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991.
Antonio Aizpuru Francisco J. Garcí a-Pacheco Consuelo Pé rez-Eslava 《Proceedings of the American Mathematical Society》2007,135(11):3571-3579
Some classical results about uniform convergence of unconditionally convergent series are generalized to weakly unconditionally Cauchy series by means of the matrix summability method for regular matrices.
992.
An improved hybrid Cartesian/immersed boundary method is proposed based on ghost point treatment. A second‐order Taylor series expansion is used to evaluate the values at the ghost points, and an inverse distance weighting method to interpolate the values due to its properties of preserving local extrema and smooth reconstruction. The present method effectively eliminates numerical instabilities caused by matrix inversion and flexibly adopts the interpolation in the vicinity of the boundary. Some typical fluid–solid flows, including viscous flow past a circular cylinder, a sphere, two cylinders in a side‐by‐side arrangement, and an array of 18 staggered cylinders, are examined. These benchmark simulations reasonably indicate the reliability and capability of the present method. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
993.
Andreas Galka Tohru Ozaki Jorge Bosch Bayard Okito Yamashita 《Journal of statistical physics》2006,124(5):1275-1315
We address the issue of inferring the connectivity structure of spatially extended dynamical systems by estimation of mutual information between pairs of sites. The well-known problems resulting from correlations within and between the time series are addressed by explicit temporal and spatial modelling steps which aim at approximately removing all spatial and temporal correlations, i.e. at whitening the data, such that it is replaced by spatiotemporal innovations; this approach provides a link to the maximum-likelihood method and, for appropriately chosen models, removes the problem of estimating probability distributions of unknown, possibly complicated shape. A parsimonious multivariate autoregressive model based on nearest-neighbour interactions is employed. Mutual information can be reinterpreted in the framework of dynamical model comparison (i.e. likelihood ratio testing), since it is shown to be equivalent to the difference of the log-likelihoods of coupled and uncoupled models for a pair of sites, and a parametric estimator of mutual information can be derived. We also discuss, within the framework of model comparison, the relationship between the coefficient of linear correlation and mutual information. The practical application of this methodology is demonstrated for simulated multivariate time series generated by a stochastic coupled-map lattice. The parsimonious modelling approach is compared to general multivariate autoregressive modelling and to Independent Component Analysis (ICA). 相似文献
994.
给出了一种新的求解含时薛定谔方程的伪谱泰勒级数方法,该方法把氢原子的含时波函数在少量分布稀疏的网格点上做拟合.结合基于泰勒级数展开的时间演化法,用相对简单的计算得到了包括时间演化步长△t高阶项贡献的含时波函数.并将该方法用于强激光场中氢原子含时波函数和高次谐波谱的计算,得到了与经典三步模型解释以及实验现象相符的结果. 相似文献
995.
Christian Brouder Alessandra Frabetti Christian Krattenthaler 《Advances in Mathematics》2006,200(2):479-524
This paper deals with two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the group law being multiplication of series, while the second is the set of formal diffeomorphisms with the group law being a composition of series. The motivation to introduce these Hopf algebras comes from the study of formal series with non-commutative coefficients. Invertible series with non-commutative coefficients still form a group, and we interpret the corresponding new non-commutative Hopf algebra as an alternative to the natural Hopf algebra given by the co-ordinate ring of the group, which has the advantage of being functorial in the algebra of coefficients. For the formal diffeomorphisms with non-commutative coefficients, this interpretation fails, because in this case the composition is not associative anymore. However, we show that for the dual non-commutative algebra there exists a natural co-associative co-product defining a non-commutative Hopf algebra. Moreover, we give an explicit formula for the antipode, which represents a non-commutative version of the Lagrange inversion formula, and we show that its coefficients are related to planar binary trees. Then we extend these results to the semi-direct co-product of the previous Hopf algebras, and to series in several variables. Finally, we show how the non-commutative Hopf algebras of formal series are related to some renormalization Hopf algebras, which are combinatorial Hopf algebras motivated by the renormalization procedure in quantum field theory, and to the renormalization functor given by the double-tensor algebra on a bi-algebra. 相似文献
996.
利用生成函数解决了从n个元素的集合中任意重复选取r个元素且这r个元素中含有不同元素的个数一定时,所构成的不同r-序列的方法数. 相似文献
997.
Guoce Xin 《Journal of Combinatorial Theory, Series A》2007,114(8):1526-1544
By studying the reciprocity property of linear Diophantine systems in light of Malcev-Neumann series, we present in this paper a new approach to and a generalization of Stanley's monster reciprocity theorem. A formula for the “error term” is given in the case when the system does not have the reciprocity property. We also give an inductive proof of Stanley's reciprocity theorem for linear homogeneous Diophantine systems. 相似文献
998.
Lei Wu Hongru Yang Xudong Li Bin Yang Gaoping Li 《Journal of Quantitative Spectroscopy & Radiative Transfer》2007,108(1):54-64
The scattering patterns and optical properties of large spherical bubbles in water are calculated by both Geometrical-optics theory and Debye-series expansion of the Mie amplitudes. In the Geometrical-optics calculations, the wave-front spreading factor and phase information are all taken into consideration. A detailed comparison between the two methods is presented. It is found that scattering patterns calculated from the Geometrical-optics approach agree reasonably with those obtained by Debye series when the size parameter is larger than approximately 400. In the case of scattering properties, the Geometrical-optics method can produce reliable results with the Debye expansion for size parameters larger than approximately 50. The Geometrical-optics results without the phase interferences are also reliable, but it cannot display the oscillations and the ripple structure as a function of size parameter. 相似文献
999.
尚丽娜 《数学的实践与认识》2007,37(18):151-154
在较一般的指数条件下,研究了全平面上零级Dirichlet级数的增长性,得到了一些新的结果. 相似文献
1000.
J. Marshall Ash Sh. T. Tetunashvili 《Proceedings of the American Mathematical Society》2006,134(6):1681-1686
If at each point of a set of positive Lebesgue measure every rearrangement of a multiple trigonometric series square converges to a finite value, then that series is the Fourier series of a function to which it converges uniformly. If there is at least one point at which every rearrangement of a multiple Walsh series square converges to a finite value, then that series is the Walsh-Fourier series of a function to which it converges uniformly.