Generalised Fractional Evolution Equations of Caputo Type

This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the solutions. These results encompass known linear and non-linear equations from classical fractional partial differential equations such as the time-space-fractional diffusion equation, as well as their far reaching extensions. \\ Meaning is given to a probabilistic generalisation of Mittag-Leffler functions.Comment: To be published in 'Chaos, Solitons & Fractals

Measuring multipole moments of Weyl metrics by means of gyroscopes

Using the technique of Rindler and Perlick we calculate the total precession per revolution of a gyroscope circumventing the source of Weyl metrics. We establish thereby a link between the multipole moments of the source and an ``observable'' quantity. Special attention deserves the case of the gamma-metric. As an extension of this result we also present the corresponding expressions for some stationary space-times.Comment: 18 pages Latex, To appear in J.Math.Phy

Watson's theorem and the NΔ(1232)N\Delta(1232) axial transition

We present a new determination of the $N\Delta$ axial form factors from neutrino induced pion production data. For this purpose, the model of Hernandez {\it et al.} [Phys. Rev. D76, 033005 (2007)] is improved by partially restoring unitarity. This is accomplished by imposing Watson's theorem on the dominant vector and axial multipoles. As a consequence, a larger $C_5^A(0)$, in good agreement with the prediction from the off-diagonal Goldberger-Treiman relation, is now obtained.Comment: 17 latex pages, 7 figures, 2 tables. Some typos correcte

Notes on proper homotopy theories associated with compact PL-manifolds

The purpose of this note is to present a bigraded sequence of functors associated with compact PL-manifolds . These functors are invariant of proper homotopy type, and distinguish topological spaces which have the same homotopy type. On the category of compact topological spaces these functors agree with the Hurewicz homotopy groups, hence the principal interest of these functors is for noncompact spaces

Probing the chiral weak Hamiltonian at finite volumes

Non-leptonic kaon decays are often described through an effective chiral weak Hamiltonian, whose couplings ("low-energy constants") encode all non-perturbative QCD physics. It has recently been suggested that these low-energy constants could be determined at finite volumes by matching the non-perturbatively measured three-point correlation functions between the weak Hamiltonian and two left-handed flavour currents, to analytic predictions following from chiral perturbation theory. Here we complete the analytic side in two respects: by inspecting how small ("epsilon-regime") and intermediate or large ("p-regime") quark masses connect to each other, and by including in the discussion the two leading Delta I = 1/2 operators. We show that the epsilon-regime offers a straightforward strategy for disentangling the coefficients of the Delta I = 1/2 operators, and that in the p-regime finite-volume effects are significant in these observables once the pseudoscalar mass M and the box length L are in the regime ML \lsim 5.0.Comment: 37 pages. v2: some additions and clarifications; published versio

Three carbon-enhanced metal-poor dwarf stars from the SDSS - Chemical abundances from CO^5BOLD 3D hydrodynamical model atmospheres

The origin of carbon-enhanced metal-poor stars enriched with both s and r elements is highly debated. Detailed abundances of these types of stars are crucial to understand the nature of their progenitors. The aim of this investigation is to study in detail the abundances of SDSS J1349-0229, SDSS J0912+0216 and SDSS J1036+1212, three dwarf CEMP stars, selected from the Sloan Digital Sky Survey. Using high resolution VLT/UVES spectra (R ~ 30 000) we determine abundances for Li, C, N, O, Na, Mg, Al, Ca, Sc, Ti, Cr, Mn, Fe, Co, Ni and 21 neutron-capture elements. We made use of CO^5BOLD 3D hydrodynamical model atmospheres in the analysis of the carbon, nitrogen and oxygen abundances. NLTE corrections for C I and O I lines were computed using the Kiel code. We classify SDSS J1349-0229 and SDSS J0912+0216 as CEMP-r+s stars. SDSS J1036+1212 belongs to the class CEMP-no/s, with enhanced Ba, but deficient Sr, of which it is the third member discovered to date. Radial-velocity variations have been observed in SDSS J1349-0229, providing evidence that it is a member of a binary system. The chemical composition of the three stars is generally compatible with mass transfer from an AGB companion. However, many details remain difficult to explain. Most notably of those are the abundance of Li at the level of the Spite plateau in SDSS J1036+1212 and the large over-abundance of the pure r-process element Eu in all three stars.Comment: 12 pages, 15 figures. Accepted for publication in A&

High-order harmonic generation driven by chirped laser pulses induced by linear and non linear phenomena

We present a theoretical study of high-order harmonic generation (HHG) driven by ultrashort optical pulses with different kind of chirps. The goal of the present work is perform a detailed study to clarify the relevant parameters in the chirped pulses to achieve a noticeable cut-off extensions in HHG. These chirped pulses are generated using both linear and nonlinear dispersive media.The description of the origin of the physical mechanisms responsible of this extension is, however, not usually reported with enough detail in the literature. The study of the behaviour of the harmonic cut-off with these kind of pulses is carried out in the classical context, by the integration of the Newton-Lorentz equation complemented with the quantum approach, based on the integration of the time dependent Schr\"odinger equation in full dimensions (TDSE-3D), we are able to understand the underlying physics.Comment: 13 pages, 8 figure