5,918 research outputs found
Inverse monoids of partial graph automorphisms
A partial automorphism of a finite graph is an isomorphism between its vertex
induced subgraphs. The set of all partial automorphisms of a given finite graph
forms an inverse monoid under composition (of partial maps). We describe the
algebraic structure of such inverse monoids by the means of the standard tools
of inverse semigroup theory, namely Green's relations and some properties of
the natural partial order, and give a characterization of inverse monoids which
arise as inverse monoids of partial graph automorphisms. We extend our results
to digraphs and edge-colored digraphs as well
Incoherent quantum feedback control of collective light scattering by Bose-Einstein condensates
It is well known that in the presence of a ring cavity the light scattering
from a uniform atomic ensemble can become unstable resulting in the collective
atomic recoil lasing. This is the result of a positive feedback due to the
cavity. We propose to add an additional electronic feedback loop based on the
photodetection of the scattered light. The advantage is a great flexibility in
choosing the feedback algorithm, since manipulations with electric signals are
very well developed. In this paper we address the application of such a
feedback to atoms in the Bose-Einstein condensed state and explore the quantum
noise due to the incoherent feedback action. We show that although the feedback
based on the photodetection does not change the local stability of the initial
uniform distribution with respect to small disturbances, it reduces the region
of attraction of the uniform equilibrium. The feedback-induced nonlinearity
enables quantum fluctuations to bring the system out of the stability region
and cause an exponential growth even if the uniform state is globally stable
without the feedback. Using numerical solution of the feedback master equation
we show that there is no feedback-induced noise in the quadratures of the
excited atomic and light modes. The feedback loop, however, introduces
additional noise into the number of quanta of these modes. Importantly, the
feedback opens an opportunity to position the modulated BEC inside a cavity as
well as tune the phase of scattered light. This can find applications in
precision measurements and quantum simulations.Comment: 7 pages, 7 figure
A Generalized Fractional Calculus of Variations
We study incommensurate fractional variational problems in terms of a
generalized fractional integral with Lagrangians depending on classical
derivatives and generalized fractional integrals and derivatives. We obtain
necessary optimality conditions for the basic and isoperimetric problems,
transversality conditions for free boundary value problems, and a generalized
Noether type theorem.Comment: This is a preprint of a paper whose final and definitive form will
appear in Control and Cybernetics. Paper submitted 01-Oct-2012; revised
25-March-2013; accepted for publication 17-April-201
Variable Order Fractional Variational Calculus for Double Integrals
We introduce three types of partial fractional operators of variable order.
An integration by parts formula for partial fractional integrals of variable
order and an extension of Green's theorem are proved. These results allow us to
obtain a fractional Euler-Lagrange necessary optimality condition for variable
order two-dimensional fractional variational problems.Comment: This is a preprint of a paper whose final and definite form will be
published in: 51st IEEE Conference on Decision and Control, December 10-13,
2012, Maui, Hawaii, USA. Article Source/Identifier: PLZ-CDC12.1240.d4462b33.
Submitted 07-March-2012; accepted 17-July-201
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