57,839 research outputs found
Coherent states, displaced number states and Laguerre polynomial states for su(1,1) Lie algebra
The ladder operator formalism of a general quantum state for su(1,1) Lie
algebra is obtained. The state bears the generally deformed oscillator
algebraic structure. It is found that the Perelomov's coherent state is a
su(1,1) nonlinear coherent state. The expansion and the exponential form of the
nonlinear coherent state are given. We obtain the matrix elements of the
su(1,1) displacement operator in terms of the hypergeometric functions and the
expansions of the displaced number states and Laguerre polynomial states are
followed. Finally some interesting su(1,1) optical systems are discussed.Comment: 16 pages, no figures, accepted by Int. J. Mod. Phy.
Classes of Measures Generated by Capacities
We introduce classes of measures in the half-space
generated by Riesz, or Bessel, or Besov capacities in , and give
a geometric characterization as Carleson-type measures
Decentralized Optimal Merging Control for Connected and Automated Vehicles
This paper addresses the optimal control of Connected and Automated Vehicles
(CAVs) arriving from two roads at a merging point where the objective is to
jointly minimize the travel time and energy consumption of each CAV. The
solution guarantees that a speed-dependent safety constraint is always
satisfied, both at the merging point and everywhere within a control zone which
precedes it. We first analyze the case of no active constraints and prove that
under certain conditions the safety constraint remains inactive, thus
significantly simplifying the determination of an explicit decentralized
solution. When these conditions do not apply, an explicit solution is still
obtained that includes intervals over which the safety constraint is active.
Our analysis allows us to study the tradeoff between the two objective function
components (travel time and energy within the control zone). Simulation
examples are included to compare the performance of the optimal controller to a
baseline with human-driven vehicles with results showing improvements in both
metrics.Comment: 16 pages, 2nd version, 20 figure
Consequences of R-Parity violating interactions for anomalies in and
We investigate the possibility of explaining the enhancement in semileptonic
decays of , the anomalies induced by in and violation of lepton
universality in
within the framework of R-parity violating (RPV) MSSM. Exchange of down type
right-handed squark coupled to quarks and leptons yield interactions which are
similar to leptoquark induced interactions that have been proposed to explain
the by tree level interactions and anomalies by loop induced interactions, simultaneously. However,
the Yukawa couplings in such theories have severe constraints from other rare
processes in and decays. Although this interaction can provide a viable
solution to anomaly, we show that with the severe constraint from
, it is impossible to solve the anomalies in process simultaneously.Comment: RevTex, 13 pages, three figures. In our earlier version, we had
neglected a contribution to C^{NP}_9 and obtained erroneous conclusions which
we have corrected them in this versio
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