Möbius Transform

2020 ◽  
pp. 151-172
Author(s):  
Federico Milano ◽  
Ioannis Dassios ◽  
Muyang Liu ◽  
Georgios Tzounas
Keyword(s):  
Möbius Transform

GENERALIZED PALEY–WIENER THEOREMS

2012 ◽  
Vol 10 (02) ◽  
pp. 1250020 ◽  
Author(s):  
QIUHUI CHEN ◽  
LUOQING LI ◽  
GUANGBIN REN
Keyword(s):  
Fourier Transform ◽  
Boundary Value ◽  
Integral Kernel ◽  
Real Variable ◽  
Transient Signals ◽  
Extension Theorems ◽  
Möbius Transform ◽  
Wiener Type

Non-harmonic Fourier transform is useful for the analysis of transient signals, where the integral kernel is from the boundary value of Möbius transform. In this note, we study the Paley–Wiener type extension theorems for the non-harmonic Fourier transform. Two extension theorems are established by using real variable techniques.

scholarly journals Dirichlet Characters, Gauss Sums, and Inverse Z Transform

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Jing Gao ◽  
Huaning Liu
Keyword(s):  
Error Estimate ◽  
Unit Circle ◽  
Series Representation ◽  
Gauss Sums ◽  
General Algorithm ◽  
Möbius Transform ◽  
Dirichlet Characters

A generalized Möbius transform is presented. It is based on Dirichlet characters. A general algorithm is developed to compute the inverseZtransform on the unit circle, and an error estimate is given for the truncated series representation.

Cardinal-Probabilistic Interaction Indices and their Applications: A Survey

2003 ◽  
Vol 7 (2) ◽  
pp. 79-85 ◽  
Author(s):  
Katsushige Fujimoto ◽  
Keyword(s):  
Choquet Integral ◽  
Axiomatic Characterization ◽  
Probability Measures ◽  
Choice Probability ◽  
Hierarchical Decomposition ◽  
Möbius Transform

The class of cardinal probabilistic interaction indices obtained as expected marginal interactions includes the Shapley, Banzhaf, and chaining interaction indices and the Möbius and co-Möbius transform so. We will survey cardinal-probabilistic interaction indices and their applications, focusing on axiomatic characterization of the class of cardinal-probabilistic interaction indices. We show that these typical cardinal-probabilistic interaction indices can be represented as the Stieltjes integrals with respect to choice-probability measures on [0,1]. We introduce a method for hierarchical decomposition of systems represented by the Choquet integral using interaction indices.

Dual Cayley–Klein parameters and Möbius transform: Theory and applications

2016 ◽  
Vol 106 ◽  
pp. 50-67 ◽  
Author(s):  
E. Pennestrì ◽  
P.P. Valentini ◽  
G. Figliolini ◽  
J. Angeles
Keyword(s):  
Möbius Transform

Performance characteristics of rectangular aerostatic thrust bearing by conformal mapping

2018 ◽  
Vol 70 (8) ◽  
pp. 1457-1475
Author(s):  
Shang-Han Gao ◽  
Sheng-Long Nong
Keyword(s):  
Conformal Mapping ◽  
Pressure Distribution ◽  
Carrying Capacity ◽  
Thrust Bearing ◽  
Performance Characteristics ◽  
Load Carrying Capacity ◽  
Möbius Transform ◽  
Content Type ◽  
Air Supply ◽  
Load Carrying

Purpose This paper aims to analyze the pressure distribution of rectangular aerostatic thrust bearing with a single air supply inlet using the complex potential theory and conformal mapping. Design/methodology/approach The Möbius transform is used to map the interior of a rectangle onto the interior of a unit circle, from which the pressure distribution and load carrying capacity are obtained. The calculation results are verified by finite difference method. Findings The constructed Möbius formula is very effective for the performance characteristics researches for the rectangular thrust bearing with a single air supply inlet. In addition, it is also noted that to obtain the optimized load carrying capacity, the square thrust bearing can be adopted. Originality/value The Möbius transform is found suitable to describe the pressure distribution of the rectangular thrust bearing with a single air supply inlet.

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