Cosine Series Representation of 3D Curves

2013 ◽  
pp. 181-202
Keyword(s):  
Series Representation ◽  
Cosine Series

Free In-Plane Vibration Analysis of Rectangular Plates With Elastically Point-Supported Edges

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Jingtao Du ◽  
Zhigang Liu ◽  
Wen L. Li ◽  
Xuefeng Zhang ◽  
Wanyou Li
Keyword(s):  
Fourier Series ◽  
Vibration Analysis ◽  
Series Representation ◽  
Fourier Method ◽  
Rectangular Plates ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Plane Vibration ◽  
Auxiliary Functions ◽  
Time In Literature

In comparison with the transverse vibrations of rectangular plates, far less attention has been paid to the in-plane vibrations even though they may play an equally important role in affecting the vibrations and power flows in a built-up structure. In this paper, a generalized Fourier method is presented for the in-plane vibration analysis of rectangular plates with any number of elastic point supports along the edges. Displacement constraints or rigid point supports can be considered as the special case when the stiffnesses of the supporting springs tend to infinity. In the current solution, each of the in-plane displacement components is expressed as a 2D Fourier series plus four auxiliary functions in the form of the product of a polynomial times a Fourier cosine series. These auxiliary functions are introduced to ensure and improve the convergence of the Fourier series solution by eliminating all the discontinuities potentially associated with the original displacements and their partial derivatives along the edges when they are periodically extended onto the entire x-y plane as mathematically implied by the Fourier series representation. This analytical solution is exact in the sense that it explicitly satisfies, to any specified accuracy, both the governing equations and the boundary conditions. Numerical examples are given about the in-plane modes of rectangular plates with different edge supports. It appears that these modal data are presented for the first time in literature, and may be used as a benchmark to evaluate other solution methodologies. Some subtleties are discussed about corner support arrangements.

FOURIER SERIES REPRESENTATION OF FRACTAL INTERPOLATION FUNCTION

Fractals ◽  
2020 ◽  
Vol 28 (04) ◽  
pp. 2050063
Author(s):  
XUEZAI PAN ◽  
MINGGANG WANG ◽  
XUDONG SHANG
Keyword(s):  
Fourier Series ◽  
Series Representation ◽  
Fractal Interpolation ◽  
Interpolation Function ◽  
Sine Series ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fractal Interpolation Function ◽  
Fourier Cosine Series ◽  
Fourier Sine Series

The purpose of this research is to show how the complicated and irregular fractal interpolation function is represented by Fourier series. First, on the closed interval [0,1], even prolongation is operated to the fractal interpolation function generated by iterated function system constituted by affine transform and Fourier cosine series representation of fractal interpolation function is proved. Second, for fractal interpolation function, odd prolongation is done and Fourier sine series formula of fractal interpolation function is proved. Final, Fourier series expansion of fractal interpolation function on the closed interval [Formula: see text] is proved. The result shows that complex fractal interpolation function can be represented by Fourier sine series and Fourier cosine series, so relatively simple Fourier series can be used to represent relatively complicated fractal interpolation function.

scholarly journals Cosine series representation of 3D curves and its application to white matter fiber bundles in diffusion tensor imaging

2010 ◽  
Vol 3 (1) ◽  
pp. 69-80 ◽  
Author(s):  
Nagesh Adluru ◽  
Andrew L. Alexander ◽  
Moo K. Chung ◽  
Janet E. Lainhart ◽  
Mariana Lazar ◽  
...  
Keyword(s):  
Diffusion Tensor Imaging ◽  
White Matter ◽  
Diffusion Tensor ◽  
Series Representation ◽  
Fiber Bundles ◽  
Cosine Series

scholarly journals R-GROUP AND WHITTAKER SPACE OF SOME GENUINE REPRESENTATIONS

2021 ◽  
pp. 1-61
Author(s):  
Fan Gao
Keyword(s):  
Series Representation ◽  
Principal Series ◽  
Symplectic Groups ◽  
Principal Series Representation ◽  
Connected Group ◽  
Covering Group ◽  
Simply Connected

Abstract For a unitary unramified genuine principal series representation of a covering group, we study the associated R-group. We prove a formula relating the R-group to the dimension of the Whittaker space for the irreducible constituents of such a principal series representation. Moreover, for certain saturated covers of a semisimple simply connected group, we also propose a simpler conjectural formula for such dimensions. This latter conjectural formula is verified in several cases, including covers of the symplectic groups.

Randomized Trees for Time Series Representation and Similarity

2021 ◽  
pp. 108097
Author(s):  
Berk Görgülü ◽  
Mustafa Gökçe Baydoğan
Keyword(s):  
Time Series ◽  
Series Representation

Representations induced from the Zelevinsky segment and discrete series in the half-integral case

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ivan Matić
Keyword(s):  
Linear Group ◽  
Local Field ◽  
General Linear Group ◽  
Discrete Series ◽  
Series Representation ◽  
General Linear ◽  
Composition Series ◽  
Induced Representations ◽  
Discrete Series Representation

AbstractLet {G_{n}} denote either the group {\mathrm{SO}(2n+1,F)} or {\mathrm{Sp}(2n,F)} over a non-archimedean local field of characteristic different than two. We study parabolically induced representations of the form {\langle\Delta\rangle\rtimes\sigma}, where {\langle\Delta\rangle} denotes the Zelevinsky segment representation of the general linear group attached to the segment Δ, and σ denotes a discrete series representation of {G_{n}}. We determine the composition series of {\langle\Delta\rangle\rtimes\sigma} in the case when {\Delta=[\nu^{a}\rho,\nu^{b}\rho]} where a is half-integral.

The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1

1973 ◽  
Vol 59 (4) ◽  
pp. 721-736 ◽  
Author(s):  
Harvey Segur
Keyword(s):  
Water Waves ◽  
Large Time ◽  
Vries Equation ◽  
Asymptotic Properties ◽  
Series Representation ◽  
Convergent Series ◽  
Asymptotic Results ◽  
De Vries ◽  
Method Of Solution

The method of solution of the Korteweg–de Vries equation outlined by Gardneret al.(1967) is exploited to solve the equation. A convergent series representation of the solution is obtained, and previously known aspects of the solution are related to this general form. Asymptotic properties of the solution, valid for large time, are examined. Several simple methods of obtaining approximate asymptotic results are considered.

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