scholarly journals Polar Map

2020 ◽  
Author(s):  
Keyword(s):  
Polar Map

scholarly journals 62. Assessment of Detection Ratio of Ischemic Heart Disease using Diagrams of Polar map

1990 ◽  
Vol 46 (8) ◽  
pp. 1036
Author(s):  
Jirou Sasaki ◽  
Yasuo Fujisawa ◽  
Kenji Kashima ◽  
Kazuhiro Yamamoto ◽  
Yasushi Matsumura
Keyword(s):  
Heart Disease ◽  
Ischemic Heart Disease ◽  
Ischemic Heart ◽  
Detection Ratio ◽  
Polar Map

Different polar-map patterns using the novel technology for myocardial perfusion imaging (MPI)

2016 ◽  
Vol 32 ◽  
pp. 113
Author(s):  
C. Scabbio ◽  
O. Zoccarato ◽  
C. Marcassa ◽  
D. Lizio ◽  
L. Leva ◽  
...  
Keyword(s):  
Myocardial Perfusion Imaging ◽  
Myocardial Perfusion ◽  
Perfusion Imaging ◽  
The Novel ◽  
Novel Technology ◽  
Polar Map

scholarly journals Degenerations of the generic square matrix, the polar map and the determinantal structure

2018 ◽  
Vol 28 (07) ◽  
pp. 1255-1297 ◽  
Author(s):  
Rainelly Cunha ◽  
Zaqueu Ramos ◽  
Aron Simis
Keyword(s):  
Hessian Matrix ◽  
Main Tool ◽  
Affirmative Answer ◽  
Ideal Theory ◽  
Geometric Means ◽  
The Matrix ◽  
Hessian Determinant ◽  
The Ideal ◽  
Polar Map ◽  
Square Matrix

One studies certain degenerations of the generic square matrix over a field [Formula: see text] along with its main related structures, such as the determinant of the matrix, the ideal generated by its partial derivatives, the polar map defined by these derivatives, the Hessian matrix and the ideal of the submaximal minors of the matrix. The main tool comes from commutative algebra, with emphasis on ideal theory and syzygy theory. The structure of the polar map is completely identified and the main properties of the ideal of submaximal minors are determined. Cases where the degenerated determinant has non-vanishing Hessian determinant show that the former is a factor of the latter with the (Segre) expected multiplicity, a problem envisaged by Landsberg–Manivel–Ressayre by geometric means. Another byproduct is an affirmative answer to a question of F. Russo concerning the codimension in the polar image of the dual variety to a hypersurface.

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