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关键词： 数学分析   现代数学   教学改革   立体教学  

摘要： 数学分析课程作为现代数学的重要分支,是数学专业的一门重要基础课.该文对数学分析课程的教学实践进行了研究,为数学专业基础课程的教学改革提供一些思考和建议.特别探讨了数学绘图软件对认识数学、探索数学的作用;通过数学软件,可让学生感受到数学的魅力与风韵.

关键词： 数学分析   数学核心素养   抽象   直观  

摘要： 本文通过探讨数学分析课程中抽象与直观的联系,旨为培养和提高高校数学专业学生的数学核心素养提供策略和思路.

关键词： 聋哑学生   特殊教育   数学  

摘要： 聋哑儿童社会适应能力和逻辑思维能力差,感性知识贫乏,学习时注意力不易集中,贪玩、稳定性差,思维不连贯,抽象概括能力差。因此,要使聋哑学生学好数学知识,是有一定困难的。那么,在新课程理念下怎样对他们实施课堂教学,以提高课堂教学效率呢?下面谈谈本人在数学课堂教学中的一些做法。

关键词： 数学  

ISBN: (数字)9787030585998 ISBN: (纸本)9787030585998

摘要： 《工科数学分析教程(上册)}是一本信息化研究型教材本书包括数列极限、函数极限与连续、导数的计算与应用、泰勒公式、不定积分、定积分的应用、广义积分、数项级数.本书体系内容由浅入深，符舍学生认知规律.每章都有提高课，内容包括混沌现象与极限、连续函数不动点定理以及应用、极值问题与数学建模、泰勒公式与科学计算、积分算子的磨光性质以及应用等系列内容，初步为学生打开现代数学的窗口.同时每章都设置了系列探索类问题，包括理论问题、应用问题，培养学生应用数学解决实际问题的能力.本教材有与之配套的MOOC 课程，充分利用多媒体信息技术，将复杂数学问题直观化，图文并茂视频课为读者营造一对一的视频授课环境，通过扫描教材中的二维码进入视频课的学习，使得学生对数学问题的理解更通透.

关键词： Out-of-sample extension   dimensionality reduction   reproducing kernel Hilbert space   Nystrom approximation  

摘要： Let X = X boolean OR Z be a data set in R-D, where X is the training set and Z is the test one. Many unsupervised learning algorithms based on kernel methods have been developed to provide dimensionality reduction (DR) embedding for a given training set Phi: X -> R-d (d << D) that maps the high-dimensional data X to its low-dimensional feature representation Y = Phi(X). However, these algorithms do not straightforwardly produce DR of the test set Z. An out-of-sample extension method provides DR of Z using an extension of the existent embedding Phi, instead of re-computing the DR embedding for the whole set X. Among various out-of-sample DR extension methods, those based on Nystrom approximation are very attractive. Many papers have developed such out-of-extension algorithms and shown their validity by numerical experiments. However, the mathematical theory for the DR extension still need further consideration. Utilizing the reproducing kernel Hilbert space (RKHS) theory, this paper develops a preliminary mathematical analysis on the out-of-sample DR extension operators. It treats an out-of-sample DR extension operator as an extension of the identity on the RKHS defined on X. Then the Nystrom-type DR extension turns out to be an orthogonal projection. In the paper, we also present the conditions for the exact DR extension and give the estimate for the error of the extension.

关键词： Caputo system   Lu -Chen system   Haar wavelet scheme   chaotic multiscroll attractor   convergence  

摘要： Strange attractors are fascinating not only for the fractal structure most of them display, but also for the freakish chaotic and multiscroll trajectories they portray. In this paper, Haar wavelet numerical method is used to address the solvability of the 3D Lu-Chen model combined with the classical Caputo fractional differentiation. The full model, named Caputo-Lu-Chen model is solved analytically and a complete error analysis is performed to test the convergence of the method. It reveals that the error made using such a technique is negligible. Numerical simulations, performed in pure fractional and standard integer cases, show that the Caputo-Lu-Chen system maintains its status of strange, chaotic and multiscroll attractor. The graphics in both cases present similar features characterized by attractors with many scrolls. Hence, the Caputo derivative order when introduced as parameter in the Lu-Chen system does not remove the multiscroll property of generated attractors;it even becomes an important control parameter able to change the dynamics of the whole system. This result can be very important in control theory.

