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LetK be a quadratic imaginary number field. Letf denote a rational integer which is coprime to 6. We letK (f 2) (resp.K(f)) denote the ray class field ofK of conductorf 2 (resp.f). We write Γ for the Galois group ofK(f 2)/K(f) and denote the unique maximal order ofK(f)Γ by . We show that the Kummer order is a free, rank one -module. An explicit generator is given by singular values of certain modular functions.  相似文献
2.
In this paper we propose a numerical method for approximating connecting orbits on a manifold and its bifurcation parameters. First we extend the standard nondegeneracy condition to the connecting orbits on a manifold. Then we construct a well-posed system such that the nondegenerate connecting orbit pair on a manifold is its regular solution. We use a difference method to discretize the ODE part in this well-posed system and we find that the numerical solutions still remain on the same manifold. We also set up a modified projection boundary condition to truncate connecting orbits on a manifold onto a finite interval. Then we prove the existence of truncated approximate connecting orbit pairs and derive error estimates. Finally, we carry out some numerical experiments to illustrate the theoretical estimates.  相似文献
3.
In this paper, we study the generalized practical stability and the totally generalized practical stability of Filippov-type piecewise smooth systems. We also apply these properties to a brake model of bike to study its practical stability. Some numerical computations are presented to illustrate our theories.  相似文献
4.
We present three cubically convergent methods for choosing the regularization parameters in linear inverse problems. The detailed algorithms are given and the convergence rates are estimated. Our basic tools are Tikhonov regularization and Morozov's discrepancy principle. We prove that, in comparison with the standard Newton method, the computational costs for our cubically convergent methods are nearly the same, but the number of iteration steps is even less. Numerical experiments for an elliptic boundary value problem illustrate the efficiency of the proposed algorithms.  相似文献
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