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1.
A Note on C-wrpp Semigroups   总被引:2,自引:0,他引:2  
唐向东 《东北数学》2001,17(1):71-74
LetRdenoteGreen sR relationonasemigroupS .WedefinearightcongruenceL onSintherule:fora ,b∈S ,(a ,b) ∈L iffforallx ,y∈S1,   (ax ,ay) ∈R (bx,by) ∈R .AsemigroupSissaidtobeaC wrppsemigroupifallidempotentsofSarecentralinSandeachL classofScontainsanidempotent(see [1 ] ) . Thep…  相似文献   

2.
§0.IntroductionAsweknow,thenonclassical(graded)simplemodularLiealgebraswhenthebackgroundfieldisofcharacteristicp>5havefourtypes:W(n,m),S(n,m),H(n,m)andK(n,m).Forthegradedmodulesofthefirstthreetypes,Shengaveacompletedescriptionbasedonhismixedproductrealizationsin…  相似文献   

3.
The Structure of NBe—rpp Semigroups   总被引:2,自引:0,他引:2  
郭小江 《东北数学》2000,16(4):398-404
§ 1.IntroductionandMainResults AsemigroupSiscalledanrppsemigroupifallprincipalrightidealsaS1(a∈S)ofS ,regardedasanS1 system ,areprojective (see,[1 ]and [2 ] ) .AsemigroupSisanrppsemigroupifandonlyifforalla∈S ,thesetMa ={e∈E S1a Seand ( x ,y∈S1)ax=ay ex=ey}isnonempty ,whereE …  相似文献   

4.
§ 1.ProblemandAssumptions Thispaperdealswiththesolutionsofthefollowingdifferentialinclusionproblem :Au∈f(x,u) ,x∈Ω ;u=0 ,x∈ Ω ,(1 )whereAu(x) =-∑Ni=1Di[ai(x ,Du(x) ) ] ,Ω RNisaboundeddomainwithpiecewiseLipschitzboundary Ω ,Du =(D1u ,D2 u ,… ,DNu) ,Diu = u xi,i=1 ,2 ,… ,N ,andf:Ω×R→ 2 Risa…  相似文献   

5.
Consideraplanarperturbedsystemoftheformx=Hy+εf(x,y),y=-Hx+εg(x,y)(1)whereH,f,garefunctionsofclasC∞.Asumeforε=0(1)tohaveahomoc...  相似文献   

6.
程细茂 《数学通讯》2001,(10):26-27
选择题1 下列各等式成立的是 (   )(A)arcsin π3=32 .(B)cos(arccos π3) =π3.(C)tg(arctg 3) =3.(D)sin(arccos12 ) =12 .2 下列命题不正确的是 (   )(A)函数 y =arccosx - π2 是奇函数 .(B)当x∈ ( 22 ,1)时 ,arcsinx >arccosx .(C)tg(arccos0 ) =0 .(D)当x∈ ( -∞ ,0 )时 ,arcctgx >arctgx .3 若 π4 <α <5π4 ,则arcsin[22 (sinα cosα) ]的值为(   )(A) π4 -α .   (B)α - π4 .(C)α - 3π4 . (D) 3π4 -…  相似文献   

7.
A New Class of Banach Spaces with Uniform Normal Structure   总被引:2,自引:0,他引:2  
高继 《东北数学》2001,17(1):103-110
§ 1.Introduction LetXbeanormedlinearspace ,andletS(X) ={x∈X :x =1 }betheunitsphereofX .In 1 94 8,BrodskiiandMilman[1]introducedthefollowinggeometricconcept: Definition 1 ABounded ,convexsubsetKofaBanachspaceXissaidtohavenormalstructureifeveryconvexsubsetHofKthatconta…  相似文献   

8.
马林 《数学通讯》2001,(17):31-32
命题 若 f(x) =Asinx Bcosx满足f(x1) =f(x2 ) =0 ,且x1-x2 ≠kπ (k∈Z) ,则f(x) ≡ 0 .证 ∵ Asinx1 Bcosx1=0Asinx2 Bcosx2 =0 (1 )而D =sinx1 cosx1sinx2  cosx2=sinx1cosx2 -cosx1sinx2 =sin(x1-x2 )≠ 0 (∵x1-x2 ≠kπ ,k∈Z) ,故关于A ,B的齐次线性方程组 (1 )只有零解A =B =0 ,则f(x) ≡ 0 .据此命题可知 :对于某些三角恒等式证明题 ,若能转化为sinx ,cosx的一次齐次式f(x) =Asinx Bcosx ,只需取特殊值…  相似文献   

