A CONSTRUCTIVE PROOF OF THE INVERSION FORMULA FOR ZONAL FUNCTIONS ON SL(2,R）

1.IntroductionLeSL(2,R)denotethemultiplicativegroupofall2x2realm8triceswithdet-nat1.InthispaPer,weuseGtodenotebothSL(2,R)andthellnearLiegroupbecausetheyareisomorphictoeachother.Forj={o,1/2},s=1 iA(whereAER,andRisthesetofallrealnumbers),letVi,8betheprincipalcolltinuousseriesofunitaryrepresentationsofG(cf.[4]).SetBytheIwasawadecomposition,anygEGcanbeuniquelywhttenasg=usatnr,u8ESK,afESA,nrESN.Al8oanyginGhasaCartandecompositionasfollows:Afunctionf0nGissaidtobeazonalfunctionifitsatisf…     

Subconvergence of Finite Elements and a Self-Adaptive Algorithm

1.IntroductionSofar,therehavebeenmanypapersconcerningwiththesuperconvergenceoffi-niteelements.Undersomecondition8,ahigherconvergenceaccuracyisobtainedatsomespecificpoints.Thisphenomenoniscalledsuperconvergence.Thetheoryofsupercovergence[1]tellsusthat,inordertogainsuperconvergence,twoconditionsmustbesatisfied.Oneisthegoodsubdivisionandthesecondistheexistenceoflocallysufficientsmooth8olution.Iftheseconditionsarenotsatisfied,e.g-,lowsmoothnessofthesolution,occursacontraryphenomenonthatsomelocale…     

竞赛综合能力训练(四)

1.计算: (1)12(1/7)×29×7/4-1.75×12(3/7)=__; (2)1/3 1/8 1/15 1/35 1/48 1/63 __。 2.n是比100小的自然数,且 8 8 …… 8 n个8是平方数,那么n的最小值是__;n的最     

A Better Difference Scheme with Four Near-Conserved Quantities for the KdV Equation

1.IntroductionThenumericaJstudiesoftheKdVequationhavebeenlargelydevelopedsinceZabuskyandKrusbousedthesecondorderaccuracyLeaWnogschemetosolvetheKdVequationandreveaJeditsimportantproperties[8].RecentlycomputationaJinstabilitiessuchassidebandandmodulationalonesusingfinitedtherenceaPproalmatingwereobservedbytheseveralscholaxs[1lI6].Notoalythat,othernumericaJmethodsfortheKdVequational8ocausethetroublesaboutcomputationalblow-upornumericalspurioussolutionswhencomputingtimeislong.Thepoilltistha…     

一个问题的简单解答

问题　已知 x,y∈ R ,且 x y =1 ,求1x2 8y2 的最小值 .文 [1 ]作者尝试“用 1代换”,得到1x2 8y2 =( 1x2 8y2 ) ( x y)=1x 8y yx2 8xy2 .思维受阻后 ,原作者询问道 :“在 ( 1x2 8y2 ) (　　 ) ,括号内应配上什么式子才能解出呢 ?”这里 ,笔者拟给出一个回答 ,并不需推广为一般性结论后再赋值 .解　∵　 x,y∈ R ,x y =1 ,∴　 1x2 8y2 =( 1x2 8y2 ) ( x y) 2　 =9 y2x2 8x2y2 2 yx 1 6 xy　 =9 ( y2x2 8xy 8xy) ( 8x2y2 yx yx)　≥ 9 33 8 33 82 =2 7,当且仅当 y2x2 =8xy 且 x y =1 ,即…     

A SMALLEST SINGULAR VALUE METHOD FOR SOLVING INVERSE EIGENVALUE PROBLEMS

1.IntroductionConsiderthefollowinginverseeigenvalueproblem:ProblemG.LetA(x)ERnxn5earealanalyticmatrix-valuedfunctionofxeR".Findapointx*eR"suchthatthematrixA(x*)ha8agiven8Pectral8etL={Al,'tA.}.HereA1,'1A.aregivencomPlexnum6ersandclosedundercomplexconjugation.Thiskindofproblemarisesofteninvariousareasofapplications(seeFreidlandetal.(1987)andreferencescontainedtherein).ThetwospecialcasesofProblemG,whicharefrequentlyencountered,arethefollowingproblemsproposedbyDowningandHouseholder(19…     

