This paper presents a numerical study of a stochastic augmented Lagrangian algorithm to solve continuous constrained global optimization problems. The algorithm approximately solves a sequence of bound constrained subproblems whose objective function penalizes equality and inequality constraints violation and depends on the Lagrange multiplier vectors and a penalty parameter. Each subproblem is...

We would like to build a general understanding of branes, the gauge fields to which they are coupled, and the gauge fields living on their world volume. First, we review electromagnetism in four dimensions. Define F (2) = dA as the field strength of the gauge field A. Then under a gauge transformation of the gauge field A by a total derivative d�, with � an arbitrary 0-form (or an arbitrary fun...

A modified system of equations of electrodynamics has been obtained. Beside the Lagrangian one an alternative gauge-like formalism has been developed to introduce the toroid moment contributions in the equations obtained. The two potential formalism that was worked out by us earlier has been developed further where along with the two vector potentials we introduce two scalar potentials thus tak...

We review Galilean Electromagnetism since the 1973 seminal paper of Jean-Marc Lévy-Leblond and Michel Le Bellac and we explain for the first time all the historical experiments of Rowland, Vasilescu Karpen, Roentgen, Eichenwald, Wilson, Wilson and Wilson, which were previously interpreted in a Special Relativistic framework by showing the uselessness of the latter for setups involving slow moti...

Material forces govern the behaviour and the evolution of a defect or of an inhomogeneity in a solid material. In elastic materials these forces are associated with the Eshelby tensor, as is known. In structured or micro-structured materials, an Eshelby–like stress can be assembled by following a simple rule. By appealing to this rule, one is able to propose an expression for the Eshelby tensor...