We consider a connected symplectic manifold M acted on properly and in a Hamiltonian fashion by a connected Lie group G. Inspired to the recent paper [3], see also [12] and [24], we study Lagrangian orbits of Hamiltonian actions. The dimension of the moduli space of the Lagrangian orbits is given and we also describe under which condition a Lagrangian orbit is isolated. If M is a compact Kähler...

in this paper, a new numerical method is presented for solvingthe optimal control problems of bang-bang type with free or xed terminaltime. the method is based on bezier polynomials which are presented inany interval as [t0; tf ]. the problems are reduced to a constrained problemswhich can be solved by using lagrangian method. the constraints ofthese problems are terminal state and conditions....

the mean and variance of the lagrangian katz family of distribution (lkd), the basiclagrangian katz distribution of type i (lkd-i) and type ii (lkd-ii) are provided in an easy method.the recurrence relation between the non-central, central and factorial moments, and the recurrencerelation between moments and cumulants of lkd, lkd-i and lkd-ii are given. the first fourcumulants of lkd-i and lkd-...

We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an overapproximation of the gradient of the solution-flows. The SF measures the discrepancy between two states propagated by the system solution from ...

This article studies the mean curvature flow of Lagrangian submanifolds. In particular, we prove the following global existence and convergence theorem: if the potential function of a Lagrangian graph in T 2n is convex, then the flow exists for all time and converges smoothly to a flat Lagrangian submanifold.

We show that the space of Lagrangian spheres inside the cotangent bundle of the 2-sphere is contractible. We then discuss the phenomenon of Lagrangian unknottedness in other Stein surfaces. There exist homotopic Lagrangian spheres which are not Hamiltonian isotopic, but we show that in a typical case all such spheres are still equivalent under a symplectomorphism.

Let X be an irreducible symplectic manifold and Def(X) the Kuranishi space. Assume that X admits a Lagrangian fibration. We prove that X can be deformed preserving a Lagrangian fibration. More precisely, there exists a smooth hypersurface H of Def(X) such that the restriction family X ×Def(X) H admits a family of Lagrangian fibrations over H.

Based on the Weinberg lagrangian or, in a new language, the lagrangian of hidden local symmetry added with the term induced by the anomalous lagrangian of Wess and Zumino, the dynamics of the decays ρ → 4π and ω → 5π is considered. The excitation curves of ρ resonance in its decay to 4π are obtained for the first time.

Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We propose a modified Lagrangian relaxation which used in (linear) combinatorial optimization with equality constraints generates an optimal integer solution. We call this new concept semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instan...