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1.
Admissible slopes for monotone and convex interpolation 总被引:1,自引:0,他引:1
Summary In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of variousC
1 interpolants which ensure a desirable shape. We discuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials,C
1 monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions. 相似文献
2.
Ioana Dumitriu Alan Edelman 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2005,41(6):1083-1099
In this paper we examine the zero and first order eigenvalue fluctuations for the β-Hermite and β-Laguerre ensembles, using tridiagonal matrix models, in the limit as β→∞. We prove that the fluctuations are described by multivariate Gaussians of covariance O(1/β), centered at the roots of a corresponding Hermite (Laguerre) polynomial. The covariance matrix itself is expressed as combinations of Hermite or Laguerre polynomials respectively.We show that the approximations are of real value even for small β; we can use them to approximate the true functions even for the traditional β=1,2,4 values. 相似文献
3.
Consider a labeled convex n-gon in the plane and a point x in general position in the interior. We associate with this a collection (x) of 3-element sets, namely those 3-element subsets of the vertices which contain x in their interior. We investigate the problem of characterizing those collections of subsets which can be represented in this matter. We give a complete characterization of this and a related problem.School of Mathematics, University of Minnesota, Minneapolis, MN 55455. This work was supported in part by NSF grant DMS-8700995.Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England. Work done while Hill Visiting Professor at the University of Minnesota. 相似文献
4.
Let Z be a centrally symmetric polygon with integer side lengths. We answer the following two questions:
- When is the associated discriminantal hyperplane arrangementfree in the sense of Saito and Terao?
- When areall of the tilings of Z by unit rhombicoherent in the sense of Billera and Sturmfels?
5.
Two methods for the synthesis of unsubstituted diethyl cyclopropylphosphonate are described. One method is a reaction between cyclopropylmagnesium bromide and diethyl chlorophosphite to give diethyl cyclopropylphosphonite, followed by oxidation with sodium periodate to the corresponding phosphonate. Alternatively, diethyl cyclopropylphosphonite was reacted with elemental sulfur or selenium to give the thio and seleno analogs, respectively. The second method involves exclusive 1,3‐elimination of HBr from diethyl 3‐bromopropylphosphonate. This method can be directed to either the 1,2‐ or the 1,3‐elimination reaction, leading to propenylphosphonate or cyclopropylphosphonate, depending on the solvent used. 相似文献
6.
U. V. Valiev J. B. Gruber D. K. Sardar B. Zandi I. S. Kachur A. K. Mukhammadiev V. G. Piryatinskaya V. Yu. Sokolov I. S. Edelman 《Physics of the Solid State》2007,49(1):91-98
The Zeeman effect in the 7 F 6 → 5 D 4 absorption band of the Tb3+ ion in the paramagnetic garnets Tb3Ga5O12 and Tb3Al5O12 was studied. The field dependences of the Zeeman splitting of some absorption lines are found to exhibit unusual behavior: as the magnetic field increases, the band splitting decreases rather than increases. Symmetry analysis relates these lines to 4f → 4f electron transitions of the doublet-quasi-doublet or quasi-doublet-doublet type, for which the field dependences of the splitting differ radically from the well-known field dependences of the Zeeman splitting for quasi-doublet-quasi-doublet or quasi-doublet-singlet transitions in a longitudinal magnetic field. 相似文献
7.
We consider a chain of nonlinear oscillators with long-range interaction of the type 1l(1+alpha), where l is a distance between oscillators and 0相似文献
8.
9.
I. S. Edelman O. S. Ivanova V. N. Zabluda D. A. Velikanov V. I. Zaikovskii S. A. Stepanov E. A. Petrakovskaya R. D. Ivantsov 《Bulletin of the Russian Academy of Sciences: Physics》2009,73(7):968-970
Germanate glasses doped simultaneously with Fe and rare earth elements Gd, Tb, Dy, and Ho in concentrations of several percent have been investigated. It is shown that the phase state of paramagnetic elements changes from isolated ions and small clusters in the initial glass to crystalline magnetic nanoparticles in the samples subjected to heat treatments. The field dependences of the magnetization of such samples are characterized by magnetic saturation in fields of about 1 kOe and large Faraday rotation in the near-IR region (up to 10 deg/cm in the range from 700 to 800 nm). 相似文献
10.
One of the greatest challenges facing the cognitive sciences is to explain what it means to know a language, and how the knowledge of language is acquired. The dominant approach to this challenge within linguistics has been to seek an efficient characterization of the wealth of documented structural properties of language in terms of a compact generative grammar—ideally, the minimal necessary set of innate, universal, exception-less, highly abstract rules that jointly generate all and only the observed phenomena and are common to all human languages. We review developmental, behavioral, and computational evidence that seems to favor an alternative view of language, according to which linguistic structures are generated by a large, open set of constructions of varying degrees of abstraction and complexity, which embody both form and meaning and are acquired through socially situated experience in a given language community, by probabilistic learning algorithms that resemble those at work in other cognitive modalities. 相似文献