Shape invariance characterization of coherent axially symmetric beams

1996 ◽  
Author(s):  
Franco Gori ◽  
Riccardo Borghi ◽  
Massimo Santarsiero ◽  
Silvia Vicalvi
Keyword(s):  
Axially Symmetric ◽  
Shape Invariance

scholarly journals Bayesian tests of symmetry for the generalized Von Mises distribution

2021 ◽  
Author(s):  
Sara Salvador ◽  
Riccardo Gatto
Keyword(s):  
Null Hypothesis ◽  
Prior Probability ◽  
Bayes Factors ◽  
Von Mises Distribution ◽  
Posterior Probabilities ◽  
Axially Symmetric ◽  
Von Mises ◽  
Flexible Model ◽  
Simulation Scheme

AbstractBayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka in Stat Methodol 4(3):341–353, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric, unimodal or bimodal. A characterization of axial symmetry is provided and taken as null hypothesis for one of the proposed Bayesian tests. The Bayesian tests are obtained by the technique of probability perturbation. The prior probability measure is perturbed so to give a positive prior probability to the null hypothesis, which would be null otherwise. This allows for the derivation of simple computational formulae for the Bayes factors. Numerical results reveal that, whenever the simulation scheme of the samples supports the null hypothesis, the null posterior probabilities appear systematically larger than their prior counterpart.

Shape-invariance error for axially symmetric light beams

1998 ◽  
Vol 34 (11) ◽  
pp. 2109-2116 ◽  
Author(s):  
S. Vicalvi ◽  
R. Borghi ◽  
M. Santarsiero ◽  
F. Gori
Keyword(s):  
Axially Symmetric ◽  
Shape Invariance ◽  
Light Beams

Characterization of triplet states of axially symmetric benzenes using the zeeman effect

1971 ◽  
Vol 10 (4) ◽  
pp. 452-454 ◽  
Author(s):  
R.M Hochstrasser ◽  
J.E Wessel ◽  
J.D Whiteman ◽  
A.H Zewail
Keyword(s):  
Zeeman Effect ◽  
Triplet States ◽  
Axially Symmetric

Ronchi ruling characterization of axially symmetric laser beams

1990 ◽  
Vol 29 (30) ◽  
pp. 4441
Author(s):  
Robert M. O’Connell ◽  
Cheng-Hao Chen
Keyword(s):  
Laser Beams ◽  
Axially Symmetric

scholarly journals THE INEQUALITY BETWEEN MASS AND ANGULAR MOMENTUM FOR AXIALLY SYMMETRIC BLACK HOLES

2008 ◽  
Vol 17 (03n04) ◽  
pp. 519-523 ◽  
Author(s):  
SERGIO DAIN
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Angular Momentum ◽  
Nonlinear Stability ◽  
Stability Problem ◽  
Total Mass ◽  
Kerr Black Hole ◽  
Axially Symmetric ◽  
Absolute Minimum

In this essay I first discuss the physical relevance of the inequality [Formula: see text] for axially symmetric (nonstationary) black holes, where m is the mass and J the angular momentum of the space–time. Then, I present a proof of this inequality for the case of one spinning black hole. The proof involves a remarkable characterization of the extreme Kerr black hole as an absolute minimum of the total mass. Finally, I conjecture about the physical implications of this characterization for the nonlinear stability problem for black holes.

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

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