We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equations. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit e...

We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equations. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit e...

one of the most important parts of power transmission in automotives is c.v. joint, which consists of four components where exterior bowl is one of them. due to its complexity, and importance in automobile and existence of high stresses, forging process is the only cost effective method of production. hence, the best method of production of this part is forging process. the exterior part of c.v...

A new method is developed to solve the condensation equation as it relates to air quality models using both semi-Lagrangian and Lagrangian  uxes to increase resolution and perform accurately under stringent conditions that occur in the atmosphere. The new method, partitioned  ux integrated semi-Lagrangian method (PFISLM), can be used with lower-order interpolators and produces highly accurate...

A new method is developed to solve the condensation equation as it relates to Air Quality Models using both semi-Lagrangian and Lagrangian fluxes to increase resolution and perform accurately under stringent conditions that occur in the atmosphere. The new method, Partitioned Flux Integrated Semi-Lagrangian Method (PFISLM), can be used with lower-order interpolators and they produce highly accu...

For a given iterate generated by the augmented Lagrangian or the Lagrangian relaxation based method, we derive estimates for the distance to the primal solution of the underlying optimization problem. The estimates are obtained using some recent contributions to the sensitivity theory, under appropriate first or second order sufficient optimality conditions. The given estimates hold in situatio...

Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel’s theorem for frozen-in vo...

Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel's theorem for frozen-in vo...

For design optimization tasks, quite often a so-called one-shot approach is used. It augments the solution of the state equation with a suitable adjoint solver yielding approximate reduced derivatives that can be used in an optimization iteration to change the design. The coordination of these three iterative processes is well established when only the state equation is considered as equality c...

This paper is devoted to the numerical resolution of unit-commitment problems, with emphasis on the French model optimizing the daily production of electricity. The solution process has two phases. First a Lagrangian relaxation solves the dual to find a lower bound; it also gives a primal relaxed solution. We then propose to use the latter in the second phase, for a heuristic resolution based o...