培养教师专业知识发展的重要途径."数学分析"是数学类专业最重要的基础课程之一,是联系初等数学与现代数学的纽带,是后续课程学习的基础.接触大学数学专业的教师和学生都了解"数学分析"的重要性."数学分析"作为数学专业的专业基础课为后续的数学专业课程开展提供了基础。我们所学习的很多数学规律以及数学思想方法都是以"数学分析"作为依据的,是学生接触数学,提升数学学习兴趣的重要引导课程。目前,很多学生在初次接触"数学分析"课程的过程中都难以理解。教师必须坚持科学发展观对学生进行教育,将教学注意力放置于过程和兴趣引导方面,而不是局限于学习成绩中。本文主要就"数学分析"课程教学进行具体探究,期望对提升高职学生"数学分析"课程教学效率有所帮助。

关键词： 数学分析课程   中学数学   重要性   应用策略  

摘要： 文章在探讨数学分析课程与中学数学的联系、数学分析课程在中学数学中应用的重要性、数学分析对中学数学的指导作用及数学分析课程在中学数学中存在的问题的基础上,提出了数学分析课程在中学数学中的具体应用,旨在为相关教育工作者提供参考和借鉴。

关键词： “无穷事物”   定量认知   无穷悖论综合症   潜无穷—实无穷   新无穷理论体系   “无穷载体”理论   “半阿基米德性”   第四代数学分析和第二代无穷集合论  

摘要： 从最原始的基础入手,研究证明了无法科学定义、互相矛盾的“潜无穷—实无穷”概念是现有经典无穷理论体系的基础,以经典无穷理论体系为基础的现有经典数学分析和集合论自古以来都存在完全相同的三个基础理论缺陷,人们只能在缺乏科学基础理论的状态下摸索前进.虽然现有经典数学分析和集合论解决了许多实际的“无穷事物”定量认知问题,但也产生了许多性质完全相同的、专门暴露相同基础理论致命缺陷的各种悬而未决的悖论家族“.抽象事物—抽象事物的载体”为基础的新无穷理论体系和系统性的“无穷载体理论”的构建,为我们开辟了一条解决现有经典集合论和数学分析基础理论中的三个缺陷及其相关悖论的新思路,决定了第四代数学分析和第二代无穷集合论的产生.

ISBN: (纸本)9787030648310

关键词： 数学分析   狄里克莱函数   反例   构造技巧  

摘要： 数学分析是大学数学类专业的重要基础课,利用狄里克莱函数构造合适的反例在数学分析的教学中起有至关重要的作用,能很好地辅助数学分析这门课程的教学.本文利用狄里克莱函数针对数学分析中不同的问题分别给出了反例的构造技巧.

关键词： 数学分析   复习课   探究式教学   二重积分  

摘要： 一堂数学分析复习课的一道例题探究式教学实践。基于实践过程开展教学反思,认识到教学效率不高,教学质量欠佳等不足。结合教学实践与教学反思,提出若干策略以优化探究式教学的过程,提高探究式教学的效率,改善探究式教学的质量。

关键词： 激光测距   激光器   脉冲恒流源   大电流  

摘要： 激光器技术是激光测距系统中的关键技术。高性能测距应用中对激光器的要求主要包括峰值功率高,稳定性好。为了实现远距离激光测距,设计了一种大电流、高稳定脉冲激光器驱动电路。建立了该电路的数学模型,使用Matlab仿真软件,分析了各关键参数对脉冲恒流源的影响。仿真结果显示了开环运放的压摆率,后级电路时间常数以及电路噪声对输出电流平均值,上升时间,稳定度的影响。最后测试结果表明,该电路模块能产生20 A的脉冲电流,稳定度约99%,能够驱动脉冲激光器正常工作,达到测距系统要求。