基于Matlab的数学分析极限概念教学实践

极限概念是数学分析理论的基础,贯穿数学分析教学的始终,在数学分析的理论体系中占有十分重要的地位.由于极限概念的严谨性和抽象性,在教学实践当中发现学生对极限概念难以理解.本文借助Matlab软件的图形处理功能,将数列极限,一元函数极限以及多元函数极限的形成过程展示出来,从而强化学生对极限概念的理解.     

Multidimensional modeling of the stenosed carotid artery: A novel CAD approach accompanied by an extensive lumped model

This study describes a multidimensional 3D/lumped parameter(LP) model which contains appropriate inflow/outflow boundary conditions in order to model the entire human arterial trees. A new extensive LP model of the entire arterial network(48 arteries) was developed including the effect of vessel diameter tapering and the parameterization of resistance, conductor and inductor variables. A computer aided-design(CAD) algorithm was proposed to effciently handle the coupling of two or more 3D models with the LP model, and substantially lessen the coupling processing time. Realistic boundary conditions and Navier–Stokes equations in healthy and stenosed models of carotid artery bifurcation(CAB) were used to investigate the unsteady Newtonian blood flow velocity distribution in the internal carotid artery(ICA). The present simulation results agree well with previous experimental and numerical studies. The outcomes of a pure LP model and those of the coupled 3D healthy model were found to be nearly the same in both cases. Concerning the various analyzed 3D zones, the stenosis growth in the ICA was not found as a crucial factor in determining the absorbing boundary conditions.This paper demonstrates the advantages of coupling local and systemic models to comprehend physiological diseases of the cardiovascular system.     

A New 3D Digitizer by Cutting and Scanning Layer-by-layer

A crucial element in the reverse engineering process is to obtain 3D data of the part or its CAD model. A new method is presented in this paper, which combines layer-by-layer cutting and scanning on each cross-section of a part with a milling machine and an image scanner respectively. The method can capture the internal and external profile informations of a complex-shaped part at the same precision simultaneously. When data files of 2D edges are imported into the 3D CAD/CAM package, the 3D data or 3D CAD model is acquired. According to the customers' requirements, the system can reach the highest accuracy of 5.4 μm, and a resolution of 2.7 μm in obtaining the 2D edges. The product is completely made now, on which experiments are conducted, which demonstrate the higher accuracy and efficiency.     

Furanose C—C‐linked γ‐lactones: a combined ESI FTICR MS and semi‐empirical calculations study

Sugars that incorporate the unsaturated carbonyl motif have become important synthetic targets not only as a result of their potential biological properties but also as precursors in the synthesis of many bioactive products. Moreover, little is known about the influence of the γ‐lactone moiety in the fragmentation pattern of furanose rings. Therefore, two α,β‐unsaturated γ‐lactones (butenolides) and two β‐hydroxy γ‐lactones, C? C linked to a furanose ring were studied using electrospray ionization FTICR mass spectrometry. The behaviour of the protonated and sodiated forms of the compounds under study has been compared considering their structural features. Fragmentation mechanisms were established and ion structures were proposed taking into account the MS² and MS³ experiments, accurate mass measurements and semi‐empirical calculations. These inexpensive methods proved to be a valuable resource for proposing protonation sites and for the establishment of fragmentation pathways. Copyright © 2010 John Wiley & Sons, Ltd.     

Electron transfer dissociation versus collisionally activated dissociation of cationized biodegradable polyesters

Biodegradable polyesters were ionized by electrospray ionization and characterized by tandem mass spectrometry using collisionally activated dissociation (CAD) and electron transfer dissociation (ETD) as activation methods. The compounds studied include one homopolymer, polylactide and two copolymers, poly(ethylene adipate) and poly(butylene adipate). CAD of [M+2Na]²⁺ ions from these polyesters proceeds via charge‐remote 1,5‐H rearrangements over the ester groups, leading to cleavages at the (CO)O–alkyl bonds. ETD of the same precursor ions creates a radical anion at the site of electron attachment, which fragments by radical‐induced cleavage of the (CO)O–alkyl bonds and by intramolecular nucleophilic substitution at the (CO)–O bonds. In contrast to CAD, ETD produces fragments in one charge state only and does not cause consecutive fragmentations, which simplifies spectral interpretation and permits conclusive identification of the correct end groups. The radical‐site reactions occurring during ETD are very similar with those reported for ETD of protonated peptides. Unlike multiply protonated species, multiply sodiated precursors form ion pairs (salt bridges) after electron transfer, thereby promoting dissociations via nucleophilic displacement in addition to the radical‐site dissociations typical in ETD. Copyright © 2012 John Wiley & Sons, Ltd.     

基于AutoCAD的画法几何解题方法研究

提出采用AutoCAD中某些绘图方法的命令替代传统画法几何的解题方法来解决画法几何中的相关问题，使画法几何题解的正确程度和精确程度得到相应提高．     

空间圆柱螺旋线的NURBS表示

O．引言用B样条方法或B6zier方法来表示自由曲线、曲面，是在CAD／CAM技术中广泛使用的数学手段．但是由于它们都不能精确地表示除抛物线或抛物面以外的圆锥曲线与初等二次曲面，因此近年来，另一种形式的参数样条-一参数有理多项式方法占据了主导地位．非均匀有理B样条（简称NURBS）已被国际标准组织（ISO）于1991年正式颁布为关于工业产品几何定义的STEP国际标准，将其作为定义产品形状的唯一数学方法．越来越多的CAD系统采用NURBS曲线与曲面来建立图形库，研究各种曲线与曲面的NURBS表示无疑是很有意义的．在描述圆锥曲线…     

G cubic transition between two circles with shape control

This paper describes a method for joining two circles with an S-shaped or with a broken back C-shaped transition curve, composed of at most two spiral segments. In highway and railway route design or car-like robot path planning, it is often desirable to have such a transition. It is shown that a single cubic curve can be used for blending or for a transition curve preserving G²$G^2$ continuity with local shape control parameter and more flexible constraints. Provision of the shape parameter and flexibility provide freedom to modify the shape in a stable manner which is an advantage over previous work by Meek, Walton, Sakai and Habib.     

CAD of Millimeter Wave Y-Junction Circulators with a Ferrite Sphere

A gradient optimization technique along with a definition of cost function is applied to the CAD of the circulator with a magnetized ferrite sphere for millimeter wave communications. A three-dimensional Finite-Difference Time-Domain (FDTD) approach for the analysis of this ferrite sphere based microstrip circulator is presented. The topology of the structure is enforced at each step of optimization and its physical dimensions are used as optimization variables. The cost function is defined using location of zeros and poles of the circulator's transmission, isolation, and reflection functions. Numerical tests show that the optimization process converges from an arbitrarily selected starting point with the new definition of the cost function.     

2kW行波加速器加速管冷却系统的数值优化设计

 利用工程设计分析软件I DEAS，对高功率加速管的冷却系统进行了计算机辅助设计研究，并通过对不同冷却条件下加速管的温度场、冷却系统的冷却效果进行的数值模拟，实现了加速管冷却系统的优化设计。这可为高束流功率低能电子直线加速器的设计提供参考。