9.
试卷 1 (3月 )1 解不等式|x- 4|- |x- 1||x- 3|-|x- 2 | <|x- 3| |x- 2||x- 4| .2 已知一个递减等差数列的前 7项的 5次幂之和等于 0 ,而它们的 4次幂之和等于 51 .求这个数列的第 7项 .3 在区间 [- 92 π ,- 32 π]上 ,求下列方程的所有的根 :cosxsin x4 91 0 sinx 2sin x4cos x2 sin x4 - 12 cos x4 - 92 0 =0 .4 经过梯形ABCD的腰AB的中点K作出AB的垂线与边CD相交于点L .已知四边形AKLD的面积是四边形BKLC的面积的 5倍 ,CL=3,DL =1 5,KC =4.求线段K…  相似文献   

10.
§1.Introduction  LetMbeacomplexmanifold.Foranyp∈MandanyX∈T1,0p(M),theKobayashiinfinitesimalpseudometric[1]ofXisF(X):=inf|a|∈C,f:DMs.t.f(0)=pandf(az)=X,whereDistheunitdiskandf∈Hol(D,M)istheholomorphicmapfromDtoM,andtheCaratheodoryinfinitesimalpeusdometricofXisE(X):=sup…  相似文献   

11.
Recent years have witnessed growing interests in solving partial differential equations by deep neural networks, especially in the high-dimensional case. Unlike classical numerical methods, such as finite difference method and finite element method, the enforcement of boundary conditions in deep neural networks is highly nontrivial. One general strategy is to use the penalty method. In the work, we conduct a comparison study for elliptic problems with four different boundary conditions, i.e., Dirichlet, Neumann, Robin, and periodic boundary conditions, using two representative methods: deep Galerkin method and deep Ritz method. In the former, the PDE residual is minimized in the least-squares sense while the corresponding variational problem is minimized in the latter. Therefore, it is reasonably expected that deep Galerkin method works better for smooth solutions while deep Ritz method works better for low-regularity solutions. However, by a number of examples, we observe that deep Ritz method can outperform deep Galerkin method with a clear dependence of dimensionality even for smooth solutions and deep Galerkin method can also outperform deep Ritz method for low-regularity solutions.Besides, in some cases, when the boundary condition can be implemented in an exact manner, we find that such a strategy not only provides a better approximate solution but also facilitates the training process.  相似文献   

12.
《Applied Mathematical Modelling》2014,38(21-22):5187-5197
Using the interpolating moving least-squares (IMLS) method to obtain the shape function, we present a novel interpolating element-free Galerkin (IEFG) method to solve two-dimensional elastoplasticity problems. The shape function of the IMLS method satisfies the property of Kronecker δ function, then in the meshless methods based on the IMLS method, the essential boundary conditions can applied directly. Based on the Galerkin weak form, we obtain the formulae of the IEFG method for solving two-dimensional elastoplasticity problems. The IEFG method has some advantages, such as simpler formulae and directly applying the essential boundary conditions, over the conventional element-free Galerkin (EFG) method. The results of three numerical examples show that the computational precision of the IEFG method is higher than that of the EFG method.  相似文献   

13.
A linear hydrodynamic stability problem corresponding to an electrohydrodynamic convection between two parallel walls is considered. The problem is an eighth order eigenvalue one supplied with hinged boundary conditions for the even derivatives up to sixth order. It is first solved by a direct analytical method. By variational arguments it is shown that its smallest eigenvalue is real and positive. The problem is cast into a second order differential system supplied only with Dirichlet boundary conditions. Then, two classes of methods are used to solve this formulation of the problem, namely, analytical methods (based on series of Chandrasekar-Galerkin type and of Budiansky-DiPrima type) and spectral methods (tau, Galerkin and collocation) based on Chebyshev and Legendre polynomials. For certain values of the physical parameters the numerically computed eigenvalues from the low part of the spectrum are displayed in a table. The Galerkin and collocation results are fairly closed and confirm the analytical results.  相似文献   

