For non-degenerate surfaces in R, a distinguished transversal bundle called affine normal plane bundle was proposed in [8]. Lagrangian surfaces have remarkable properties with respect to this normal bundle, like for example, the normal bundle being Lagrangian. In this paper we characterize those surfaces which are Lagrangian with respect to some parallel symplectic form in R. Mathematics Subjec...

Properties of the Dirac-Born-Infeld Lagrangian analogous to those of the Nambu-Goto String are analysed. In particular the Lagrangian is shown to be constant or zero on the space of solutions of the equations of motion if the Lagrangian is taken to any power other than 1 2 . ∗e-mail: [email protected] 1

We present a Lagrangian for the bilinear discrete KP (or HirotaMiwa) equation. Furthermore, we show that this Lagrangian can be extended to a Lagrangian 3-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus we establish the multiform structure as proposed in [8] in a higher dimensional case.

Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We study a modified Lagrangian relaxation which generates an optimal integer solution. We call it semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instances of the p-median problem.

In this paper, a green transportation location problem is considered with uncertain demand parameter. Increasing robustness influences the number of trucks for sending goods and products, caused consequently, increase the air pollution. In this paper, two green approaches are introduced which demand is the main uncertain parameter in both. These approaches are addressed to provide a trade-off b...

A Hamiltonian stationary Lagrangian submanifold of a Kähler manifold is a Lagrangian submanifold whose volume is stationary under Hamiltonian variations. We find a sufficient condition on the curvature of a Kähler manifold of real dimension four to guarantee the existence of a family of small Hamiltonian stationary Lagrangian tori. Mathematics Subject Classification (2000) 58J37 · 35J20 · 35J48...

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 construct in a manifestly supersymmetric form the leading and subleading terms in momentum for an effective supersymmetric chiral Lagrangian in terms of complex pions and their superpartners. A soft supersymmetry breaking term is included and below the super-symmetry breaking scale the Lagrangian reduces to the usual bosonic chiral Lagrangian in terms of real pions.

This paper completes the classification of regular Lagrangian fibrations over compact surfaces. [13] classifies regular Lagrangian fibrations over T. The main theorem in [8] is used to in order to classify integral affine structures on the Klein bottle K and, hence, regular Lagrangian fibrations over this space.