scholarly journals The Geometrical Basis of đť’«đť’Ż Symmetry

Symmetry â—˝  
10.3390/sym10100494 â—˝  
2018 â—˝  
Vol 10 (10) â—˝  
pp. 494 â—˝  
Author(s):  
Luis Sánchez-Soto â—˝  
Juan Monzón
Keyword(s):  
Transfer Matrix â—˝  
Complex Plane â—˝  
Physical Meaning â—˝  
Pt Symmetry â—˝  
Möbius Transformation â—˝  
Invariant System â—˝  
Complex Conjugation â—˝  
Basic Properties â—˝  
Mobius Transformation

We reelaborate on the basic properties of PT symmetry from a geometrical perspective. The transfer matrix associated with these systems induces a Möbius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and parallel displacements. We find that a PT invariant system can be pictured as a complex conjugation followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system.

scholarly journals The Geometrical Basis of PT Symmetry

2018 â—˝  
Author(s):  
Luis Sanchez-Soto â—˝  
Juan J. Monzón
Keyword(s):  
Transfer Matrix â—˝  
Complex Plane â—˝  
Physical Meaning â—˝  
Pt Symmetry â—˝  
Invariant System â—˝  
Complex Conjugation â—˝  
Basic Properties

We reelaborate on the basic properties of PT symmetry from a geometrical Perspective. The transfer matrix associated with these systems induces a Möbius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and parallel displacements. We find that a PT invariant system can be pictured as a complex conjugation followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system.

scholarly journals Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics

10.1155/2012/560246 â—˝  
2012 â—˝  
Vol 2012 â—˝  
pp. 1-15 â—˝  
Author(s):  
Sunhong Lee â—˝  
Hyun Chol Lee â—˝  
Mi Ran Lee â—˝  
Seungpil Jeong â—˝  
Gwang-Il Kim
Keyword(s):  
Complex Plane â—˝  
Hermite Interpolation â—˝  
Möbius Transformation â—˝  
Möbius Transformations â—˝  
Interpolation Problems â—˝  
Pythagorean Hodograph â—˝  
Improved Stability â—˝  
Mobius Transformation â—˝  
Extra Parameter â—˝  
Mobius Transformations

We present an algorithm forC1Hermite interpolation using Möbius transformations of planar polynomial Pythagoreanhodograph (PH) cubics. In general, with PH cubics, we cannot solveC1Hermite interpolation problems, since their lack of parameters makes the problems overdetermined. In this paper, we show that, for each Möbius transformation, we can introduce anextra parameterdetermined by the transformation, with which we can reduce them to the problems determining PH cubics in the complex planeℂ. Möbius transformations preserve the PH property of PH curves and are biholomorphic. Thus the interpolants obtained by this algorithm are also PH and preserve the topology of PH cubics. We present a condition to be met by a Hermite dataset, in order for the corresponding interpolant to be simple or to be a loop. We demonstrate the improved stability of these new interpolants compared with PH quintics.

Power Dependent Impedance Measurement Exploiting an Oscilloscope and Möbius Transformation

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

Möbius transformation and conformal relativity

10.1007/bf02058086 â—˝  
1996 â—˝  
Vol 26 (2) â—˝  
pp. 223-242 â—˝  
Author(s):  
Reijo Piirainen
Keyword(s):  
Möbius Transformation â—˝  
Mobius Transformation

Möbius Transformation

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