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Fourier series

About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.


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Journal ArticleDOI
Z. Zhong1, E. T. Shang1
TL;DR: In this article, an exact analysis of a functionally graded piezothermo-electric rectangular plate that is simply supported, electrically grounded and isothermal on its four lateral edges is presented.
Abstract: This paper presents an exact analysis of a functionally graded piezothermo-electric rectangular plate that is simply supported, electrically grounded and isothermal on its four lateral edges. The governing equations are established for an orthotropic functionally graded piezothermoelectric plate under an assumption that the mechanical, electrical, and thermal properties of the material have the same exponential dependence on the thickness-coordinate. An exact three-dimensional general solution in the form of double Fourier series is derived for arbitrary distributions of combined mechanical, electrical, and thermal loadings at the top and bottom surfaces of the plate. Numerical results are presented for three special cases of uniformly distributed loads at the top and bottom surfaces of the plate, and the effect of truncation of the series on the accuracy of the solution is discussed.

58 citations

Journal ArticleDOI
TL;DR: In this article, the authors compare the algebra A* with the regular Banach space of smooth functions, showing that A* has many properties similar to those of A, but there are certain essential distinctions.
Abstract: Beurling's algebra \(A^*=\{f:\sum_{k=0}^{\infty} \sup_{k\le |m|} |\hat f (m)| < \infty \}\) is considered. A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener's algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means. Certainly, both algebras are used in some other areas. A* has many properties similar to those of A, but there are certain essential distinctions. A* is a regular Banach algebra, its space of maximal ideals coincides with \([-\pi,\pi],\) and its dual space is indicated. Analogs of Herz's and Wiener-Ditkin's theorems hold. Quantitative parameters in an analog of the Beurling-Pollard theorem differ from those for A. Several inclusion results comparing the algebra A* with certain Banach spaces of smooth functions are given. Some special properties of the analogous space for Fourier transforms on the real axis are presented. The paper ends with a summary of some open problems.

58 citations

Proceedings ArticleDOI
12 May 1998
TL;DR: A full generalization is presented where both the autocorrelation function and power spectral density are defined in terms of a general basis set and a partial generalization where the density is the Fourier transform of the characteristic function but the characteristicfunction is defined in Terms of an arbitrary basis set.
Abstract: We generalize the Wiener-Khinchin theorem. A full generalization is presented where both the autocorrelation function and power spectral density are defined in terms of a general basis set. In addition, we present a partial generalization where the density is the Fourier transform of the autocorrelation function but the autocorrelation function is defined in terms of an arbitrary basis set. Both the deterministic and random cases are considered.

57 citations

Posted Content
TL;DR: In this paper, the authors introduce moduli spaces of abelian varieties which are arithmetic models of Shimura varieties attached to unitary groups of signature (n-1, 1).
Abstract: We introduce moduli spaces of abelian varieties which are arithmetic models of Shimura varieties attached to unitary groups of signature (n-1, 1). We define arithmetic cycles on these models and study their intersection behaviour. In particular, in the non-degenerate case, we prove a relation between their intersection numbers and Fourier coefficients of the derivative at s=0 of a certain incoherent Eisenstein series for the group U(n, n). This is done by relating the arithmetic cycles to their formal counterpart from Part I via non-archimedean uniformization, and by relating the Fourier coefficients to the derivatives of representation densities of hermitian forms. The result then follows from the main theorem of Part I and a counting argument.

57 citations

Journal ArticleDOI
TL;DR: In this paper, a Haar Wavelet Discretization (HWD) method is presented for free vibration analysis of functionally graded (FG) spherical and parabolic shells of revolution with arbitrary boundary conditions.
Abstract: The objective of this work is to present a Haar Wavelet Discretization (HWD) method-based solution approach for the free vibration analysis of functionally graded (FG) spherical and parabolic shells of revolution with arbitrary boundary conditions. The first-order shear deformation theory is adopted to account for the transverse shear effect and rotary inertia of the shell structures. Haar wavelet and their integral and Fourier series are selected as the basis functions for the variables and their derivatives in the meridional and circumferential directions, respectively. The constants appearing in the integrating process are determined by boundary conditions, and thus the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations. The proposed approach directly deals with nodal values and does not require special formula for evaluating system matrices. Also, the convenience of the approach is shown in handling general boundary conditions. Numerical examples are given for the free vibrations of FG shells with different combinations of classical and elastic boundary conditions. Effects of spring stiffness values and the material power-law distributions on the natural frequencies of shells are also discussed. Some new results for the considered shell structures are presented, which may serve as benchmark solutions.

57 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023270
2022702
2021511
2020510
2019589
2018580