scholarly journals On the Harmonic Möbius Transformations

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Rodrigo Hernández ◽  
María J. Martín
Keyword(s):  
Möbius Transformations ◽  
Mobius Transformations

scholarly journals Möbius geometry for hypersurfaces in S4

1995 ◽  
Vol 139 ◽  
pp. 1-20 ◽  
Author(s):  
Changping Wang
Keyword(s):  
Invariant System ◽  
Principal Curvatures ◽  
Möbius Transformations ◽  
Möbius Geometry ◽  
Mobius Transformations

Our purpose in this paper is to study Möbius geometry for those hypersurfaces in S4 which have different principal curvatures at each point. We will give a complete local Möbius invariant system for such hypersurface in S4 which determines the hypersurface up to Möbius transformations. And we will classify the so-called Möbius homogeneous hypersurfaces in S4.

MÖBIUS TRANSFORMATIONS IN QUANTUM AMPLITUDE AMPLIFICATION WITH GENERALIZED PHASES

2010 ◽  
Vol 08 (06) ◽  
pp. 923-935 ◽  
Author(s):  
CÉSAR BAUTISTA-RAMOS ◽  
NORA CASTILLO-TÉPOX
Keyword(s):  
Error Probability ◽  
Quantum Algorithm ◽  
Linear Transformations ◽  
Möbius Transformations ◽  
Good State ◽  
Quantum Amplitude ◽  
Initial States ◽  
Phase Angles ◽  
Amplitude Amplification ◽  
Mobius Transformations

The iteration of the operators employed in quantum amplitude amplification with generalized phases is analyzed by using elementary properties (geometric and algebraic) of the Möbius transformations (fractional linear transformations). It is shown that, for a given quantum algorithm without measurement, which produces a good state with probability a of success, if the phase angles φ and ϕ which mark the good and initial states respectively satisfy φ = ϕ with a small enough, then, for a number n of iterations with [Formula: see text] we get an error probability that is at most O(aϕ2).

scholarly journals Ellipses, near ellipses, and harmonic Möbius transformations

2005 ◽  
Vol 133 (9) ◽  
pp. 2705-2710 ◽  
Author(s):  
Martin Chuaqui ◽  
Peter Duren ◽  
Brad Osgood
Keyword(s):  
Möbius Transformations ◽  
Mobius Transformations
Sign in / Sign up

Export Citation Format

Share Document