scholarly journals Transfer operators and Hankel transforms between relative trace formulas, I: Character theory

2021 ◽  
pp. 108010
Author(s):  
Yiannis Sakellaridis
2017 ◽  
Vol 60 (2) ◽  
pp. 411-421
Author(s):  
Luchezar Stoyanov

AbstractWe prove a comprehensive version of the Ruelle–Perron–Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is that the Hölder constant of the function generating the operator appears only polynomially, not exponentially as in previously known estimates.


1956 ◽  
Vol 9 (3) ◽  
pp. 128-131
Author(s):  
A. G. Mackie

In his book on Hydrodynamics, Lamb obtained a solution for the potential flow of an incompressible fluid through a circular hole in a plane wall. More recently Sneddon (Fourier Transforms, New York, 1951) obtained Lamb's solution by an elegant application of Hankel transforms.Since the streamlines in this solution are symmetric about the wall, it is not of particular physical interest. In this note, Sneddon's method is used to give a solution in which the fluid is infinite in extent on one side of the aperture but issues as a jet of finite diameter on the other side.


2012 ◽  
Vol 22 (11) ◽  
pp. 1250261 ◽  
Author(s):  
ERIK M. BOLLT

Synchronization of chaotic oscillators has become well characterized by errors which shrink relative to a synchronization manifold. This manifold is the identity function in the case of identical systems, or some other slow manifold in the case of generalized synchronizaton in the case of nonidentical components. On the other hand, since many decades beginning with the Smale horseshoe, chaotic oscillators can be well understood in terms of symbolic dynamics as information producing processes. We study here the synchronization of a pair of chaotic oscillators as a process for sharing information bearing bits transferred between each other, by measuring the transfer entropy tracked as the global system transitions to the synchronization state. Further, we present for the first time the notion of transfer entropy in the measure theoretic setting of transfer operators.


2010 ◽  
Vol 74 (5) ◽  
pp. 434-471 ◽  
Author(s):  
Cath Crosby

This article considers the basis upon which a person should be held to be criminally liable, and to do so, it is necessary to examine the leading theories of character and choice that underpin the State holding a person to be culpable of a criminal offence, i.e. the link between culpability and fault. The case of R v Kingston1 is used to examine the application of these leading theories and it is observed that choice theorists would not excuse such a defendant from criminal liability even though his capacity to make a choice to refrain from law breaking was made extremely difficult by external factors beyond his control. Only character theory could possibly offer exculpation in such circumstances on the basis that the defendant acted ‘out of character’ and his deed did not deserve the full censure and punishment of the criminal law. The Court of Appeal in R v Kingston would have been prepared to excuse, but the House of Lords, and most recently the Law Commission have adopted a pragmatic approach to the involuntarily intoxicated offender. This case serves as a reminder that while justice is the aim of the criminal justice system, it is not an absolute standard.


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