221,235 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

### 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

### Monte Carlo Study of the S=1/2 and S=1 Heisenberg Antiferromagnet on a Spatially Anisotropic Square Lattice

We present a quantum Monte Carlo study of a Heisenberg antiferromagnet on a
spatially anisotropic square lattice, where the coupling strength in the
x-direction ($J_x$) is different from that in the y-direction ($J_y$). By
varying the anisotropy $\alpha$ from 0 to 1, we interpolate between the
one-dimensional chain and the two-dimensional isotropic square lattice. Both
$S=1/2$ and S=1 systems are considered separately in order to facilitate
comparison. The temperature dependence of the uniform susceptibility and the
spin-spin correlation length are computed down to very low temperatures for
various values of $\alpha$. For S=1, the existence of a quantum critical point
at $\alpha^{S=1}_c=0.040(5)$ as well as the scaling of the spin gap is
confirmed. Universal quantities predicted from the ${\cal O}(3)$ nonlinear
$\sigma$ model agree with our results at $\alpha=0.04$ without any adjustable
parameters. On the other hand, the $S=1/2$ results are consistent with
$\alpha^{S=1/2}_c=0$, as discussed by a number of previous theoretical studies.
Experimental implications for $S=1/2$ compounds such as Sr$_2$CuO$_3$ are also
discussed.Comment: 8 pages, 7 figures, to be published in Phys. Rev.

### Renormalization analysis of intermittency in two coupled maps

The critical behavior for intermittency is studied in two coupled
one-dimensional (1D) maps. We find two fixed maps of an approximate
renormalization operator in the space of coupled maps. Each fixed map has a
common relavant eigenvaule associated with the scaling of the control parameter
of the uncoupled one-dimensional map. However, the relevant ``coupling
eigenvalue'' associated with coupling perturbation varies depending on the
fixed maps. These renormalization results are also confirmed for a
linearly-coupled case.Comment: 11 pages, RevTeX, 2 eps figure

### 20 K superconductivity in heavily electron doped surface layer of FeSe bulk crystal

A superconducting transition temperature Tc as high as 100 K was recently
discovered in 1 monolayer (1ML) FeSe grown on SrTiO3 (STO). The discovery
immediately ignited efforts to identify the mechanism for the dramatically
enhanced Tc from its bulk value of 7 K. Currently, there are two main views on
the origin of the enhanced Tc; in the first view, the enhancement comes from an
interfacial effect while in the other it is from excess electrons with strong
correlation strength. The issue is controversial and there are evidences that
support each view. Finding the origin of the Tc enhancement could be the key to
achieving even higher Tc and to identifying the microscopic mechanism for the
superconductivity in iron-based materials. Here, we report the observation of
20 K superconductivity in the electron doped surface layer of FeSe. The
electronic state of the surface layer possesses all the key spectroscopic
aspects of the 1ML FeSe on STO. Without any interface effect, the surface layer
state is found to have a moderate Tc of 20 K with a smaller gap opening of 4
meV. Our results clearly show that excess electrons with strong correlation
strength alone cannot induce the maximum Tc, which in turn strongly suggests
need for an interfacial effect to reach the enhanced Tc found in 1ML FeSe/STO.Comment: 5 pages, 4 figure

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