4,829 research outputs found
Clique Vectors of -Connected Chordal Graphs
The clique vector of a graph is the sequence in , where is the number of cliques in
with vertices and is the largest cardinality of a clique in . In
this note, we use tools from commutative algebra to characterize all possible
clique vectors of -connected chordal graphs
Warm inflation with an oscillatory inflaton in the non-minimal kinetic coupling model
In the cold inflation scenario, the slow roll inflation and reheating via
coherent rapid oscillation, are usually considered as two distinct eras. When
the slow roll ends, a rapid oscillation phase begins and the inflaton decays to
relativistic particles reheating the Universe. In another model dubbed warm
inflation, the rapid oscillation phase is suppressed, and we are left with only
a slow roll period during which the reheating occurs. Instead, in this paper,
we propose a new picture for inflation in which the slow roll era is suppressed
and only the rapid oscillation phase exists. Radiation generation during this
era is taken into account, so we have warm inflation with an oscillatory
inflaton. To provide enough e-folds, we employ the non-minimal derivative
coupling model. We study the cosmological perturbations and compute the
temperature at the end of warm oscillatory inflation.Comment: 22 pages, typos fixed, accepted by EPJ
Extended Kalman Filter on SE(3) for Geometric Control of a Quadrotor UAV
An extended Kalman filter (EKF) is developed on the special Euclidean group,
SE(3) for geometric control of a quadrotor UAV. It is obtained by performing an
extensive linearization on SE(3) to estimate the state of the quadrotor from
noisy measurements. Proposed estimator considers all the coupling effects
between rotational and translational dynamics, and it is developed in a
coordinate-free fashion. The desirable features of the proposed EKF are
illustrated by numerical examples and experimental results for several
scenarios. The proposed estimation scheme on SE(3) has been unprecedented and
these results can be particularly useful for aggressive maneuvers in GPS denied
environments or in situations where parts of onboard sensors fail.Comment: arXiv admin note: text overlap with arXiv:1304.6765, arXiv:1411.298
Temperature in warm inflation in non minimal kinetic coupling model
Warm inflation in the non minimal derivative coupling model with a general
dissipation coefficient is considered. We investigate conditions for the
existence of the slow roll approximation and study cosmological perturbations.
The spectral index, and the power spectrum are calculated and the temperature
of the universe at the end of the slow roll warm inflation is obtained.Comment: 18 pages, major revision, accepted by the European Physical Journal
Connectivity of pseudomanifold graphs from an algebraic point of view
The connectivity of graphs of simplicial and polytopal complexes is a
classical subject going back at least to Steinitz, and the topic has since been
studied by many authors, including Balinski, Barnette, Athanasiadis and
Bjorner. In this note, we provide a unifying approach which allows us to obtain
more general results. Moreover, we provide a relation to commutative algebra by
relating connectivity problems to graded Betti numbers of the associated
Stanley--Reisner rings.Comment: 4 pages, minor change
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