46,862 research outputs found
On Krein-like theorems for noncanonical Hamiltonian systems with continuous spectra: application to Vlasov-Poisson
The notions of spectral stability and the spectrum for the Vlasov-Poisson
system linearized about homogeneous equilibria, f_0(v), are reviewed.
Structural stability is reviewed and applied to perturbations of the linearized
Vlasov operator through perturbations of f_0. We prove that for each f_0 there
is an arbitrarily small delta f_0' in W^{1,1}(R) such that f_0+delta f_0f_0$ is perturbed by an area preserving rearrangement, f_0 will
always be stable if the continuous spectrum is only of positive signature,
where the signature of the continuous spectrum is defined as in previous work.
If there is a signature change, then there is a rearrangement of f_0 that is
unstable and arbitrarily close to f_0 with f_0' in W^{1,1}. This result is
analogous to Krein's theorem for the continuous spectrum. We prove that if a
discrete mode embedded in the continuous spectrum is surrounded by the opposite
signature there is an infinitesimal perturbation in C^n norm that makes f_0
unstable. If f_0 is stable we prove that the signature of every discrete mode
is the opposite of the continuum surrounding it.Comment: Submitted to the journal Transport Theory and Statistical Physics. 36
pages, 12 figure
Price-Based Resource Allocation for Spectrum-Sharing Femtocell Networks: A Stackelberg Game Approach
This paper investigates the price-based resource allocation strategies for
the uplink transmission of a spectrum-sharing femtocell network, in which a
central macrocell is underlaid with distributed femtocells, all operating over
the same frequency band as the macrocell. Assuming that the macrocell base
station (MBS) protects itself by pricing the interference from the femtocell
users, a Stackelberg game is formulated to study the joint utility maximization
of the macrocell and the femtocells subject to a maximum tolerable interference
power constraint at the MBS. Especially, two practical femtocell channel
models: sparsely deployed scenario for rural areas and densely deployed
scenario for urban areas, are investigated. For each scenario, two pricing
schemes: uniform pricing and non-uniform pricing, are proposed. Then, the
Stackelberg equilibriums for these proposed games are studied, and an effective
distributed interference price bargaining algorithm with guaranteed convergence
is proposed for the uniform-pricing case. Finally, numerical examples are
presented to verify the proposed studies. It is shown that the proposed
algorithms are effective in resource allocation and macrocell protection
requiring minimal network overhead for spectrum-sharing-based two-tier
femtocell networks.Comment: 27 pages, 7 figures, Submitted to JSA
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