Extending work of M. Zarzar, we evaluate the potential of Goppa-type evaluation codes constructed from linear systems on projective algebraic surfaces with small Picard number. Putting this condition on the Picard number provides some control over the numbers of irreducible components of curves on the surface and hence over the minimum distance of the codes. We find that such surfaces do not au...

We derive here a variant of the 2D Green-Naghdi equations that model the propagation of two-directional, nonlinear dispersive waves in shallow water. This new model has the same accuracy as the standard 2D GreenNaghdi equations. Its mathematical interest is that it allows a control of the rotational part of the (vertically averaged) horizontal velocity, which is not the case for the usual Green...

In this article we first discuss the existence and uniqueness of a solution for the coincidence problem: Find p ∈ X such that Tp = Sp, where X is a nonempty set, Y is a complete metric space, and T,S :X → Y are two mappings satisfying a Wardowski type condition of contractivity. Later on, we will state the convergence of the Picard-Juncgk iteration process to the above coincidence problem as we...

We investigate effectiveness of an acceleration method applied to the modified Picard iteration for simulations of variably saturated flow. We solve nonlinear systems using both unaccelerated and accelerated modified Picard iteration as well as Newton’s method. Since Picard iterations can be slow to converge, the advantage of acceleration is to provide faster convergence while maintaining advan...

has been studied by many authors from the pioneering work of Picard 1 , who proved the existence of a solution by an application of the well-known method of successive approximations under a Lipschitz condition on g and a smallness condition on T . Sharper results were obtained by Hamel 2 in the special case of a forced pendulum equation see also 3, 4 . The existence of periodic solutions for t...

The notion of H-covariant strong Morita equivalence is introduced for ∗-algebras over C = R(i) with an ordered ring R which are equipped with a ∗-action of a Hopf ∗-algebra H . This defines a corresponding H-covariant strong Picard groupoid which encodes the entire Morita theory. Dropping the positivity conditions one obtains H-covariant ∗-Morita equivalence with its H-covariant ∗-Picard groupo...

We consider regularization methods for numerical solution of linear illposed problems, in particular, image deblurring, when the singular value decomposition (SVD) of the operator is available. We assume that the noise-free problem satisfies the discrete Picard condition and define the Picard parameter, the index beyond which the data, expressed in the coordinate system of the SVD, are dominate...

Ill-posed linear equations are pervasive in computer vision. A popular way to solve an ill-posed problem is regularization. In this paper, we propose a new criterion for designing the regularizing filter. This criterion reveals the implicit assumption made by regularizing filters. Then with the help of the discrete Picard condition, we refine the exponential filter using our criterion. The effe...

Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let g be its Lie algebra. First we correct and generalise a well-known result about the Picard group of G. Then we prove that, if the derived group is simply connected and g satisfies a mild condition, the algebra K[G] of regular functions on G that are invariant under the act...

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we prove that, given a such variety X which is not exceptional, then X is smooth if and only if an appropriate toric variety contained in X is smooth. keywords:...