One-Dimensional Fourier Series

2021 ◽  
pp. 1-31
Author(s):  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
One Dimensional

scholarly journals An approach for one dimensional periodic arbitrary lithography based on Fourier series

2020 ◽  
Author(s):  
Mahdi Kordi ◽  
Seyed Mohammad Reza Vaziri ◽  
Fahimeh Armin ◽  
Mojtaba Joodaki
Keyword(s):  
Fourier Series ◽  
One Dimensional

Nonlinear Inverse Heat Conduction With a Moving Boundary: Heat Flux and Surface Recession Estimation

1999 ◽  
Vol 121 (3) ◽  
pp. 708-711 ◽  
Author(s):  
V. Petrushevsky ◽  
S. Cohen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fourier Series ◽  
Heat Conduction ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Variable Order ◽  
Inverse Heat Conduction ◽  
One Dimensional

A one-dimensional, nonlinear inverse heat conduction problem with surface ablation is considered. In-depth temperature measurements are used to restore the heat flux and the surface recession history. The presented method elaborates a whole domain, parameter estimation approach with the heat flux approximated by Fourier series. Two versions of the method are proposed: with a constant order and with a variable order of the Fourier series. The surface recession is found by a direct heat transfer solution under the estimated heat flux.

scholarly journals Classical-quantum versus exact quantum results for a particle in a box

2012 ◽  
Vol 34 (2) ◽  
Author(s):  
Salvatore De Vincenzo
Keyword(s):  
Quantum Mechanics ◽  
Fourier Series ◽  
Classical Particle ◽  
Quantization Rule ◽  
One Dimensional ◽  
Exact Quantum ◽  
Classical Quantum

The problems of a free classical particle inside a one-dimensional box: (i) with impenetrable walls and (ii) with penetrable walls, were considered. For each problem, the classical amplitude and mechanical frequency of the T -th harmonic of the motion of the particle were identified from the Fourier series of the position function. After using the Bohr-Sommerfeld-Wilson quantization rule, the respective quantized amplitudes and frequencies (i.e., as a function of the quantum label n ) were obtained. Finally, the classical-quantum results were compared to those obtained from modern quantum mechanics, and a clear correspondence was observed in the limit of n » τ.

Uniform estimates for families of singular integrals and double Fourier series

1986 ◽  
Vol 41 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Elena Prestini
Keyword(s):  
Fourier Series ◽  
Hilbert Transform ◽  
Singular Integrals ◽  
Double Fourier Series ◽  
Variable Coefficients ◽  
Partial Sums ◽  
One Dimensional ◽  
Uniform Estimates ◽  
Almost Everywhere ◽  
The One

AbstractIt is an open problem to establish whether or not the partial sums operator SNN2f(x, y) of the Fourier series of f ∈ Lp, 1 < p < 2, converges to the function almost everywhere as N → ∞. The purpose of this paper is to identify the operator that, in this problem of a.e. convergence of Fourier series, plays the central role that the maximal Hilbert transform plays in the one-dimensional case. This operator appears to be a singular integral with variable coefficients which is a variant of the maximal double Hilbert transform.

A robust one-dimensional regressive discrete Fourier series

2010 ◽  
Vol 24 (3) ◽  
pp. 835-840 ◽  
Author(s):  
José Roberto de França Arruda
Keyword(s):  
Fourier Series ◽  
Discrete Fourier Series ◽  
One Dimensional

scholarly journals Mechanical and Thermal Stresses in a FGPM Hollow Cylinder due to Radially Symmetric Loads

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
M. Jabbari ◽  
M. Meshkini ◽  
M. R. Eslami
Keyword(s):  
Fourier Series ◽  
Heat Conduction ◽  
Steady State ◽  
Material Properties ◽  
Radial Direction ◽  
Thermal Stresses ◽  
Functionally Graded ◽  
Power Functions ◽  
One Dimensional ◽  
Complex Fourier Series

The general solution of steady-state on one-dimensional Axisymmetric mechanical and thermal stresses for a hollow thick made of cylinder Functionally Graded porous material is developed. Temperature, as functions of the radial direction with general thermal and mechanical boundary-conditions on the inside and outside surfaces. A standard method is used to solve a nonhomogenous system of partial differential Navier equations with nonconstant coefficients, using complex Fourier series, rather power functions method and solve the heat conduction. The material properties, except poisson's ratio, are assumed to depend on the variable , and they are expressed as power functions of .

scholarly journals Generalization of the Hardy-Littlewood theorem on Fourier series

2021 ◽  
Vol 104 (4) ◽  
pp. 49-55
Author(s):  
S. Bitimkhan ◽  
Keyword(s):  
Fourier Series ◽  
Trigonometric Series ◽  
Lebesgue Space ◽  
Fourier Coefficients ◽  
Double Fourier Series ◽  
Function Spaces ◽  
Dimensional Case ◽  
One Dimensional ◽  
Littlewood Theorem ◽  
The One

In the theory of one-dimensional trigonometric series, the Hardy-Littlewood theorem on Fourier series with monotone Fourier coefficients is of great importance. Multidimensional versions of this theorem have been extensively studied for the Lebesgue space. Significant differences of the multidimensional variants in comparison with the one-dimensional case are revealed and the strengthening of this theorem is obtained. The Hardy-Littlewood theorem is also generalized for various function spaces and various types of monotonicity of the series coefficients. Some of these generalizations can be seen in works of M.F. Timan, M.I. Dyachenko, E.D. Nursultanov, S. Tikhonov. In this paper, a generalization of the Hardy-Littlewood theorem for double Fourier series of a function in the space L_qϕ(L_q)(0,2π]^2 is obtained.

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