3,082 research outputs found
Multi-fractal analysis of weighted networks
In many real complex networks, the fractal and self-similarity properties
have been found. The fractal dimension is a useful method to describe fractal
property of complex networks. Fractal analysis is inadequate if only taking one
fractal dimension to study complex networks. In this case, multifractal
analysis of complex networks are concerned. However, multifractal dimension of
weighted networks are less involved. In this paper, multifractal dimension of
weighted networks is proposed based on box-covering algorithm for fractal
dimension of weighted networks (BCANw). The proposed method is applied to
calculate the fractal dimensions of some real networks. Our numerical results
indicate that the proposed method is efficient for analysis fractal property of
weighted networks
Simultaneous eigenstates of the number-difference operator and a bilinear interaction Hamiltonian derived by solving a complex differential equation
As a continuum work of Bhaumik et al who derived the common eigenvector of
the number-difference operator Q and pair-annihilation operator ab (J. Phys. A9
(1976) 1507) we search for the simultaneous eigenvector of Q and
(ab-a^{+}b^{+}) by setting up a complex differential equation in the bipartite
entangled state representation. The differential equation is then solved in
terms of the two-variable Hermite polynomials and the formal hypergeometric
functions. The work is also an addendum to Mod. Phys. Lett. A 9 (1994) 1291 by
Fan and Klauder, in which the common eigenkets of Q and pair creators are
discussed
[(E)-10-(2,6-Dimethylphenylimino)-9-methyl-9,10-dihydrophenanthren-9-olato]pentamethyldialuminum(III)
The two Al atoms in the title compound, [Al2(CH3)5(C23H20NO)], are four-coordinated in a distorted tetrahedral environment. The coordination of one Al atom includes three methyl-C atoms and the O atom from the ligand, whereas the second Al atom is surrounded by the O atom and one N atom from the ligand as well as by two methyl-C atoms. In the ligand, the dihedral angle between the two phenyl rings in the 9,10-dihydrophenanthren unit is 20.64 (12)°
Toolbox for entanglement detection and fidelity estimation
The determination of the state fidelity and the detection of entanglement are
fundamental problems in quantum information experiments. We investigate how
these goals can be achieved with a minimal effort. We show that the fidelity of
GHZ and W states can be determined with an effort increasing only linearly with
the number of qubits. We also present simple and robust methods for other
states, such as cluster states and states in decoherence-free subspaces.Comment: 5 pages, no figures, v3: final version, to appear as a Rapid
Communication in PR
H∞ filtering for nonlinear discrete-time stochastic systems with randomly varying sensor delays
This is the post print version of the article. The official published version can be obained from the link - Copyright 2009 Elsevier LtdThis paper is concerned with the H∞ filtering problem for a general class of nonlinear discrete-time stochastic systems with randomly varying sensor delays, where the delayed sensor measurement is governed by a stochastic variable satisfying the Bernoulli random binary distribution law. In terms of the Hamilton–Jacobi–Isaacs inequalities, preliminary results are first obtained that ensure the addressed system to possess an l2-gain less than a given positive scalar γ. Next, a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the H∞ performance constraint for all nonzero exogenous disturbances under the zero-initial condition. Such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation. Furthermore, it is shown that our main results can be readily specialized to the case of linear stochastic systems. Finally, a numerical simulation example is used to demonstrate the effectiveness of the results derived.This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor James Lam under the direction of Editor Ian R. Petersen. This work was supported by the Shanghai Natural Science Foundation under Grant 07ZR14002, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany
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