Shadowing and Antishadowing in Neutrino Deep Inelastic Scattering

The coherence of multiscattering quark nuclear processes leads to shadowing and antishadowing of the electromagnetic nuclear structure functions in agreement with measurements. This picture leads to substantially different antishadowing for charged and neutral current processes, particularly in anti-neutrino reactions, thus affecting the extraction of the weak-mixing angle $\sin^2\theta_W$.Comment: 4 pages, 1 figure, Prepared for the International Conference on QCD and Hadronic Physics, Beijing, China, June 16-20 200

Electromagnetic Pulse from Final Gravitational Stellar Collapse

We employ an effective gravitational stellar final collapse model which contains the relevant physics involved in this complex phenomena: spherical radical infall in the Schwarzschild metric of the homogeneous core of an advanced star, giant magnetic dipole moment, magnetohydrodynamic material response and realistic equations of state (EOS). The electromagnetic pulse is computed both for medium size cores undergoing hydrodynamic bounce and large size cores undergoing black hole formation. We clearly show that there must exist two classes of neutron stars, separated by maximum allowable masses: those that collapsed as solitary stars (dynamical mass limit) and those that collapsed in binary systems allowing mass accretion (static neutron star mass). Our results show that the electromagnetic pulse spectrum associated with black hole formation is a universal signature, independent of the nuclear EOS. Our results also predict that there must exist black holes whose masses are less than the static neutron star stability limit.Comment: 9 pages, 8 figures, to be published in Astronomy and Astrophysic

Fractional Fourier approximations for potential gravity waves on deep water

In the framework of the canonical model of hydrodynamics, where fluid is assumed to be ideal and incompressible, waves are potential, two-dimensional, and symmetric, the authors have recently reported the existence of a new type of gravity waves on deep water besides well studied Stokes waves (Phys. Rev. Lett., 2002, v. 89, 164502). The distinctive feature of these waves is that horizontal water velocities in the wave crests exceed the speed of the crests themselves. Such waves were found to describe irregular flows with stagnation point inside the flow domain and discontinuous streamlines near the wave crests. Irregular flows produce a simple model for describing the initial stage of the formation of spilling breakers when a localized jet is formed at the crest following by generating whitecaps. In the present work, a new highly efficient method for computing steady potential gravity waves on deep water is proposed to examine the above results in more detail. The method is based on the truncated fractional approximations for the velocity potential in terms of the basis functions $1/\bigr(1-\exp(y_0-y-ix)\bigl)^n$, $y_0$ being a free parameter. The non-linear transformation of the horizontal scale $x = \chi - \gamma \sin\chi, 0<\gamma<1,$ is additionally applied to concentrate a numerical emphasis on the crest region of a wave for accelerating the convergence of the series. Fractional approximations were employed for calculating both steep Stokes waves and irregular flows. For lesser computational time, the advantage in accuracy over ordinary Fourier expansions in terms the basis functions $\exp\bigl(n (y+ix)\bigr)$ was found to be from one to ten decimal orders depending on the wave steepness and flow parameters.Comment: 14 pages, 8 figures, submitted to Nonlinear Processes in Geophysic

Associative nil-algebras over finite fields

The nilpotency degree of a relatively free finitely generated associative algebra with the identity $x^n=0$ is studied over finite fields.Comment: 12 page