Comments on "A Note on the General Solution of the Two-Dimensional Linear Elasticity Problem in Polar Coordinates"

AIAA Journal ◽  
1968 ◽  
Vol 6 (3) ◽  
pp. 568-569 ◽  
Author(s):  
B. I. HYMAN
Keyword(s):  
General Solution ◽  
Linear Elasticity ◽  
Elasticity Problem ◽  
Polar Coordinates ◽  
Two Dimensional

A general solution method for two-dimensional nonplanar oxidation

1983 ◽  
Vol 30 (9) ◽  
pp. 993-998 ◽  
Author(s):  
Daeje Chin ◽  
Soo-Young Oh ◽  
R.W. Dutton
Keyword(s):  
General Solution ◽  
Solution Method ◽  
Two Dimensional

scholarly journals The Solvability of a Class of Convolution Equations Associated with 2D FRFT

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1928
Author(s):  
Zhen-Wei Li ◽  
Wen-Biao Gao ◽  
Bing-Zhao Li
Keyword(s):  
Fourier Transform ◽  
Convolution Operator ◽  
Fractional Fourier Transform ◽  
Hankel Transform ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Spatial Shift ◽  
Fractional Hankel Transform ◽  
The Relationship ◽  
Convolution Equations

In this paper, the solvability of a class of convolution equations is discussed by using two-dimensional (2D) fractional Fourier transform (FRFT) in polar coordinates. Firstly, we generalize the 2D FRFT to the polar coordinates setting. The relationship between 2D FRFT and fractional Hankel transform (FRHT) is derived. Secondly, the spatial shift and multiplication theorems for 2D FRFT are proposed by using this relationship. Thirdly, in order to analyze the solvability of the convolution equations, a novel convolution operator for 2D FRFT is proposed, and the corresponding convolution theorem is investigated. Finally, based on the proposed theorems, the solvability of the convolution equations is studied.

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