14.
This paper presents the comparison of physical spline finite element method (PSFEM), in which differential equations are incorporated into interpolations of basic elements, with least-squares finite element method (LSFEM) and mixed Galerkin finite element method (MGFEM) on the numerical solution of one dimensional Helmholtz equation applied to an acoustic scattering problem. Firstly, all three methods are explained in detail and then it is shown that PSFEM reaches higher precision in a shorter time with fewer nodes than the other methods. It is also observed that this method is well suited for high frequency acoustic problems. Consequently, the results of PSFEM point out better efficiency in terms of number of unknowns and accuracy level.  相似文献   

15.
We develop and analyze a first-order system least-squares spectral method for the second-order elhptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the Lw^2- and Hw^-1- norm of the residual equations and then we eplace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.  相似文献   

16.
Recently Miller and his co-workers proposed a moving finite element method based on a least squares principle. This was followed by a similar method by the present authors using a Petrov—Galerkin approach. In this paper the two methods are compared. In particular, it is shown that both methods move their nodes according to an approximate equidistributing principle. This observation leads to a criterion for the placement of the nodes. It is also shown that the penalty function designed by Miller may also be used with the Petrov—Galerkin method. Finally, numerical examples are given, illustrating the performance of the two methods.  相似文献   

17.
1. IntroductionIn the numerical simulation of the Navier-Stokes equations one encounters three seriousdifficulties in the case of large Reynolds numbers f the treatment of the incomPressibility con-dition divu = 0, the treatment of the noIilinear terms and the large time integration. For thetreatment of the incoInPressibility condition, one use the penalty method in the case of finiteelemellts [1--2l and for the treatmen of the noulinar terms and the large tfor integration, oneuse the nonlin…  相似文献   

18.
Numerical tests are used to evaluate the accuracy of two finite element formulations associated with the discrete ordinates method for solving the radiative transfer equation: the Least Square and the Discontinuous Galerkin finite element formulations. The results show that the use of a penalization method to set the Dirichlet boundary conditions leads to a more accurate solution than the weakly type setting where the Least Square method is seen to be more sensitive. Convergence in mesh size shows that, while both methods give accurate results, the Discontinuous Galerkin formulation uses five times more degrees of freedom than the Least Square formulation, which may lead to large systems to handle when the number of mesh elements is large. The comparison of both methods using the Sn and the Tn angular quadratures has shown that the Discontinuous Galerkin gives more accurate solutions, as expected, for problems with strong discontinuities, but may exhibit some oscillations due to the Galerkin procedure. A last test featuring a collimated irradiation shows that both methods give the same accuracy due to the separation of the radiative intensity into transmitted and scattered components, which removes the discontinuities in the implementation of the boundary conditions.  相似文献   

19.
We study hybrid methods for the solution of linear ill-posed problems. Hybrid methods are based on he Lanczos process, which yields a sequence of small bidiagonal systems approximating the original ill-posed problem. In a second step, some additional regularization, typically the truncated SVD, is used to stabilize the iteration. We investigate two different hybrid methods and interpret these schemes as well-known projection methods, namely least-squares projection and the dual least-squares method. Numerical results are provided to illustrate the potential of these methods. This gives interesting insight in to the behavior of hybrid methods in practice.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

20.
1引言考虑多孔介质中两相不可压缩可混溶渗流驱动问题,它是由一组非线性耦合的椭园型压力方程和抛物型浓度方程组成:dVV。—一山人V什)gVV却)一q,VEn,(.1)&,,。_.、。。—一。x)_+u·grade-dlv(D(u)grade)一(1-c)q-,xEn,tEJ,(1.2)&”--’”””‘”-”””——-’——,、—’一其中a()一a(x,c)一是(x)/卢(c),J一[0,Ti,DcyR‘为水平油藏区域.方程式(1.l)一(1.2)中各物理量的意义如下:广为流体压力,c为流体的浓度,u为流体的Darer速度,叶为源汇项,/一—。x(q,O),…  相似文献   

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