小学珠心算数学

用眼睛扫一遍数字,把数字反映到后象之中;然后用手划写数字,口喊三八一四八二……第四节6组生字6组生字是:346746888877124513为了方便记忆,我们可以用脑照相方法记忆:381482训练四遍至五遍,可以复述下来。认字:346678878888788348674776474386746774887884876487487868884476用同样办法可以记住(注意交换律):3.笔算4.用珠算计算3+8=6+8=6+7=7+4=4+8=8+3=5.用听算计算7+8=6+8=8+4=8+3=8+6=6+7=8+7=3+8=4+7=4+8=8+7=3+8=6+8=8+3=7+6=4+7=6+8=4+8=6.珠算(双手操作)7.笔算3+1=1+1=8+5=4+5=6+7=3+7=6+8=4+8=2+1=6+5=3+1=5+5=1+7=6+2=9+3=1+6=5+3…     

Algebraic-Geometry Foundation for Constructing Smooth Interpolants on Curved Sides Element

1.IntroductionThealgebraicgeometrytheoryplaysaveryimportantroleinmanyareas-Forex-ample,thefundamentaltheoreminthemultiwriatepolynomialillterpolationtheoryl8]isestablishedbymeansofBezout'8theorem,thefundamentaJtheoreticalframeofmultivariatesplinefunctionsisgeneratedbymeansofcompatiblecthfactormethodI8]whichisalsocloselyrelatedwithBezout'stheo.em[9].ThepiecewisesmoothfunctionskillisusedfrequentlyinCAGD,FECandscattereddatafitting,etc.Inusingtheskin,thesmoothinginterpolationschemeanditsexplic…     

The Application of Integral Equations to the Numerical Solution of Nonlinear Singular Perturbation Problems

1.AContinuousProblemWeconsiderthefOllowingsingularlyperturbedboundaryvalueprob1em:whereEisasmallpositiveparameter.WeassumethatAccordingto[2],wecanproveLemma1.Suppo8ethatcondition(2)ls8atisfied.Therecxistsaunique8olutionuEC'(I)topro5lem(1),andthefOllowingrepresentationholds:u(x)=uo(x) Vo(x) Vl(x),whereVo(x)=atexp(-ry-),Vl(x)=Mexp(-ryap),andIu8t)(x)ISM,i=O,1,',6,xEI(ThroughoutthepaperMdenotesanyconstantindePendentOfE).Theproofofthefollowinglemmaisbasedonthemonotonicityof(l),andcanb…     

条件"x+y=1"下1/xn+λ/yn的最小值

1　问题的提出我们经常遇到下列问题 :(1)已知 x,y∈ R ,且 x y =1,求 1x 4y 的最小值 ;(2 )已知 x,y∈ R ,且 x y =1,求 1x2 8y2 的最小值 ;问题 (1)“用 1代换”不难求得 :1x 4y =(1x 4y) (x y)　　 =5 yx 4 xy ≥ 5 2 yx .4 xy =9,当且仅当 yx =4 xy,即　 y =2 x时取等号 .问题 (2 )能否“用 1代换”呢 ?1x2 8y2 =(1x2 8y2 ) (x y) ,　 =1x 8y yx2 8xy2 ,虽然有　 1x 8y ≥ 2 8xy ,yx2 8xy2 ≥ 2 8xy 且　 1xy≥ 2x y,但三式等号分别在 y =8x,y =2 x与 y =x时成立 ,故等号不能同时成立 .在 (1x…     

THE MULTIGRID METHOD OF WILSONELEMENT ON ARBITRARYQUADRILATERAL MESHES WITH TWONEW VARIATIONAL FORMULATIONS

1.IntroductionShiZhongci[']hasshownthattheWilsonelementonarbitraryquadrilateralmesheswasconvergelltunderacertainconditionwithoutmodificationsofthevariationalformulation.P.LesaintandM.Zlamal[2]gaveamathematicalanalysisoftheconvergenceofthemodifiedWilsonelemeflt.Withtheseideas,thispapergivestwosimplevariationalformulationsforthequadrilateralWilsonelementandshowstheirconvergencewiththenewvariationalformulations.Usingthenewvariationalformulations,wecanreduceourcomputationalcostsbecausetwotermsa…     

非正则条件下类Wilson元的构造及其应用

本文在非正则性条件下，研究了窄四边形上的类Wilson元。通过参考元上类Wilson元的构造，证明了由此产生的有限元对任意窄四边形剖分通过Irons分片检查，得到了二阶问题的误差估计。结果表明，该单元的收敛性质与Wilson元的类似。     

求解Stokes问题的一类新混合元格式

利用Specht九参数元的分析技巧 ,通过对Adini元增加一个自由度 ,本文构造一类求解Stokes问题的新二阶混合有限元格式 .该格式简单实用且自由度较已有的许多二阶格式少 .     

