121 research outputs found
A Novel Approach to Detect Malicious User Node by Cognition in Heterogeneous Wireless Networks
Cognitive Networks are characterized by their intelligence and adaptability. Securing layered heterogeneous network architectures has always posed a major challenge to researchers. In this paper, the Observe, Orient, Decide and Act (OODA) loop is adopted to achieve cognition. Intelligence is incorporated by the use of discrete time dynamic neural networks. The use of dynamic neural networks is considered, to monitor the instantaneous changes that occur in heterogeneous network environments when compared to static neural networks. Malicious user node identification is achieved by monitoring the service request rates generated to the cognitive servers. The results and the experimental study presented in this paper prove the improved efficiency in terms of malicious node detection and malicious transaction classification when compared to the existing systems
Coherent states for polynomial su(1,1) algebra and a conditionally solvable system
In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105],
we constructed a class of coherent states for a polynomially deformed
algebra. In this paper, we first prepare the discrete representations of the
nonlinearly deformed algebra. Then we extend the previous procedure
to construct a discrete class of coherent states for a polynomial su(1,1)
algebra which contains the Barut-Girardello set and the Perelomov set of the
SU(1,1) coherent states as special cases. We also construct coherent states for
the cubic algebra related to the conditionally solvable radial oscillator
problem.Comment: 2 figure
Superintegrability and higher order polynomial algebras II
In an earlier article, we presented a method to obtain integrals of motion
and polynomial algebras for a class of two-dimensional superintegrable systems
from creation and annihilation operators. We discuss the general case and
present its polynomial algebra. We will show how this polynomial algebra can be
directly realized as a deformed oscillator algebra. This particular algebraic
structure allows to find the unitary representations and the corresponding
energy spectrum. We apply this construction to a family of caged anisotropic
oscillators. The method can be used to generate new superintegrable systems
with higher order integrals. We obtain new superintegrable systems involving
the fourth Painleve transcendent and present their integrals of motion and
polynomial algebras.Comment: 11 page
Master equations for effective Hamiltonians
We reelaborate on a general method for obtaining effective Hamiltonians that
describe different nonlinear optical processes. The method exploits the
existence of a nonlinear deformation of the su(2) algebra that arises as the
dynamical symmetry of the original model. When some physical parameter (usually
related to the dispersive limit) becomes small, we immediately get a diagonal
effective Hamiltonian that represents correctly the dynamics for arbitrary
states and long times. We apply the same technique to obtain how the noise
terms in the original model transform under this scheme, providing a systematic
way of including damping effects in processes described in terms of effective
Hamiltonians.Comment: 10 pages, no figure
An algebraic approach to the Tavis-Cummings problem
An algebraic method is introduced for an analytical solution of the
eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on
polynomially deformed su(2), i.e. su_n(2), algebras. In this method the
eigenvalue problem is solved in terms of a specific perturbation theory,
developed here up to third order. Generalization to the N-atom case of the Rabi
frequency and dressed states is also provided. A remarkable enhancement of
spontaneous emission of N atoms in a resonator is found to result from
collective effects.Comment: 13 pages, 7 figure
Coherent states for Hamiltonians generated by supersymmetry
Coherent states are derived for one-dimensional systems generated by
supersymmetry from an initial Hamiltonian with a purely discrete spectrum for
which the levels depend analytically on their subindex. It is shown that the
algebra of the initial system is inherited by its SUSY partners in the subspace
associated to the isospectral part or the spectrum. The technique is applied to
the harmonic oscillator, infinite well and trigonometric Poeschl-Teller
potentials.Comment: LaTeX file, 26 pages, 3 eps figure
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