Abstract:
We show that almost all metric--affine theories of gravity yield Einstein equations with a non--null cosmological constant $\Lambda$. Under certain circumstances and for any dimension, it is also possible to incorporate a Weyl vector field $W_\mu$ and therefore the presence of an anisotropy. The viability of these field equations is discussed in view of recent astrophysical observations.

Abstract:
. Some double integral inequalities are established. These inequalities give upper and lower error bounds for the well-known mid-point and trapezoid quadrature rules. Some inequalities for convex and concave functions are derived. Applications in numerical integration are also given.

Abstract:
An optimal 3-point quadrature formula of closed type is derived. Various error inequalities are established. Applications in numerical integration are also given.

Abstract:
An error analysis for some Newton-Cotes quadrature formulae is presented. Peano-like error bounds are obtained. They are generally, but not always, better than the usual Peano bounds.

Abstract:
A state of an electron in a quantum wire or a thin film becomes metastable, when a static electric field is applied perpendicular to the wire direction or the film surface. The state decays via tunneling through the created potential barrier. An additionally applied magnetic field, perpendicular to the electric field, can increase the tunneling decay rate for many orders of magnitude. This happens, when the state in the wire or the film has a velocity perpendicular to the magnetic field. According to the cyclotron effect, the velocity rotates under the barrier and becomes more aligned with the direction of tunneling. This mechanism can be called cyclotron enhancement of tunneling.

Abstract:
an optimal 3-point quadrature formula of closed type is derived. the obtained optimal quadrature formula has better estimations of error than the well-known simpson's formula. a few error inequalities for this formula are established.

Abstract:
An optimal 3-point quadrature formula of closed type is derived. The obtained optimal quadrature formula has better estimations of error than the well-known Simpson's formula. A few error inequalities for this formula are established. Se establece una fórmula de cuadratura óptima de 3 puntos de tipo cerrado. Dicha fórmula mejora la estimación de error de la bien conocida fórmula de Simpson. Se establecen algunas desigualdades de error para esta fórmula.

Abstract:
The effect of three-body interatomic contributions in the equation of state of 4He are investigated. A recent two-body potential together with the Cohen and Murrell (Chem. Phys. Lett. 260, 371 (1996)) three-body potential are applied to describe bulk helium. The triple-dipole dispersion and exchange energies are evaluated subjected only to statistical uncertainties. An extension of the diffusion Monte Carlo method is applied in order to compute very small energies differences. The results show how the three-body contributions affects the ground-state energy, the equilibrium, melting and freezing densities.

Abstract:
The stability of a recently proposed general relativistic model of galaxies is studied in some detail. This model is a general relativistic version of the well known Miyamoto-Nagai model that represents well a thick galactic disk. The stability of the disk is investigated under a general first order perturbation keeping the spacetime metric frozen (no gravitational radiation is taken into account). We find that the stability is associated with the thickness of the disk. We have that flat galaxies have more not-stable modes than the thick ones i.e., flat galaxies have a tendency to form more complex structures like rings, bars and spiral arms.