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11.
In this paper we present a new limit relation for the equidistant Lagrange interpolation polynomials to |x|, (0, 1] on the internal [–1, 1]. The result extends a well-known result of D. L. Berman and S. M. Losinskii. Furthermore, we briefly discuss on a possible connection of the limit relation to another prominent constant in best uniform polynomial approximation for |x| - the so-called Bernstein constant. 相似文献
12.
Solvothermal reaction of [WS4]2-with CuCN and trithiocyanuric acid(L1) in orga-nic solvents gave rise to a new W/Cu/S polymer with a 2D anionic network,namely [Et4N]2[WS4Cu3(C3N3S3H1.5)2](1).The anionic layer of 1 is constructed by the T-shaped {WS4Cu3} subunits as nodes and L1 as linkers and features a(4,4) topology.Both 1 and its isomorphous compound [Et4N]2[MoS4Cu3(C3N3S3H1.5)2](2) have been fully characterized by X-ray crystal analysis,IR and microanalyses.Compounds 1 and 2 show optical transitions with band gaps of 2.17 and 1.84 eV,respectively. 相似文献
13.
Synchronization of complex community networks with nonidentical nodes and adaptive coupling strength
In this Letter, the complex dynamical networks with community structure and nonidentical nodes are considered. The globally asymptotical synchronization of the time-delayed complex community networks onto any uniformly smooth state is studied. Some simple and useful criteria are derived by constructing an effective control scheme and adjusting automatically the adaptive coupling strength. Finally, the developed techniques are applied to two complex community networks which are respectively synchronized to a chaotic trajectory and a periodic orbit, and numerical simulations are provided to show the feasibility of the developed methods. 相似文献
14.
15.
V. A. Ivnitskii 《Queueing Systems》1995,19(3):319-329
A queueing network consisting of multiserver nodes with different sources of customers is considered. We investigate stationary probability distributions of network states. Their invariance with respect to the functional form of distributions of input and service processes is established under fixed expectations of these distributions and service discipline when any entering customer has a preemptive resume discipline. 相似文献
16.
S.M.Lozinskii指出了函数|x|基于等距节点的Lagrange插值多项式在零点的收敛速度.2000年,M.Revers把S.M.Lozinskii的结果推广到|x|~α(0<α1).本文考虑的是把等距节点改为修改的Chebyshev节点,从而把零点处的收敛速度从M.Revers证明的O(n-α)提高O(n-2α). 相似文献
17.
Miguel Ángel García-MarchFernando Giménez Francisco R. VillatoroJezabel Pérez Pedro Fernández de Córdoba 《Applied mathematics and computation》2011,217(18):7427-7431
A new and straightforward proof of the unisolvability of the problem of multivariate polynomial interpolation based on Coatmèlec configurations of nodes, a class of properly posed set of nodes defined by hyperplanes, is presented. The proof generalizes a previous one for the bivariate case and is based on a recursive reduction of the problem to simpler ones following the so-called Radon-Bézout process. 相似文献
18.
Len Bos 《Journal of Computational and Applied Mathematics》2011,236(4):504-510
It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut’s rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results suggest that the Lebesgue constant behaves similarly for interpolation at Chebyshev as well as logarithmically distributed nodes. 相似文献
19.
The goal here is to give a simple approach to a quadrature formula based on the divided diffierences of the integrand at the zeros of the nth Chebyshev polynomial of the first kind,and those of the(n-1)st Chebyshev polynomial of the second kind.Explicit expressions for the corresponding coefficients of the quadrature rule are also found after expansions of the divided diffierences,which was proposed in[14]. 相似文献
20.
A generalization of the Hilbert basis theorem in the geometric setting is proposed. It asserts that, for any well-describable (in a certain sense) family of polynomials, there exists a number C such that if P is an everywhere dense (in a certain sense) subfamily of this family, a is an arbitrary point, and the first C polynomials in any sequence from P vanish at the point a, then all polynomials from P vanish at a. 相似文献