scholarly journals Linearization of Poisson actions and singular values of matrix products

2001 ◽  
Vol 51 (6) ◽  
pp. 1691-1717 ◽  
Author(s):  
Anton Alekseev ◽  
Eckhard Meinrenken ◽  
Chris Woodward

2020 ◽  
Vol 48 (3) ◽  
pp. 1372-1410
Author(s):  
Phil Kopel ◽  
Sean O’Rourke ◽  
Van Vu




2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Huamin Zhang ◽  
Feng Ding

This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vec-permutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of the Kronecker products.





Bernoulli ◽  
2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Rohit Chaudhuri ◽  
Vishesh Jain ◽  
Natesh S. Pillai


1997 ◽  
Vol 264 ◽  
pp. 109-115 ◽  
Author(s):  
Bo-Ying Wang ◽  
Bo-Yan Xi


Author(s):  
Chauhan Usha ◽  
Singh Rajeev Kumar

Digital Watermarking is a technology, to facilitate the authentication, copyright protection and Security of digital media. The objective of developing a robust watermarking technique is to incorporate the maximum possible robustness without compromising with the transparency. Singular Value Decomposition (SVD) using Firefly Algorithm provides this objective of an optimal robust watermarking technique. Multiple scaling factors are used to embed the watermark image into the host by multiplying these scaling factors with the Singular Values (SV) of the host image. Firefly Algorithm is used to optimize the modified host image to achieve the highest possible robustness and transparency. This approach can significantly increase the quality of watermarked image and provide more robustness to the embedded watermark against various attacks such as noise, geometric attacks, filtering attacks etc.



2011 ◽  
Vol 33 (9) ◽  
pp. 2039-2044 ◽  
Author(s):  
Xin-peng Zhou ◽  
Feng Han ◽  
Guo-hua Wei ◽  
Si-liang Wu


2015 ◽  
Vol 76 (2) ◽  
pp. 205-218 ◽  
Author(s):  
L. A. Mironovskii ◽  
T. N. Solov’eva


2020 ◽  
Vol 18 (1) ◽  
pp. 1727-1741
Author(s):  
Yoonjin Lee ◽  
Yoon Kyung Park

Abstract We study the modularity of Ramanujan’s function k ( τ ) = r ( τ ) r 2 ( 2 τ ) k(\tau )=r(\tau ){r}^{2}(2\tau ) , where r ( τ ) r(\tau ) is the Rogers-Ramanujan continued fraction. We first find the modular equation of k ( τ ) k(\tau ) of “an” level, and we obtain some symmetry relations and some congruence relations which are satisfied by the modular equations; these relations are quite useful for reduction of the computation cost for finding the modular equations. We also show that for some τ \tau in an imaginary quadratic field, the value k ( τ ) k(\tau ) generates the ray class field over an imaginary quadratic field modulo 10; this is because the function k is a generator of the field of the modular function on Γ 1 ( 10 ) {{\mathrm{\Gamma}}}_{1}(10) . Furthermore, we suggest a rather optimal way of evaluating the singular values of k ( τ ) k(\tau ) using the modular equations in the following two ways: one is that if j ( τ ) j(\tau ) is the elliptic modular function, then one can explicitly evaluate the value k ( τ ) k(\tau ) , and the other is that once the value k ( τ ) k(\tau ) is given, we can obtain the value k ( r τ ) k(r\tau ) for any positive rational number r immediately.



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