A higher-order Godunov method for the radiation subsystem of radiation hydro-dynamics is presented. A key ingredient of the method is the direct coupling of stiff source term effects to the hyperbolic structure of the system of conservation laws; it is composed of a predictor step that is based on Duhamel's principle and a corrector step that is based on Picard iteration. The method is second-o...

s of 2010 LSU Math REU talks • Name: Suzanne Carter Title: Calculating Picard Fuchs Differential Equations Abstract: Families of algebraic varieties have an associated Picard Fuchs differential equation, with a solution space spanned by the periods of the variety. These periods are integrals of differentials taken over chains in the primitive cohomology of the varieties. The, often unique, holo...

Let L2 denote the stable homotopy category of v−1 2 BP -local spectra at the prime three. In [2], it is shown that the Picard group of L2 consisting of isomorphic classes of invertible spectra is isomorphic to either the direct sum of Z and Z/3 or the direct sum of Z and two copies of Z/3. In this paper, we conclude the Picard group is isomorphic to the latter group by showing the existence of ...

We study nonsingular branched coverings of a homogeneous space X. There is a vector bundle associated with such a covering which was conjectured by O. Debarre to be ample when the Picard number of X is one. We prove this conjecture, which implies Barth-Lefschetz type theorems, for lagrangian grassmannians, and for quadrics up to dimension six. We propose a conjectural extension to homogeneous s...

A new method of constructing elliptic finite-gap solutions of the stationary Korteweg-de Vries (KdV) hierarchy, based on a theorem due to Picard, is illustrated in the concrete case of the Lamé-Ince potentials −s(s+1)P(z), s ∈ N (P(.) the elliptic Weierstrass function). Analogous results are derived in the context of the stationary modified Korteweg-de Vries (mKdV) hierarchy for the first time.

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...

Dynamic iteration methods for treating linear systems of diierential equations are considered. It is shown that the discretized Picard-Lindell of (waveform relaxation) iteration can be accelerated by solving the defect equations with a larger timestep, or by using a recursive procedure based on a succession of increasing timesteps. A discussion of convergence is presented, including analysis of...

We summarize some recent results on partial linear functional systems. By associating a finite-dimensional linear functional system to a Laurent-Ore module, Picard-Vessiot extensions are generalized from linear ordinary differential (difference) equations to finite-dimensional linear functional systems. A generalized Beke’s method is also presented for factoring Laurent-Ore modules and it will ...

In this paper we study dynamic iteration techniques for nonlinear differential equations with mixed modification of the argument. The dynamic iteration method generalizes the well known Picard iterations, improving significantly the convergence speed of the iterative process. It also have the advantage of decoupling the part containing the modified argument so the iteration steps consist in sol...