拟协调元的位移函数及节点误差

直接从拟协调元的应变关系式出发,构造具有明确物理意义的幂级数形式的位移函数,从而得出拟协调元的常应变和线性应变系数是唯一确定的,它只能收敛到常应变的结论;刚性位移项可采用多种构造方法,不同的方法得出的节点参数与单元的本身的节点参数存在不同阶次的误差,这与常规位移法有限元不同。     

A finite element method for interface problems in domains with smooth boundaries and interfaces

This paper is concerned with the analysis of a finite element method for nonhomogeneous second order elliptic interface problems on smooth domains. The method consists in approximating the domains by polygonal domains, transferring the boundary data in a natural way, and then applying a finite element method to the perturbed problem on the approximate polygonal domains. It is shown that the error in the finite element approximation is of optimal order for linear elements on a quasiuniform triangulation. As such the method is robust in the regularity of the data in the original problem.     

PRECONDITIONING MIXED ELEMENT METHOD FOR NONSELFADJOINT AND INDEFINITE SECOND ORDER ELLIPTIC PROBLEMS*

In this paper, an equivalence between mixed element method and nonconforming element method for nonselfad joint and indefinite second order elliptic problems is established without using any bubble functions. It is proved that the H~1-condition number of preconditioned operator B_h~(-1)A_h is uniformly bounded and its B_h-singular values cluster in a positive finite interval, where A_h is the equivalent nonconforming element discretization of nonselfad joint and indefinite second order elliptic operator A, B_h is usual noncon forming element discretization of selfadjoint and positive definite second order elliptic operator B. Finally a simple V-cycle multigrid implementation of B_h~(-1) is given.     

Derivative superconvergent points in finite element solutions of harmonic functions-- A theoretical justification

Finite element derivative superconvergent points for harmonic functions under local rectangular mesh are investigated. All superconvergent points for the finite element space of any order that is contained in the tensor-product space and contains the intermediate family can be predicted. In the case of the serendipity family, results are given for finite element spaces of order below 6. The results justify the computer findings of Babuska, et al.

     

MODIFIED MORLEY ELEMENT METHOD FOR A FOURTH ORDER ELLIPTIC SINGULAR PERTURBATION PROBLEM

This paper proposes a modified Morley element method for a fourth order ellipticsingular perturbation problem. The method also uses Morley element or rectangle Morleyelement, but linear or bilinear approximation of finite element functions is used in the lowerpart of the bilinear form. It is shown that the modified method converges uniformly in theperturbation parameter.     

A new rotated nonconforming pyramid element

In this paper, a new nonparametric nonconforming pyramid finite element is introduced. This element takes the five face mean values as the degrees of the freedom and the finite element space is a subspace of P₂. Different from the other nonparametric elements, the basis functions of this new element can be expressed explicitly without solving linear systems locally, which can be achieved by introducing a new reference pyramid. To evaluate the integration, a class of new quadrature formulae with only two/three equally weighted points on pyramid are constructed. We present the error estimation in the presence of quadrature formulae. Numerical results are shown to confirm the optimality of the convergence order for the second order elliptic problems.     

导数小片插值恢复技术与超收敛性

１．引言 有限元超收敛的研究自七十年代起至今方兴未艾．现有的研究工作基本遵循两种途径：一是找出有限元插值逼近的超收敛点,然后再利用插值弱估计等手段导出有限元解本身所具有的超收敛性质［１,２］;二是利用各种后处理技术,如平均技术,投影技术,外插技术和插值有限元技术等[3,6],来导出经过后处理的有限元解的超收敛性．近年来一种新的超收敛后处理技术,即所谓的“Ｚ-Ｚ导数小片恢复技术”,得到众多的研究［７-１１］,并被 Ｂａｂｕｓｋａ等人认为是用于渐进准确的后验误差估计效果最好的技术之一［１２］．这种技术是利用…