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