44,189 research outputs found
Sufficient conditions for unique global solutions in optimal control of semilinear equations with nonlinearity
We consider a semilinear elliptic optimal control problem possibly
subject to control and/or state constraints. Generalizing previous work we
provide a condition which guarantees that a solution of the necessary first
order conditions is a global minimum. A similiar result also holds at the
discrete level where the corresponding condition can be evaluated explicitly.
Our investigations are motivated by G\"unter Leugering, who raised the question
whether our previous results can be extended to the nonlinearity
. We develop a corresponding analysis and present several
numerical test examples demonstrating its usefulness in practice
Throughput Scaling Laws for Wireless Networks with Fading Channels
A network of n communication links, operating over a shared wireless channel,
is considered. Fading is assumed to be the dominant factor affecting the
strength of the channels between transmitter and receiver terminals. It is
assumed that each link can be active and transmit with a constant power P or
remain silent. The objective is to maximize the throughput over the selection
of active links. By deriving an upper bound and a lower bound, it is shown that
in the case of Rayleigh fading (i) the maximum throughput scales like
(ii) the maximum throughput is achievable in a distributed fashion. The upper
bound is obtained using probabilistic methods, where the key point is to upper
bound the throughput of any random set of active links by a chi-squared random
variable. To obtain the lower bound, a decentralized link activation strategy
is proposed and analyzed.Comment: Submitted to IEEE Transactions on Information Theory (Revised
Squeezed States and Hermite polynomials in a Complex Variable
Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec
[J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of
coherent states, related to the Hermite polynomials in a complex variable which
are orthogonal with respect to a non-rotationally invariant measure. We
investigate relations between these coherent states and obtain the relationship
between them and the squeezed states of quantum optics. We also obtain a second
realization of the canonical coherent states in the Bargmann space of analytic
functions, in terms of a squeezed basis. All this is done in the flavor of the
classical approach of V. Bargmann [Commun. Pur. Appl. Math. 14, 187 (1961)].Comment: 15 page
Corrections to Decay in the 2HDM
QCD corrections to the inclusive decay are
investigated within the two - Higgs doublet extension of the standard model
(2HDM). The analysis is performed in the so - called off-resonance region; the
dependence of the obtained results on the choice of the renormalization scale
is examined in details. It is shown that corrections can suppress
the decay width up to times (depending on the
choice of the dilepton invariant mass and the low - energy scale ). As
a result, in the experimentally allowed range of the parameters space, the
relations between the branching ratio and the new physics
parameters are strongly affected. It is found also that though the
renormalization scale dependence of the branching is
significantly reduced, higher order effects in the perturbation theory can
still be nonnegligible.Comment: 16 pages, latex, including 6 figures and 3 table
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