scholarly journals Antipodal Identification in the Schwarzschild Spacetime

2020 ◽  
Vol 5 (3) ◽  
Author(s):  
Miguel Socolovsky ◽  
Keyword(s):  
Conical Singularity ◽  
Möbius Transformation ◽  
Curvature Singularity ◽  
Schwarzschild Spacetime ◽  
Null Geodesics ◽  
Mobius Transformation ◽  
Simply Connected ◽  
Antipodal Identification ◽  
Bending Light

"Through a Möbius transformation, we study aspects like topology, ligth cones, horizons, curvature singularity, lines of constant Schwarzschild coordinates r and t, null geodesics, and transformed metric, of the spacetime (SKS/2)^' that results from: i) the antipode identification in the Schwarzschild-Kruskal-Szekeres (SKS) spacetime, and ii) the suppression of the consequent conical singularity. In particular, one obtains a non simply-connected topology: (SKS/2)^' = R^2* ×S^2 and, as expected, bending light cones."

Power Dependent Impedance Measurement Exploiting an Oscilloscope and Möbius Transformation

2017 ◽  
Vol E100.C (10) ◽  
pp. 918-923
Author(s):  
Sonshu SAKIHARA ◽  
Masaru TAKANA ◽  
Naoki SAKAI ◽  
Takashi OHIRA
Keyword(s):  
Impedance Measurement ◽  
Möbius Transformation ◽  
Mobius Transformation

Möbius Transformation

2004 ◽  
pp. 249-249
Author(s):  
David Berman ◽  
Hugo Garcia-Compean ◽  
Paulius Miškinis ◽  
Miao Li ◽  
Daniele Oriti ◽  
...  
Keyword(s):  
Möbius Transformation ◽  
Mobius Transformation

scholarly journals A Novel Image Encryption Technique Based on Mobius Transformation

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Muhammad Asif ◽  
Sibgha Mairaj ◽  
Zafar Saeed ◽  
M. Usman Ashraf ◽  
Kamal Jambi ◽  
...  
Keyword(s):  
Image Encryption ◽  
General Linear Group ◽  
Block Cipher ◽  
Correlation Energy ◽  
Image Data ◽  
Galois Field ◽  
Möbius Transformation ◽  
Encryption Scheme ◽  
Mobius Transformation ◽  
Projective General Linear Group

The nonlinear transformation concedes as S-box which is responsible for the certainty of contemporary block ciphers. Many kinds of S-boxes are planned by various authors in the literature. Construction of S-box with a powerful cryptographic analysis is the vital step in scheming block cipher. Through this paper, we give more powerful and worthy S-boxes and compare their characteristics with some previous S-boxes employed in cryptography. The algorithm program planned in this paper applies the action of projective general linear group P G L 2 , G F 2 8 on Galois field G F 2 8 . The proposed S-boxes are constructed by using Mobius transformation and elements of Galois field. By using this approach, we will encrypt an image which is the preeminent application of S-boxes. These S-boxes offer a strong algebraic quality and powerful confusion capability. We have tested the strength of the proposed S-boxes by using different tests, BIC, SAC, DP, LP, and nonlinearity. Furthermore, we have applied these S-boxes in image encryption scheme. To check the strength of image encryption scheme, we have calculated contrast, entropy, correlation, energy, and homogeneity. The results assured that the proposed scheme is better. The advantage of this scheme is that we can secure our confidential image data during transmission.

scholarly journals The Proof of a Conjecture Relating Catalan Numbers to an Averaged Mandelbrot-Möbius Iterated Function

2021 ◽  
Vol 5 (3) ◽  
pp. 92
Author(s):  
Pavel Trojovský ◽  
K Venkatachalam
Keyword(s):  
Julia Sets ◽  
Catalan Numbers ◽  
Iteration Step ◽  
Möbius Transformation ◽  
Iterated Function ◽  
Mobius Transformation

In 2021, Mork and Ulness studied the Mandelbrot and Julia sets for a generalization of the well-explored function ηλ(z)=z2+λ. Their generalization was based on the composition of ηλ with the Möbius transformation μ(z)=1z at each iteration step. Furthermore, they posed a conjecture providing a relation between the coefficients of (each order) iterated series of μ(ηλ(z)) (at z=0) and the Catalan numbers. In this paper, in particular, we prove this conjecture in a more precise (quantitative) formulation.

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