Hermite插值多项式的导数逼近函数的导数

给出基于混合型Jacobi气点的Hermite插值多项式的导数和函数的县数之间的偏差的点态估计．     

Cayley-Bacharach定理在沿平面代数曲线插值问题中的应用

1 引 言 本文是讨论关于沿平面代数曲线的Lagrange插值问题,该问题与在二维实平面R~2上的二元Lagrange插值有关.设n为非负整数并且e_n=1/2(n+1)(n_2).P_n代表所有全     

An algebraic approach to approximate evaluation of a polynomial on a set of real points

The previous best algorithm for approximate evaluation of a polynomial on a real set was due to Rokhlin and required of the order ofmu+nu ³ infinite precision arithmetic operations to approximate [on a fixed bounded setX(m) ofm+1 real points] a degreen polynomial within the error bound . We develop an approximation algorithm which exploits algebraic computational techniques and decreases Rokhlin's record estimate toO(mlog² u+nmin-u, logn}). For logu=o(logn), this result may also be favorably compared with the record boundO(m+n)log² n) on the complexity of the exact multipoint polynomial evaluation. The new algorithm can be performed in the fields (or rings) generated by the input values, which enables us to decrease the precision of the computations [by using modular (residue) arithmetic] and to simplify our computations further in the case whereu=O(logn). Our algorithm allows NC and simultaneously processor efficient parallel implementation. Because of the fundamental nature of the multipoint polynomial evaluation, our results have further applications to numerical and algebraic computational problems. In passing, we also show a substantial improvement in the Chinese remainder algorithm for integers based on incorporating Kaminski's fast residue computation.     

“Spatial nodes” in discrete location problems

Discrete location models often assume an underlying network where demands originate at point nodes. To apply these models to planar regions with continuously distributed demand, the region is usually partitioned into zones and the demand from each zone is assumed to originate at a point, usually the zone centroid. Thus, the point node in the underlying network represents a spatial zone with a finite area. This paper examines the effect of approximating these spatial nodes by point nodes. In some problem scenarios, the approximation does not affect the solution. However, especially when the locational criterion includes the consideration of intra-zonal travel cost variances (e.g. travel time variance) and demands may originate anywhere within zones of nonzero area, point nodes do not give an accurate evaluation of the performance of a locational design. To illustrate the application of the concept of spatial nodes, a model is formulated for locatingp (fire-fighting) units in a region having continuously distributed demand with the objective of minimizing a nonlinear function of arrival times of the first and second closest units to any (fire) incident. A heuristic site-substitution procedure is presented that solves the formulated model.     

基于全局可达点的中国教育网平均最短路径近似算法

平均最短路径长度是复杂网络的一个重要特性,但由于计算时间的限制,求解大规模网络的平均最短路径长度很困难.以中国教育网数据为例,分析了中国教育网的拓扑结构,提出了全局可达点和局部可达点的概念,发现整个网络的平均最短路径长度由全局可达点决定.通过分析全局可达点的平均单源最短路径长度分布,发现整个网络的平均最短路径长度可由少数随机选取的点的平均最短路径长度来近似.通过三个网络验证了近似计算方法的有效性,并通过随机选取的数百个点,计算得到了含49041472个点的中国教育网的平均最短路径长度在14-15之间.     

(0, 2) Pál-type interpolation on a circle in the complex plane involving Möbius transforms

We study the regularity of certain (0,?2) Pál-type interpolation problems involving the Möbius transforms of the zeros of z ²ⁿ ?ρ ²ⁿ to the circle ∣z∣?=?ρ′.     

Guest-Responsive Reversible Electron Transfer in a Crystalline Porous Framework Supported by a Dynamic Building Node

We demonstrate a redox-active, crystalline donor–acceptor (D-A) assembly in which the electron transfer (ET) process can be reversibly switched. This ET process, induced by a guest-responsive structural transformation at room temperature, is realized in a porous, metal–organic framework (MOF), having anthracene (D)–naphthalenediimide (A) as struts. A control MOF structure obtained by a solvent-assisted linker exchange (SALE) method, replacing an acceptor strut with a neutral one, supported the switchable electronic states in the D-A MOF. Combined investigations with X-ray diffraction, spectroscopy, and theoretical analyses revealed the dynamic metal paddle-wheel node as a critical unit for controlling structural flexibility and the corresponding unprecedented ET process.     

Limiting theorems for the nodes in binary search trees

We consider three random variables X_n, Y_n and Z_n, which represent the numbers of the nodes with 0, 1, and 2 children, in the binary search trees of size n. The expectation and variance of the three above random variables are got, and it is also shown that X_n, Y_n and Z_n are all asymptotically normal as n→∞by applying the contraction method.     

The numerical solution of problems in calculus of variation using Chebyshev finite difference method

The Chebyshev finite difference method is used for finding the solution of the ordinary differential equations which arise from problems of calculus of variations. Our approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference scheme. Some numerical results are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and yields very accurate results.     

Reducing the bias and uncertainty of free energy estimates by using regression to fit thermodynamic integration data

This report presents the application of polynomial regression for estimating free energy differences using thermodynamic integration data, i.e., slope of free energy with respect to the switching variable λ. We employ linear regression to construct a polynomial that optimally fits the thermodynamic integration data, and thus reduces the bias and uncertainty of the resulting free energy estimate. Two test systems with analytical solutions were used to verify the accuracy and precision of the approach. Our results suggest that use of regression with high degree of polynomials provides the most accurate free energy difference estimates, but often with slightly larger uncertainty, compared to commonly used quadrature techniques. High degree polynomials possess the flexibility to closely fit the thermodynamic integration data but are often sensitive to small changes in the data points. Thus, we also used Chebyshev nodes to guide in the selection of nonequidistant λ values for use in thermodynamic integration. We conclude that polynomial regression with nonequidistant λ values delivers the most accurate and precise free energy estimates for thermodynamic integration data for the systems considered here. Software and documentation is available at http://www.phys.uidaho.edu/ytreberg/software . © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009