Numerical solution of fractional order differential equations by extrapolation

We present an extrapolation type algorithm for the numerical solution of fractional order differential equations. It is based on the new result that the sequence of approximate solutions of these equations, computed by means of a recently published algorithm by Diethelm [6], possesses an asymptotic expansion with respect to the stepsize. From this we conclude that the application of extrapolation is justified, and we obtain a very efficient differential equation solver with practically no additional numerical costs. This is also illustrated by a number of numerical examples. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the Crossing Number of Circular Graphs

1.IntroductionInVLSIchipdesign,thetwo-layerroutingofgraphGplayanimportantrole.Thatis,theupperlayercanonlybeusedforverticalwiringandthesecondlaer,theloweroneonlyforhorizontalwiring.Soweconsidertheplanarprojectionofth.etwolayers,i.e.,consideratwodimensionalgridasapropergraphmodel.ThenoneobviousconditiontoberequiredisthateveryvertexofGhasitsdegreeatmost4.Withoutlossofgeneralitylweonlyconsider4regUlargraphs.IfGisaplanargraphwitha(G)S4,alinearalgorithmhadbeenprovidedforfindingarectilineajrrout…     

Effects of the drawing form and draw ratio on the fiber structure and mechanical properties of CO2-laser-heated-drawn poly(ethylene terephthalate) fibers

The structure, mechanical properties, and thermomechanical properties of poly(ethylene terephthalate) (PET) fibers obtained by laser-heated drawing were investigated in terms of their dependence on the draw ratio and feed speed and the differences between neck-drawn fibers and flow-drawn fibers. The long period at a draw ratio of 6.0 reached 19.0 nm, notably larger than at lower ratios, whereas the tilting angle of the laminar structure was constant at about 60°, regardless of the draw ratio. A maximum value of 15.0 GPa was attained for the initial modulus, and 1.07 GPa was attained for the tensile strength. A higher tensile strength orientation-induced crystallized fiber at the same initial modulus was obtained from higher molecular weight PET. The relationship between the compliance and molecular orientation of the amorphous phase was studied with a series model of crystalline and amorphous phases. The results revealed that, in the high-draw-ratio fibers, the compliance of the amorphous phase decreased with the draw ratio at a higher rate than indicated by extrapolation to intrinsic values. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 79–90, 2004     

Melt spinning and laser‐heated drawing of a new semiaromatic polyamide,PA9‐T fiber

Fibers of PA9‐T, a new semiaromatic polyamide containing a long aliphatic chain, were prepared by melt spinning. As‐spun fibers were subsequently drawn with a CO₂ laser‐heated drawing system at different draw ratios and various drawing velocities. On‐line observations of drawing points deciphered two drawing states; namely, flow drawing and neck drawing, over the entire range of drawing. Drawing stress revealed that flow drawing is induced by slight drawing stress under a low draw ratio up to 3, and neck drawing is induced by relatively high drawing stress under a higher draw ratio. The effect of drawing stress and drawing velocity on the development of the structure and properties has been characterized through analysis of birefringence, density, WAXD patterns, and tensile, thermal, and dynamic viscoelastic properties. For the neck‐drawn fibers, almost proportional enhancements of crystallinity and molecular orientation with drawing stress were observed. The flow‐drawn fibers have an essentially amorphous structure, and birefringence and density do not always have a linear relation with properties. The fibers drawn at high drawing speed exhibit improved fiber structure and superior mechanical properties. The maximum tensile strength and Young's modulus of PA9‐T drawn fibers were found to be 652 MPa and 5.3 GPa, respectively. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 433–444, 2004     

放射系衰变纲图的扩充

根据放射性核素数据，对原来的四个放射系做了全面的扩充，做出了新的衰变纲图，讨论了有关问题。     

B-convergence of the implicit midpoint rule and the trapezoidal rule

We present upper bounds for the global discretization error of the implicit midpoint rule and the trapezoidal rule for the case of arbitrary variable stepsizes. Specializing our results for the case of constant stepsizes they easily prove second order optimal B-convergence for both methods.1980 AMS Subject Classification: 65L05, 65L20.     

离心风机梯形截面蜗壳内旋涡流动的数值分析

本文求解时均N-S方程和“Baldwin-Lomax”湍流模式,使用基于时间推进法的Jameson格式计算方法,对一离心风机的梯形截面蜗壳内部流场进行了数值模拟。计算结果表明,在蜗壳各径向截面上都存在着一个旋转方向相反、强度交替变化的涡对。该涡对会随着径向截面位置与蜗壳运行工的变化发生复杂的变化。对该涡对演化细节的研究有助于探讨蜗壳内流动损失的一些机理。     

用Word绘图功能绘制电路图

先绘制基本的电子元件图 ,将他们添加到自动图文集中 ,然后新建一个“电路图”工具栏 ,在该工具栏中添加各元件按钮、绘图按钮、文本框按钮、引脚按钮等 ,最后对按钮可进行优化设置。为了使用方便 ,也可新建“电路图”菜单及相关按钮     

Paper-based all-solid-state flexible asymmetric micro-supercapacitors fabricated by a simple pencil drawing methodology

A simple and novel methodology was developed for manufacturing interdigitated asymmetric all-solid-state flexible micro-supercapacitors (MSCs) by a facile pencil drawing process followed by electrodepositing MnO₂ on one of the as-drawn graphite electrode as anode and the other as cathode.     

基于“互联网+”的拉丝模激光衍射孔型测量研究

为解决目前接触式拉丝模具测量系统存在精度低、 响应时间长、测量参数不能实时采集、 传输和处理等问题,本文系统引入激光衍射旋转法进行拉丝模孔型的测量。本文测量系统主 要由机械、光学成像、数据采集处理及网络传输等4部分构成,在测量过程中不断 旋转拉丝模中心轴,在CCD上分别形成圆和椭圆的衍射图样,利用衍射图样和旋转角度 之间的函数关系实现拉丝模孔型参数的测量。同时,系统还将“互联网+”引入到系统中, 将 每一个拉丝模具作为一个节点,通过组网技术将其组成互联网测量系统,实现拉丝模测量数 据的实时采集、分析和处理。实验表明,本文测量系统精度可达到0.01mm,在拉丝模孔型测量中具用较高的工程实用价值。