In this paper we established the condition for a curve to satisfy stochastic generalized fractional HP (Hamilton-Pontryagin) equations. These equations are described using Itô integral. We have also considered the case of stochastic generalized fractional Hamiltonian equations, for a hyperregular Lagrange function. From the stochastic generalized fractional Hamiltonian equations, Langevin gener...

Impulse formulations of Hall magnetohydrodynamic (MHD) equations are developed. The Lagrange invariance of a generalized magnetic helicity is established for Hall MHD. The physical implications of this Lagrange invariant are discussed. The discussion is then extended to compressible Hall MHD. Compressibility effects are show not to affect, as to be expected, the physical implications of the gen...

A Schwarz Waveform Relaxation (SWR) algorithm is proposed to solve by Domain Decomposition Method (DDM) linear and nonlinear Schrödinger equations. The symbols of the transparent fractional transmission operators involved in Optimized Schwarz Waveform Relaxation (OSWR) algorithms are approximated by low order Lagrange polynomials to derive Lagrange-Schwarz Waveform Relaxation (LSWR) algorithms ...

In recent years, parallel computers have changed techniques to solve problems in various kinds of fields. In parallel computers of distributed memory type, data can be shared by communication procedures called message-passing, whose speed is slower than that of computations in a processor. From a practical point of view, it is important to reduce the amount of message-passing. Domain-decomposit...

A class of quadratic optimization problems in Hilbert spaces is considered, where pointwise box constraints and constraints of bottleneck type are given. The main focus is to prove the existence of regular Lagrange multipliers in L-spaces. This question is solved by investigating the solvability of a Lagrange dual quadratic problem. The theory is applied to different optimal control problems fo...