Restrictions and extensions of potentials of Hp distributions

In this note we consider extensions and restrictions of anisotropic classes of distributions which include the usual global or homogeneous Lipschitz classes Λ(B, X) as well as the Sobolev classes $\text{L}{}_{\mathrm{\alpha }}{}^{\mathrm{p}}$. The novelty of our approach is that our results remain valid for all values of p (0 < p < ∞) as well as the critical index $\text{α =}\text{1}\text{p}$.     

Random replicators with high-order interactions

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random mutual interactions, as well as via deterministic self-interactions of order p>/=2. We show that the main effect of increasing the order of the interactions among the species is to make the system less competitive, in the sense that the fraction of extinct species is greatly reduced. In addition, we find that for p>2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.     

Band-dependent quasiparticle dynamics in the hole-doped Ba-122 iron pnictides

We report on band-dependent quasiparticle dynamics in the hole-doped Ba-122 pnictides measured by ultrafast pump-probe spectroscopy. In the superconducting state of the optimal and over hole-doped samples, we observe two distinct relaxation processes: a fast component whose decay rate increases linearly with excitation density and a slow component whose relaxation is independent of excitation strength. We argue that these two components reflect the recombination of quasiparticles in the two hole bands through intraband and interband processes. We also find that the thermal recombination rate of quasiparticles increases quadratically with temperature in all samples. The temperature and excitation density dependence of the decays indicates fully gapped hole bands and nodal or very anisotropic electron bands.     

Weighted Local Estimates for Fractional Type Operators

In this note we prove the estimate \(M^{\sharp }_{0,s}(Tf)(x) \le c\,M_{\gamma } f(x)\) for general fractional type operators T, where \(M^{\sharp }_{0,s}\) is the local sharp maximal function and M _γ the fractional maximal function, as well as a local version of this estimate. This allows us to express the local weighted control of T f by M _γ f. Similar estimates hold for T replaced by fractional type operators with kernels satisfying Hörmander-type conditions or integral operators with homogeneous kernels, and M _γ replaced by an appropriate maximal function M _T . We also prove two-weight, \({L^{p}_{\text {\textit {v}}}}\) - \({L^{q}_{\text {\textit {w}}}}\) estimates for the fractional type operators described above for 1 < p < q < ∞ and a range of q. The local nature of the estimates leads to results involving generalized Orlicz-Campanato and Orlicz-Morrey spaces.     

The atomic decomposition in

In this paper we present an atomic decomposition of integrable functions. As an application we compute the distance of in to the Hardy space .

     

Liquid plasma crystal: Coulomb crystallization of cylindrical macroscopic grains in a gas-discharge plasma

Ordered structures formed of 300-μm-long cylindrical nylon grains with diameters of 15 and 7.5 μm are obtained. In contrast to conventional spherical monodisperse grains, which, under certain conditions, form the plasma-dust Coulomb crystal, the cylindrical grains in the plasma acquire a charge of ～7×10⁵ electrons and form a structure similar to a liquid crystal. The parameter characterizing the nonideality of the dusty component of the plasma attains 10⁶. Grains are suspended in the striation in the horizontal plane and line up in parallel with each other.     

Transport of microparticles in weakly ionized gas-discharge plasmas under microgravity conditions

Measurements of effective structural (pair correlation function) and transport (diffusion constant) characteristics of the system of microparticles in dc and rf gas-discharge plasmas under microgravity conditions are reported. The comparison between these measurements and numerical simulations is used for complex plasma diagnostics.     

Analysis of a conical horn fed by a slightly oversized waveguide

This paper discusses the case of a submillimetre conical feedhorn system which is overmoded due to an oversized waveguide, but is not in the geometric optics regime. The motivation for this system is to use the same feed as a multi-frequency receiver. Increased background loading is the greatest disadvantage in overmoded optics; and aperture efficiency also suffers due to non-optimum horn dimensions. The analysis is done using the Laguerre-Gauss beam expansion method.