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关键词： 数学分析   高等代数   解法融合  

摘要： 数学分析、高等代数两门课程的理论和思想有着很大的不同,但两者之间又有着密切的联系。本文通过典型的例题,结合不同的解题思想,探究数学分析和高等代数有关问题及解法的相互融合和渗透。

关键词： 对分课堂   数学分析   差距分析  

摘要： 本文介绍了学生在学习过程中,从学习起点到目标的差距类型。以数列极限的内容为例,探讨了对分课堂在《数学分析》课程中跨越各类差距的策略。

关键词： Blocking probability   Cognitive radio   Game theory   Queuing theory   Resource allocation  

摘要： A novel mathematical analysis comprising a hybrid combination of queuing and game theories to reduce the blocking probability for cognitive radio systems is presented in this work. This combination also considers modulation and adaptive coding schemes that determine which resources are designated to each user involved in the queue. The proposed mathematical model shows convergence to the performed simulations. The results show that the blocking probability of the primary and secondary users is considerably reduced with the proposed strategies when compared to a conventional system, meaning without the use of any specific strategy. The blocking probability for the different tested scenarios reduces by a factor of 10 or above, if the maximum available resources are considered. As a consequence, this improves the system performance by using as many assets as possible without interference among users in the assigned spectrum. The results show that for a cognitive system, the strategies proposed in this work improve general performance and decrease blocking probability.

ISBN: (纸本)9787030669032

关键词： Corona virus   Stability analysis   Real data   Control theory   Numerical simulations  

摘要： Number of well-known contagious diseases exist around the world that mainly include HIV, Hepatitis B, influenzas etc., among these, a recently contested coronavirus (COVID-19) is a serious class of such transmissible syndromes. Abundant scientific evidence the wild animals are believed to be the primary hosts of the virus. Majority of such cases are considered to be human-to-human transmission, while a few are due to wild animals-to-human transmission and substantial burdens on healthcare system following this spread. To understand the dynamical behavior such diseases, we fitted a susceptible-infectious-quarantined model for human cases with constant proportions. We proposed a model that provide better constraints on understanding the climaxes of such unseen disastrous spread, relevant consequences, and suggesting future imperative strategies need to be adopted. The main features of the work include the positivity, boundedness, existence and uniqueness of solution of the model. The conditions were derived under which the COVID-19 may extinct or persist in the population. Sensitivity and estimation of those important parameters have been carried out that plays key role in the transmission mechanism. To optimize the spread of such disease, we present a control problem for further analysis using two control measures. The necessary conditions have been derived using the Pontryagin's maximum principle. Parameter values have been estimated from the real data and experimental numerical simulations are presented for comparison as well as verification of theoretical results. The obtained numerical results also present the verification, accuracy, validation, and robustness of the proposed scheme. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Kuramoto   Synchronization   Bidirectionally coupled oscillators   Non all-to-all interaction  

摘要： This article is concerned about the synchronization problem of the bidirectionally coupled Kuramoto model. In this model, each oscillator only interacts with the oscillators with adjacent labeling numbers. Namely, the oscillator theta(i) only interacts with theta(i+1) and theta(i-1). In real applications, this is a typical setting of concatenation connection. We first prove the global convergence of frequency synchronization for the identical oscillators. Also, we present two results of phase synchronization for the identical case in relatively wide initial configuration regimes. In the case that the coupling strength is sufficiently large (equivalent to the difference of the natural frequencies is sufficiently small), we show that for non-identical oscillators within a suitable initial configuration regime, the bidirectionally coupled Kuramoto model achieves a frequency synchronization. The supportive numerical simulations are presented as well. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Nonlinear system   Existence of solutions   Tumor growth   Acid-mediated tumor invasion   Chemotherapy  

摘要： We present a new mathematical model for acid-mediated tumor invasion encompassing chemotherapy treatment. The model consists of a mixed ODE-PDE system with four differential equations, describing the spatio-temporal dynamics of normal cells, tumor cells, lactic acid concentration, and chemotherapy drug concentration. The model assumes non-local diffusion coefficients for tumor cells. We provide an analysis on the existence and uniqueness of model solutions. We also provide numerical simulations illustrating the model behavior, showing the invasion and the treatment phases, and comparing the model solutions with the case of constant diffusion coefficients instead of the non-local terms.

关键词： Thermal stratification   Hyperbolic-tangent liquid   Hydromagnetic flow   Heat generation   Radiation aspect   Heat sink or source  

摘要： In current communication, we opted four constant (hyperbolic-tangent) liquid model highlighting shear thinning attributes. Consideration of this model together with MHD (magneto-hydrodynamic) is of prodigious importance owing to diverse industrial utilizations. Besides, MHD has several usages in heat exchangers fabrication, space vehicle strength, thermal fortification, polymer technology, power generators, petroleum industry, crude oil purification and fluid dews sprigs. Such implications motivated us to endeavor further towards hydromagnetic characteristics under convective and stratified constraints. Heat sink or source and radiation aspects elaborate heat transportation mechanism. Non-linear PDEs are transfigured to ODEs via implementation of transformation procedure. Homotopy method is chosen for simulations. Attributes of dimensionless factors are highlighted through graphs. We found lower velocity subject to higher Hartman number estimations.

关键词： 数学分析   教学改革   探索与实践  

摘要： 结合数学分析课程特点,对金融数学专业数学分析课程进行教学改革,对于激发学生的学习兴趣,提高教学效率,从而提高数学分析的教学质量具有重要的意义。