关键词： essential fructosuria   fructose metabolism   mathematical modeling  

摘要： Fructose is a major component of Western diets and is implicated in the pathogenesis of obesity and type 2 diabetes. In response to an oral challenge, the majority of fructose is cleared during "first-pass" liver metabolism, primarily via phosphorylation by ketohexokinase (KHK). A rare benign genetic deficiency in KHK, called essential fructosuria (EF), leads to altered fructose metabolism. The only reported symptom of EF is the appearance of fructose in the urine following either oral or intravenous fructose administration. Here we develop and use a mathematical model to investigate the adaptations to altered fructose metabolism in people with EF. First, the model is calibrated to fit available data in normal healthy subjects. Then, to mathematically represent EF subjects, we systematically implement metabolic adaptations such that model simulations match available data for this phenotype. We hypothesize that these modifications represent the major metabolic adaptations present in these subjects. This modeling approach suggests that several other aspects of fructose metabolism, beyond hepatic KHK deficiency, are altered and contribute to the etiology of this benign condition. Specifically, we predict that fructose absorption into the portal vein is altered, peripheral metabolism is slowed, renal reabsorption of fructose is mostly ablated, and alternate pathways for hepatic metabolism of fructose are upregulated. Moreover, these findings have implications for drug discovery and development, suggesting that the therapeutic targeting of fructose metabolism could lead to unexpected metabolic adaptations, potentially due to a physiological response to high-fructose conditions.

关键词： elementary flux modes   signalling   flux sampling   modelling  

摘要： The muscarinic M-2 receptor is a prominent member of the GPCR family and strongly involved in heart diseases. Recently published experimental work explored the cellular response to iperoxo-induced M-2 receptor stimulation in Chinese hamster ovary (CHO) cells. To better understand these responses, we modelled and analysed the muscarinic M-2 receptor-dependent signalling pathway combined with relevant secondary messenger molecules using mass action. In our literature-based joint signalling and secondary messenger model, all binding and phosphorylation events are explicitly taken into account in order to enable subsequent stoichiometric matrix analysis. We propose constraint flux sampling (CFS) as a method to characterize the expected shift of the steady state reaction flux distribution due to the known amount of cAMP production and PDE4 activation. CFS correctly predicts an experimentally observable influence on the cytoskeleton structure (marked by actin and tubulin) and in consequence a change of the optical density of cells. In a second step, we use CFS to simulate the effect of knock-out experiments within our biological system, and thus to rank the influence of individual molecules on the observed change of the optical cell density. In particular, we confirm the relevance of the protein RGS14, which is supported by current literature. A combination of CFS with Elementary Flux Mode analysis enabled us to determine the possible underlying mechanism. Our analysis suggests that mathematical tools developed for metabolic network analysis can also be applied to mixed secondary messenger and signalling models. This could be very helpful to perform model checking with little effort and to generate hypotheses for further research if parameters are not known.

关键词： Nonlinear absorbance   Beer's law deviation   Phthalocyanine   J-type dimer  

摘要： In this paper, we propose new approach to accurate calculation of the molar attenuation coefficient epsilon and the threshold concentration C-del, exceeding of which it results in a deviation from Beer's law. The method is based on the asymptotic approximation of the equality of integrals associated with the true values of C-del and e as well as their approximate values C-i and epsilon(i) within max. rapprochement: Delta C = min {C-i - C-del} and Delta epsilon = min {epsilon - epsilon(i)} when C-i -> C-del and epsilon(i) -> epsilon. After reaching the acceptable accuracy, the infinite iterative cycle is interrupted that allows to significantly saving the computing resources. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Zika virus   Basic reproduction number   Steady states   Stability analysis   Optimal control  

摘要： The Zika virus is transmitted to humans primarily through Aedes mosquitoes and through sexual contact. It is documented that the virus can be transmitted to newborn babies from their mothers. We consider a deterministic model for the transmission dynamics of the Zika virus infectious disease that spreads in, both humans and vectors, through horizontal and vertical transmission. The total populations of both humans and mosquitoes are assumed to be constant. Our models consist of a system of eight differential equations describing the human and vector populations during the different stages of the disease. We have included the hospitalization/isolation class in our model to see the effect of the controlling strategy. We determine the expression for the basic reproductive number R-0 in terms of horizontal as well as vertical disease transmission rates. An in-depth stability analysis of the model is performed, and it is consequently shown, that the model has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R-0 < 1. It is also shown that when R-0 > 1, there exists a unique endemic equilibrium. We showed that the endemic equilibrium point is globally asymptotically stable when it exists. We were able to prove this result in a reduced model. Furthermore, we conducted an uncertainty and sensitivity analysis to recognize the impact of crucial model parameters on R-0. The uncertainty analysis yields an estimated value of the basic reproductive number R-0 = 1.54. Assuming infection prevalence in the population under constant control, optimal control theory is used to devise an optimal hospitalization/isolation control strategy for the model. The impact of isolation on the number of infected individuals and the accumulated cost is assessed and compared with the constant control case.