symmetry criterion
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2019 ◽  
Vol 9 (2) ◽  
pp. 20-25
Author(s):  
Parastoo Kabi-Nejad ◽  

In the present paper, we derive generalized symmetries of order three of the Camassa–Holm equation by infinite prolongation of a generalized vector field and applying infinitesimal symmetry criterion. In addition, one-dimensional optimal system of Lie subalgebras investigated by applying the adjoint representation. Furthermore, determining equation for multipliers and the 2- dimensional homotopy formula employed to construct higher–order conservation laws for the Camassa–Holm equation.



Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 577 ◽  
Author(s):  
Tianwen Sun ◽  
Da Wang

This paper investigates the destruction of the symmetrical structure of the noise-perturbed Mandelbrot set (M-set). By applying the “symmetry criterion” method, we quantitatively compare the damages to the symmetry of the noise-perturbed Mandelbrot set resulting from additive and multiplicative noises. Because of the uneven distribution between the core positions and the edge positions of the noise-perturbed Mandelbrot set, the comparison results reveal a paradox between the visual sense and quantified result. Thus, we propose a new “visual symmetry criterion” method that is more suitable for the measurement of visual asymmetry.



2017 ◽  
Vol 127 ◽  
pp. 438-449 ◽  
Author(s):  
Yipeng Gao ◽  
Suliman A. Dregia ◽  
Yunzhi Wang


2015 ◽  
Vol 26 (1-3) ◽  
pp. 45-51
Author(s):  
Ahmad Y. Al-Dweik ◽  
M.T. Mustafa ◽  
Raed A. Mara’Beh ◽  
F.M. Mahomed


2013 ◽  
Vol 255 (7) ◽  
pp. 2082-2099 ◽  
Author(s):  
Graziano Crasta ◽  
Ilaria Fragalà


2012 ◽  
Vol 91 (3-4) ◽  
pp. 517-527
Author(s):  
A. M. Zubkov ◽  
D. O. Men’shenin


Biometrics ◽  
2011 ◽  
Vol 68 (1) ◽  
pp. 85-91 ◽  
Author(s):  
Russell T. Shinohara ◽  
Constantine E. Frangakis ◽  
Constantine G. Lyketsos


2006 ◽  
Vol 1996 (9) ◽  
pp. 1401-1406 ◽  
Author(s):  
Uwe Brand ◽  
Siegfried Hünig ◽  
Hans-Dieter Martin ◽  
Bernhard Mayer
Keyword(s):  


1996 ◽  
Vol 69 (5) ◽  
pp. 373
Author(s):  
Solomon W. Golomb


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