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991.
992.
SangDongKIM ByeongChunSHIN 《计算数学(英文版)》2003,21(2):113-124
The bounds for the eigenvalues of the stiffness matrices in the finite element discretiza-tion corresponding to Lu:=-u″with zero boundary conditions by quadratic hierarchical basic are shown explicitly.The condition numberof the resulting system behaves like O(1/h)where h is the mesh size.We also analyze a main diagonal preconditioner of the stiffness matrix which reduces the condition number of the preconditioned system to O(1). 相似文献
993.
This paper introduces a new algorithm for solving mixed integer programs. The core of the method is an iterative technique for changing the representation of the original mixed integer optimization problem.
Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.Supported by a Gerhard-Hess-Preis and grant WE 1462 of the Deutsche Forschungsgemeinschaft, and by the European DONET program TMR ERB FMRX-CT98-0202.Mathematics Subject Classification (1991):90C11 相似文献
994.
There have been extensive studies on non-uniform Gabor bases and frames in recent years. But interestingly there have not been a single example of a compactly supported orthonormal Gabor basis in which either the frequency set or the translation set is non-uniform. Nor has there been an example in which the modulus of the generating function is not a characteristic function of a set. In this paper, we prove that in the one dimension and if we assume that the generating function g(x) of an orthonormal Gabor basis is supported on an interval, then both the frequency and the translation sets of the Gabor basis must be lattices. In fact, the Gabor basis must be the trivial one in the sense that |g(x)|=c(x) for some fundamental interval of the translation set. We also give examples showing that compactly supported non-uniform orthonormal Gabor bases exist in higher dimensions. 相似文献
995.
We prove that for any fixed the generating function of the projection of the set of integer points in a rational -dimensional polytope can be computed in polynomial time. As a corollary, we deduce that various interesting sets of lattice points, notably integer semigroups and (minimal) Hilbert bases of rational cones, have short rational generating functions provided certain parameters (the dimension and the number of generators) are fixed. It follows then that many computational problems for such sets (for example, finding the number of positive integers not representable as a non-negative integer combination of given coprime positive integers ) admit polynomial time algorithms. We also discuss a related problem of computing the Hilbert series of a ring generated by monomials.
996.
Gangsong Leng 《Proceedings of the American Mathematical Society》2003,131(10):3039-3042
For any -dimensional simplex , we confirm a conjecture of Klamkin and Pook (1988) that there are always at least acute dihedral angles in .
997.
The basis number of a graph G was defined by Schmeichel to be the least integer h such that G has an h-fold basis for its cycle space. He proved that for m, n 5, the basis number b(K
m,n
) of the complete bipartite graph K
m,n
is equal to 4 except for K
6,10, K
5,n
and K
6,n
with n = 5, 6, 7, 8. We determine the basis number of some particular non-planar graphs such as K
5,n
and K
6,n
, n = 5, 6, 7, 8, and r-cages for r = 5, 6, 7, 8, and the Robertson graph. 相似文献
998.
It is known that the pattern containment order on permutations is not a partial well-order. Nevertheless, many naturally defined subsets of permutations are partially well-ordered, in which case they have a strong finite basis property. Several classes are proved to be partially well-ordered under pattern containment. Conversely, a number of new antichains are exhibited that give some insight as to where the boundary between partially well-ordered and not partially well-ordered classes lies. 相似文献
999.
Completing a series of works begun by Wiener [34], Paley and Wiener [28] and Ingham [9], a far-reaching generalization of
Parseval"s identity was obtained by Beurling [4] for nonharmonic Fourier series whose exponents satisfy a uniform gap condition.
Later this gap condition was weakened by Ullrich [33], Castro and Zuazua [5], Jaffard, Tucsnak and Zuazua [11] and then in
[2] in some particular cases. In this paper we prove a general theorem which contains all previous results. Furthermore, applying
a different method, we prove a variant of this theorem for nonharmonic Fourier series with vector coefficients. This result, partly motivated by control-theoretical applications, extends several earlier results obtained
in [15] and [2]. Finally, applying these results we obtain an optimal simultaneous observability theorem concerning a system
of vibrating strings.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
1000.
This contribution is concerned with a generalization of Itoh and Tsujii's algorithm for inversion in extension fields
. Unlike the original algorithm, the method introduced here uses a standard (or polynomial) basis representation. The inversion method is generalized for standard basis representation and relevant complexity expressions are established, consisting of the number of extension field multiplications and exponentiations. As the main contribution, for three important classes of fields we show that the Frobenius map can be explored to perform the exponentiations required for the inversion algorithm efficiently. As an important consequence, Itoh and Tsujii's inversion method shows almost the same practical complexity for standard basis as for normal basis representation for the field classes considered. 相似文献