261,143 research outputs found

### New q-Euler numbers and polynomials associated with p-adic q-integrals

In this paper we study q-Euler numbers and polynomials by using p-adic
q-fermionic integrals on Z_p. The methods to study q-Euler numbers and
polynomials in this paper are new.Comment: 13 page

### Coupled oscillators and Feynman's three papers

According to Richard Feynman, the adventure of our science of physics is a
perpetual attempt to recognize that the different aspects of nature are really
different aspects of the same thing. It is therefore interesting to combine
some, if not all, of Feynman's papers into one. The first of his three papers
is on the ``rest of the universe'' contained in his 1972 book on statistical
mechanics. The second idea is Feynman's parton picture which he presented in
1969 at the Stony Brook conference on high-energy physics. The third idea is
contained in the 1971 paper he published with his students, where they show
that the hadronic spectra on Regge trajectories are manifestations of
harmonic-oscillator degeneracies. In this report, we formulate these three
ideas using the mathematics of two coupled oscillators. It is shown that the
idea of entanglement is contained in his rest of the universe, and can be
extended to a space-time entanglement. It is shown also that his parton model
and the static quark model can be combined into one Lorentz-covariant entity.
Furthermore, Einstein's special relativity, based on the Lorentz group, can
also be formulated within the mathematical framework of two coupled
oscillators.Comment: 31 pages, 6 figures, based on the concluding talk at the 3rd Feynman
Festival (Collage Park, Maryland, U.S.A., August 2006), minor correction

### Optimal circular flight of multiple UAVs for target tracking in urban areas

This work is an extension of our previous result in which a novel single-target tracking
algorithm for fixed-wing UAVs (Unmanned Air Vehicles) was proposed. Our previous
algorithm firstly finds the centre of a circular flight path, rc, over the interested ground
target which maximises the total chance of keeping the target inside the camera field of view
of UAVs, , while the UAVs fly along the circular path. All the UAVs keep their maximum
allowed altitude and fly along the same circle centred at rc with the possible minimum turn
radius of UAVs. As discussed in [1,4], these circular flights are highly recommended for
various target tracking applications especially in urban areas, as for each UAV the
maximum altitude flight ensures the maximum visibility and the minimum radius turn
keeps the minimum distance to the target at the maximum altitude.
Assuming a known probability distribution for the target location, one can quantify ,
which is incurred by the travel of a single UAV along an arbitrary circle, using line-of-sight
vectors. From this observation, (the centre of) an optimal circle among numerous feasible
ones can be obtained by a gradient-based search combined with random sampling, as
suggested in [1]. This optimal circle is then used by the other UAVs jointly tracking the
same target. As the introduction of multiple UAVs may minimise further, the optimal
spacing between the UAVs can be naturally considered. In [1], a typical line search method
is suggested for this optimal spacing problem. However, as one can easily expect, the
computational complexity of this search method may undesirably increase as the number of
UAVs increases.
The present work suggests a remedy for this seemingly complex optimal spacing problem.
Instead of depending on time-consuming search techniques, we develop the following
algorithm, which is computationally much more efficient. Firstly, We calculate the
distribution (x), where x is an element of , which is the chance of capturing the target by
one camera along . Secondly, based on the distribution function, (x), find separation
angles between UAVs such that the target can be always tracked by at least one UAV with a
guaranteed probabilistic measure. Here, the guaranteed probabilistic measure is chosen by
taking into account practical constraints, e.g. required tracking accuracy and UAVs'
minimum and maximum speeds. Our proposed spacing scheme and its guaranteed
performance are demonstrated via numerical simulations

### Quantum-disordered slave-boson theory of underdoped cuprates

We study the stability of the spin gap phase in the U(1) slave-boson theory
of the t-J model in connection to the underdoped cuprates. We approach the spin
gap phase from the superconducting state and consider the quantum phase
transition of the slave-bosons at zero temperature by introducing vortices in
the boson superfluid. At finite temperatures, the properties of the bosons are
different from those of the strange metal phase and lead to modified gauge
field fluctuations. As a result, the spin gap phase can be stabilized in the
quantum critical and quantum disordered regime of the boson system. We also
show that the regime of quantum disordered bosons with the paired fermions can
be regarded as the strong coupling version of the recently proposed nodal
liquid theory.Comment: 5 pages, Replaced by the published versio

### Einstein, Wigner, and Feynman: From E = mc^{2} to Feynman's decoherence via Wigner's little groups

The 20th-century physics starts with Einstein and ends with Feynman. Einstein
introduced the Lorentz-covariant world with E = mc^{2}. Feynman observed that
fast-moving hadrons consist of partons which act incoherently with external
signals. If quarks and partons are the same entities observed in different
Lorentz frames, the question then is why partons are incoherent while quarks
are coherent. This is the most puzzling question Feynman left for us to solve.
In this report, we discuss Wigner's role in settling this question. Einstein's
E = mc^{2}, which takes the form E = \sqrt{m^{2} + p^{2}}, unifies the
energy-momentum relations for massive and massless particles, but it does not
take into account internal space-time structure of relativistic particles. It
is pointed out Wigner's 1939 paper on the inhomogeneous Lorentz group defines
particle spin and gauge degrees of freedom in the Lorentz-covariant world.
Within the Wigner framework, it is shown possible to construct the internal
space-time structure for hadrons in the quark model. It is then shown that the
quark model and the parton model are two different manifestations of the same
covariant entity. It is shown therefore that the lack of coherence in Feynman's
parton picture is an effect of the Lorentz covariance.Comment: LaTex 15 pages, 1 figure, presented at the Wigner Centennial
Conference held in Pecs, Hungary (July 2002), published in the proceedings
(Acta Physica Hungarica, 2003), minor corrections to the original versio

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