A continuous function space with a Faber basis

Let be compact with #S=∞ and let C(S) be the set of all real continuous functions on S. We ask for an algebraic polynomial sequence (P_n)_n=0^∞ with deg P_n=n such that every fC(S) has a unique representation f=∑_i=0^∞ α_iP_i and call such a basis Faber basis. In the special case of , 0<q<1, we prove the existence of such a basis. A special orthonormal Faber basis is given by the so-called little q-Legendre polynomials. Moreover, these polynomials state an example with A(S_q)≠U(S_q)=C(S_q), where A(S_q) is the so-called Wiener algebra and U(S_q) is the set of all fC(S_q) which are uniquely represented by its Fourier series.     

A novel method for automated grid generation of ice shapes for local‐flow analysis

Modelling a complex geometry, such as ice roughness, plays a key role for the computational flow analysis over rough surfaces. This paper presents two enhancement ideas in modelling roughness geometry for local flow analysis over an aerodynamic surface. The first enhancement is use of the leading‐edge region of an airfoil as a perturbation to the parabola surface. The reasons for using a parabola as the base geometry are: it resembles the airfoil leading edge in the vicinity of its apex and it allows the use of a lower apparent Reynolds number. The second enhancement makes use of the Fourier analysis for modelling complex ice roughness on the leading edge of airfoils. This method of modelling provides an analytical expression, which describes the roughness geometry and the corresponding derivatives. The factors affecting the performance of the Fourier analysis were also investigated. It was shown that the number of sine–cosine terms and the number of control points are of importance. Finally, these enhancements are incorporated into an automated grid generation method over the airfoil ice accretion surface. The validations for both enhancements demonstrate that they can improve the current capability of grid generation and computational flow field analysis around airfoils with ice roughness. Copyright © 2004 John Wiley & Sons, Ltd.     

Apparatus for High-Resolution Solid Hydrogen Matrix Isolation Spectroscopy and Its Application

Apparatus integrating a Fourier transform-infrared (FT-IR) spectrometer and a mid-infrared difference frequency generation (DFG) laser spectrometer was built for the study of the matrix isolation spectrum in solid molecular hydrogen. A 3-cm-long molecular hydrogen crystal was grown in a liquid-helium Dewar, and its infrared absorption spectrum in the 1-5 μm region was recorded to test the system. The W₀(0) (ν=0←0, J=6←0) line around 2410 cm⁻¹ of solid hydrogen was investigated with the DFG laser spectroscopy. High-resolution matrix isolation spectrum of CO² co-deposited with hydrogen on a BaF₂ cold plate at liquid-helium temperature was studied.     

MC^2电缆介质结构及阻抗分析

本文将用数学和实验两种方法证实MC～2电缆不仅能保证特性阻抗变化不超出电缆技术规范。而且能保证在设计频率范围内电缆结构反射损耗最小。     

数字图像纯位相编码分析

研究了图像傅立叶变换过程中的振幅与位相问题，突出了位相在整个变换中的重要性，并利用双位相函数对图像进行加密编码和解码，计算机模拟表明双位相编码和解码能有效的抑制附加噪声。     

智能化红外焊缝检测仪的实时信号自相关分析

详细介绍了在改进红外焊缝检测仪的过程中实时信号的一种抗干扰方法－－自相关方法。重点离自相关方法的数学模型，软件框图及设计思想，并给出了实验结果。     

Cramér theorem on symmetric spaces of noncompact type

We prove the Cramér theorem forK-invariant Gaussian measures on irreducible symmetric spacesX=G/K withG semisimple noncompact. To do this we use a kind of Abel transform ofK-invariant measures onX.This research is supported by KBN Grant.     

Characterization of measures by potentials

Let μ be a measure in a Banach spaceE, f be an even function onR. We consider the potentialg(a)=f _E f(‖x?a‖)dμ(x). The question is as follows: For whichf does the potentialg determine μ uniquely? In this article we give answers in the cases whereE=l _∞ ⁿ and wheref(t)=|t| ^p andE is a finite dimensional Banach space with symmetric analytic norm. Calculating the Fourier transform of the functionf(‖x‖ _∞) we give a new proof of the J. Misiewicz's result that the functionf(‖x‖ _∞) is positive definite only iff is a constant function.     

On pasting -weights

Theorem 3 gives a condition when two -weights can be ``pasted' together to yield another -weight. It is subsequently used in Example 6 to give an example that shows that a necessary condition by Gohberg, Krupnik, and Spitkovsky is not sufficient.

     

Bias in modal parameters due to aliasing in the time domain

This paper deals with some aliasing effects in the time domain that can lead to unacceptable misestimations of modal parameters. When a frequency response function of a vibrating system is sampled and inverse Fourier transformed, the resulting impulse response is given by an infinite geometric series, the single term of which is the impulse response itself shifted in time. For this reason, some modal parameters, if estimated in the time domain, are biased; in particular, while the damping factor and the natural frequency are not influenced by the aliasing phenomenon, the magnitude and phase of the residue can be highly biased. Corrective terms are theoretically evaluated and their efficiency is shown in numerical simulations.

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Sommario In questo articolo e' presentato un metodo per correggere gli errori che si compiono nella stima di alcuni parametri modali, quando essi vengono ricavati nel dominio del tempo. Infatti se la funzione di risposta in frequenza e' ottenuta con eccitazioni particolari—quali ad esempio lo pseudo-random, lo stepped-sine a passo costante o lo sweep in frequenza-la risposta impulsiva, ottenuta per mezzo dell'antitrasformata discreta di Fourier, risulta periodica, con periodo pari all'inverso della spaziatura tra le righe spettrali. Cio' comporta un errore nella stima dell'ampiezza e della fase del residuo, mentre nessuna conseguenza si ha sulla frequenza naturale e sul fattore di smorzamento. L'errore sulle stime risulta tanto piu' grande, quanto meno smorzata e' la risposta impulsiva all'interno dell'intervallo di osservazione.Partendo dall'inviluppo e dalla fase istantanea dei segnali complessi, ottenibili per mezzo della trasformata di Hilbert, si sono ricavati i termini correttivi sia per il modulo, che per la fase del residuo. La validita' delle correzioni e' mostrata con esempi numerici.