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991.
992.
Spectral radial basis functions for full sphere computations 总被引:1,自引:1,他引:0
Philip W. Livermore Chris A. Jones Steven J. Worland 《Journal of computational physics》2007,227(2):1209-1224
The singularity of cylindrical or spherical coordinate systems at the origin imposes certain regularity conditions on the spectral expansion of any infinitely differentiable function. There are two efficient choices of a set of radial basis functions suitable for discretising the solution of a partial differential equation posed in either such geometry. One choice is methods based on standard Chebyshev polynomials; although these may be efficiently computed using fast transforms, differentiability to all orders of the obtained solution at the origin is not guaranteed. The second is the so-called one-sided Jacobi polynomials that explicitly satisfy the required behavioural conditions. In this paper, we compare these two approaches in their accuracy, differentiability and computational speed. We find that the most accurate and concise representation is in terms of one-sided Jacobi polynomials. However, due to the lack of a competitive fast transform, Chebyshev methods may be a better choice for some computationally intensive timestepping problems and indeed will yield sufficiently (although not infinitely) differentiable solutions provided they are adequately converged. 相似文献
993.
Using an algebraic technique based on the Lie algebra of the group SO(2, 1) the eigenvalues of the triple-well anharmonic
oscillator are calculated for all ranges of the coupling constant. Approximate analytic formulas for the eigenvalues up to
second order are given. The results obtained are compared with those of other authors. 相似文献
994.
令M是Z[v]的由v-1和奇素数p生成的理想,U是A=Z[v]M上相伴于对称Cartan矩阵的量子代数.k是特征为零的代数闭域,A→k(v(?)ξ)是环同态.U_k=U(?)_Ak,u_k是U_k的无穷小量子代数.令ξ是1的p次本原根.本文证明了:若有限维可积U_k模M,V中至少有一个是内射模,或者M,V中有一个模作为u_k模是平凡的,则有U_k模同构M(?)V≌V(?)M.我们还证明了:若有限维可积U_k模V作为u_k模是不可分解的,有限维可积U_k模M是不可分解的,且M|_(uk)是平凡的,则V(?)M是不可分解U_k模.令V和M是有限维可积U_k模,作为u_k模是同构的且具有单基座,本文证明V和M作为U_k模也是同构的.由此得到:不可分解内射u_k模提升为U_k模是唯一的. 相似文献
995.
本文揭示了单洞 Cata 型六角系统的共振多项式与广义冠的匹配多项式的关系、将1977年 Gutman 提出的方法推广应用到有洞的六角系统,并得到一些共振多项式的比较定理. 相似文献
996.
Gerhard RÖhrle 《Geometriae Dedicata》1997,66(1):51-64
The principal aim of this paper is to show that every maximal parabolic subgroup P of a classical reductive algebraic group G operates with a finite number of orbits on its unipotent radical. This is a consequence of the fact that each parabolic subgroup of a group of type A
n
whose unipotent radical is of nilpotent class at most two has this finiteness property. 相似文献
997.
Homotopy continuation methods can be applied to compute all finite solutions to a given polynomial system. Computations will be performed more efficiently if the symmetric structure of the system can be exploited. This paper presents the construction of a symmetric homotopy. Using this homotopy, only the paths according to the generating solutions have to be traced during continuation. 相似文献
998.
Francisco M. García Olmedo Antonio J. Rodríguez Salas 《Mathematical Logic Quarterly》1995,41(2):249-256
In this paper an algebraic version for temporal algebras of the logical filtrations for modal and temporal logics is analysed. A structure theorem for free temporal algebras and also some results with regard to the variety of temporal algebras are obtained. 相似文献
999.
For modular group algebras over an arbitrary field we define new type of blocks: blocks with nilpotent extensions, and describe their source algebras. To do it, a general pattern is proposed for relations between the source algebra of a block and the source algebra of a block appearing in its decomposition in a suitable extension of the field of coefficients. 相似文献
1000.
Calculations are presented of flow characteristics in the vicinity of disks and cylinders rotating at speeds typical of those found in modern mechatronics machinery. The rotational speeds are slow or intermittent, and the generated boundary layers are laminar and transitional. Comparison is made with existing experimental data and exact, though idealised, analytical solutions. A three-dimensional finite volume procedure with time dependence was employed as the solution method, and two grid geometries were used, namely, axisymmetric and cartesian. Use of a cartesian grid is very important, as it is compatible with the design of the interiors of mechatronics machinery, and present practice is to model these interiors with computationally economical cartesian grids. Expanding grids were generated normal to surfaces for each of the grid geometries so as to capture the thin boundary layers. To alleviate numerical difficulties, when using the cartesian geometry, an expanding and contracting grid was generated normal to the axis of the disks and cylinders with the grid spacing based on a shifted Chebyshev polynomial. 相似文献