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关键词： 概念教学   等比数列   自然   函数知识   基础知识   数学分析   新旧知识   关联比  

摘要： “数列的概念与简单的表示法”是“数列”一章的开篇课,在教材中占据着重要位置,它既是函数知识的延续,又是等差、等比数列学习的基础,更是大学数学分析学习的重要基础知识之一.这一节内容小概念较多,与函数知识关联比较密切.如何让新知自然出台？如何让新旧知识自然关联？

关键词： 翻转课堂   《数学分析》课程   教学方式  

摘要： 利用"翻转课堂"教学模式,从教学视频的制作、教学内容的设计、翻转课堂的开展等方面对《数学分析》课程教学模式进行了探讨。旨在转变教师的教学方式,培养学生的自主学习能力、研究能力和创造性思维能力,为学生的可持续发展打下基础。

关键词： 数学分析   习题课   问题驱动的教学方法  

摘要： 数学分析习题课是教学过程中必不可少的一个重要环节,本文从逻辑性教学、指导性教学、问题驱动的教学三个方面讨论了数学分析习题课教学中应注意的一些问题,对数学分析习题课的教学方法进行了有益的探索。

关键词： cardiac anatomy/pathological anatomy   CHD/univentricular heart   circulatory hemodynamics   Fontan  

摘要： The first stage of surgical treatment for hypoplastic left heart syndrome (HLHS) includes the creation of artificial systemic-to-pulmonary connections to provide pulmonary blood flow. The modified Blalock-Taussig (mBT) shunt has been the technique of choice for this procedure;however, a right ventricle-pulmonary artery (RV-PA) shunt has been introduced into clinical practice with encouraging but still conflicting outcomes when compared with the mBT shunt. The aim of this study is to explore mathematical modeling as a tool for describing physical profiles that could assist the surgical team in predicting complications related to stenosis and malfunction of grafts in an attempt to find correlations with clinical outcomes from clinical studies that compared both surgical techniques and to assist the anesthesiologist in making decisions to manage patients with this complex cardiac anatomy. Mathematical modeling to display the physical characteristics of the chosen surgical shunt is a valuable tool to predict flow patterns, shear stress, and rate distribution as well as energetic performance at the graft level and relative to ventricular efficiency. Such predictions will enable the surgical team to refine the technique so that hemodynamic complications be anticipated and prevented, and are also important for perioperative management by the anesthesia team.

关键词： Vector-borne model   Fractional derivative   Global stability   Parameter estimation  

摘要： In the last few years, fractional order derivatives have been used in epidemiology to capture the memory phenomena. However, these models do not have proper biological justification in most of the cases and lack a derivation from a stochastic process. In this present manuscript, using theory of a stochastic process, we derived a general time dependent single strain vector borne disease model. It is shown that under certain choice of time dependent transmission kernel this model can be converted into the classical integer order system. When the time-dependent transmission follows a power law form, we showed that the model converted into a vector borne disease model with fractional order transmission. We explicitly derived the disease-free and endemic equilibrium of this new fractional order vector borne disease model. Using mathematical properties of nonlinear Volterra type integral equation it is shown that the unique disease-free state is globally asymptotically stable under certain condition. We define a threshold quantity which is epidemiologically known as the basic reproduction number (R-0). It is shown that if R-0 > 1, then the derived fractional order model has a unique endemic equilibrium. We analytically derived the condition for the local stability of the endemic equilibrium. To test the model capability to capture real epidemic, we calibrated our newly proposed model to weekly dengue incidence data of San Juan, Puerto Rico for the time period 30th April 1994 to 23rd April 1995. We estimated several parameters, including the order of the fractional derivative of the proposed model using aforesaid data. It is shown that our proposed fractional order model can nicely capture real epidemic. (C) 2017 Elsevier Inc. All rights reserved.

关键词： rate equations   Circles   PH   Solutions   approximate analysis   Ordinary differential equation   Kinetics   RATE CONSTANT   ANALYTICAL SOLUTION   mathematical analysis   Azo Compounds  

摘要： ORAC (oxygen radical absorbance capacity), a method widely used for measuring the total antioxidant capacity of biological samples, can also be used for the determination of the relative reactivity of an antioxidant compound (XH) by examining the dependence of the rate of consumption of the probe (PH) on the concentration of XH;initial conditions are chosen in such a way that the rate of consumption of the starting reactants may be assumed to follow a drastically simplified kinetic scheme, and the steady-state approximation for the concentration of the azo compound peroxyl (ROO circle) radical is invoked to simplify the analysis. Here we first attempted to find an analytical solution to the coupled first-order ordinary differential equations (ODEs) of the minimal ORAC kinetic system, applying Lie symmetry group theory without any precondition. However, the Lie symmetry transformations applied to the Chini equation, which appeared after mathematical transformations, showed that the form of the coefficients of the Chini equation precluded the analytical solution of the minimal ORAC kinetic system through symmetry reduction. Consequently, an approximate analytical solution was sought, valid for the case when the bimolecular rate constant of XH with ROO circle i.e., kx) was much larger than that of PH with ROO circle (i.e., kp).Using numerical solutions of the original set of ODEs of the ORAC kinetic system, the quality of the approximate solution was inspected under conditions that correspond to those employed in several ORAC methods together with a low initial concentration of the azo compound radical initiator. The simulations allowed us to conclude that the approximate analytical solution of the ODEs of the minimal ORAC kinetic system was not entirely devoid of academic interest, but its applicability was restricted to conditions where both k(x) >> k(p) and the initial concentration of XH was higher than that of PH. (C) 2017 Wiley Periodicals, Inc.

关键词： Electric vehicle (EV)   EV supporting infrastructure   Multiple routes   Multiple stops  

摘要： As environmental issues become more prominent, electric vehicles (EV) have attracted an increasing amount of attention. However, the continuous cruising distance of an EV is limited to approximately 160 km, which is insufficient for everyday use. Battery capacity is the limiting factor in long-distance EV travel, because the vehicles need to stop at EV recharging stations multiple times. In Japan, there are more than 2,000 EV charge stations, but there are, at most, two rapid chargers. When multiple users converge at the station, a queuing (or waiting) condition is created, which may lead to a call-loss condition. In other words, an appropriate number of chargers must be installed at each station when planning the EV infrastructure. Therefore, the number of vehicles entering the station must be estimated. In this study, a mathematical model based on the supporting infrastructure for widespread EV use is proposed to estimate the number of vehicles arriving at each charge station.

关键词： upper bound method   finite element   streamlined dies   extrusion process   ANSYS software  

摘要： In the present investigation, an analysis using three-dimensional upper-bound method based on continuous velocity filed has been carried out for the extrusion of circular, square, and rhomboidal sections from round billets. The die surface representation in the present work could easily be applied to the extrusion of many different shapes just by defining the functions that describe the entry and exit sections and putting them into the general formulation. The die profile was tested for the third-and fifth-order polynomial functions. The extrusion process is also simulated using the finite element code, ANSYS (V 14.0), in order to assist the mathematical solution and to show the stress and strain distributions for the products when the strain hardening effect is taking into the account. Effects of friction, shape complexity, reduction of area, and die length on the extrusion pressure were also investigated. The results obtained in this work were compared with the theoretical results of other workers and found to be in highly compatible.

关键词： Cancer imaging   Cancer models  

摘要： Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm(3) to 62 mm(3), even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.