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1.
一类高阶方程的中量定理及其逆定理   总被引:2,自引:0,他引:2       下载免费PDF全文
本文对于高阶方程(?)在文[2]中量定义的基础上,利用Asgeirsson中量定理,得到了中量所满足的方程,即M(r,s)+M(s,r)满足E-P-D方程,同时也证明了其逆定理也成立.  相似文献
2.
In the paper we carry out a complete analysis of several efficientnumerical methods for the solution of boundary integral equationsdefined on a non-smooth boundary. In particular the solutionof the Helmholtz equation in the exterior of a closed wedgeis studied. The analytical behaviour of the solution of theresulting boundary integral equation (with a non-compact operator)near the wedge is investigated. Numerical analysis of the collocationand iterated collocation method for the problem is presented.Graded meshes are used to reflect the ‘singular’behaviour of the analytical solution, as well as the degreeof the polynomial approximant, in order to yield results with‘optimal convergence rates’. Finally the convergenceanalysis of some modified two-grid iterative methods for thefast solution of the resulting linear systems is given and numericalresults are presented which agree with the theoretical predictions.  相似文献
3.
一类高阶超双曲型方程的中量定理及其逆定理   总被引:1,自引:0,他引:1  
Asgeirsson中量定理表明超双曲型方程的Cauchy问题一般是不适应的,对Asgeirsson中量定理的推广就有重要意义,目前关于高阶方程解的中量只有初步探讨,尚未得到具体结果,本文直接利用Asgeisson中量定理结果和积分,微分的性质与关系,得到了高阶方程解的中量满足广义双轴对称位势方程,同时还证明了其逆定理,利用关于广义双轴对称位势方程正则解的表达式及雅可比多项式的特殊性质,得到了高阶方程解的中量公式,从而使得关于解的拓展性和适定性的讨论将有可能。  相似文献
4.
Efficient measurement of the performance index (the distance of a loading parameter from the voltage collapse point) is one of the key problems in power system operations and planning and such an index indicates the severity of a power system with regard to voltage collapse. There exist many interesting methods and ideas to compute this index. However, some successful methods are not yet mathematically justified while other mathematically sound methods are often proposed directly based on the bifurcation theory and they require the initial stationary state to be too close to the unknown turning point to make the underlying methods practical.This paper first gives a survey of several popular methods for estimating the fold bifurcation point including the continuation methods, bifurcation methods and the test function methods (Seydel's direct solution methods, the tangent vector methods and the reduced Jacobian method) and discuss their relative advantages and problems. Test functions are usually based on scaling of the determinant of the Jacobian matrix and it is generally not clear how to determine the behaviour of such functions. As the underlying nonlinear equations are of a particular type, this allows us to do a new analysis of the determinants of the Jacobian and its submatrices in this paper. Following the analysis, we demonstrate how to construct a class of test functions with a predictable analytical behaviour so that a suitable index can be produced. Finally, examples of two test functions from this class are proposed. For several standard IEEE test systems, promising numerical results have been achieved.  相似文献
5.
The variational partial differential equation (PDE) approach for image denoising restoration leads to PDEs with nonlinear and highly non-smooth coefficients. Such PDEs present convergence difficulties for standard multigrid methods. Recent work on algebraic multigrid methods (AMGs) has shown that robustness can be achieved in general but AMGs are well known to be expensive to apply. This paper proposes an accelerated algebraic multigrid algorithm that offers fast speed as well as robustness for image PDEs. Experiments are shown to demonstrate the improvements obtained.  相似文献
6.
徐克安  陈晓剑 《运筹与管理》2007,16(6):21-25,32
降低供应链中处于不同阶段的物料(原材料、在制品以及成品)的库存水平已经成为供应链管理的研究焦点之一。其中供应商管理的库存VMI(vendor-managed-inventory)策略不论在理论上还是在不同企业的实践中都到了广泛的关注。本文首先给出了一个考虑一个供应商和多个不同的订货商,订货商有共同的订货补充期,并且考虑广告费对需求影响的VMI集成模型;其次,给出了模型的相应算法;最后,给出了算例加以说明。  相似文献
7.
A flip-chip-type gradiometer has been constructed with a 10 mm×5 mm planar DC-SQUID gradiometer fabricated on a SrTiO3 bicrystal substrate and a flux transformer made from a YBCO*/YBCO/CeO2/YSZ multilayer on a φ50.8 mm Si wafer. The coupling coefficient between the flux transformer and the planar gradiometer is 0.18. The transformer increases effectively the resolution of the gradiometer. A magnetic field gradient resolution of 73 fT·cm-1·Hz-1/2 in the white region and 596 fT·cm-1Hz-1/2 at 1 Hz has been obtained. High quality magnetocardiogram signals have been successfully measured by using this flip-chip-type gradiometer in an unshielded environment.  相似文献
8.
A flip-chip-type gradiometer has been constructed with a 10 mm × 5 mm planar DCSQUID gradiometer fabricated on a SrTiO3 bicrystal substrate and a flux transformer made from a YBCO*/YBCO/CeO2/YSZ multilayer on ϕ50.8 mm Si wafer. The coupling coefficient between the flux transformer and the planar gradiometer is 0.18. The transformer increases effectively the resolution of the gradiometer. A magnetic field gradient resolution of 73 fT.cm−1Hz−1/2 in the white region and 596 fT.cm−1Hz−1/2 at 1 Hz has been obtained. High quality magnetocardiogram signals have been successfully measured by using this flip-chip-type gradiometer in an unshielded environment.  相似文献
9.
Digital image restoration has drawn much attention in the recent years and a lot of research has been done on effective variational partial differential equation models and their theoretical studies. However there remains an urgent need to develop fast and robust iterative solvers, as the underlying problem sizes are large. This paper proposes a fast multigrid method using primal relaxations. The basic primal relaxation is known to get stuck at a ‘local’ non-stationary minimum of the solution, which is usually believed to be ‘non-smooth’. Our idea is to utilize coarse level corrections, overcoming the deadlock of a basic primal relaxation scheme. A further refinement is to allow non-regular coarse levels to correct the solution, which helps to improve the multilevel method. Numerical experiments on both 1D and 2D images are presented.  相似文献
10.
We present a new technique for generating error equi-distributing meshes that satisfy both local quasi-uniformity and a preset minimal mesh spacing. This is first done in the one-dimensional case by extending the Kautsky and Nichols method and then in the two-dimensional case by generalizing the tensor product methods to alternating curved line equi-distributions. With the new meshing approach, we have achieved better accuracy in approximation using interpolatory radial basis functions. Furthermore, improved accuracy in numerical results has been obtained when the interpolatory strategy is applied to the dual reciprocity boundary element method for solving a class of linear and nonhomogeneous partial differential equations.  相似文献
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