A. This article address two issues. First, we explore to what extend the techniques of Piunikhin, Salamon and Schwarz in [PSS96] can be carried over to Lagrangian Floer homology. In [PSS96] an isomorphism between Hamiltonian Floer homology and singular homology is established. In contrast, Lagrangian Floer homology is not isomorphic to the singular homology of the Lagrangian submanifold,...

The motion of a mechanical system is related via a set of dynamic equations to the forces and torques it is subject to. In this work we will be primarily interested in robots consisting of a collection of rigid links connected through joints that constrain the relative motion between the links. There are two main formalisms for deriving the dynamic equations for such mechanical systems: (1) New...

We introduce some approximate optimal solutions and a generalized augmented Lagrangian in nonlinear programming, establish dual function and dual problem based on the generalized augmented Lagrangian, obtain approximate KKT necessary optimality condition of the generalized augmented Lagrangian dual problem, prove that the approximate stationary points of generalized augmented Lagrangian problem...

In the past few years there have been several striking results about the topology of Lagrangian surfaces in symplectic four-manifolds. The general tendency of these results is that many isotopy classes of embedded surfaces do not contain Lagrangian representatives. This is called the topological unknottedness of Lagrangian surfaces; see [4] for a survey. The aim of this paper is to complement t...

This paper introduces a geometrically constrained variational problem for the area functional. We consider the area restricted to the lagrangian surfaces of a Kähler surface, or, more generally, a symplectic 4-manifold with suitable metric, and study its critical points and in particular its minimizers. We apply this study to the problem of finding canonical representatives of the lagrangian ho...

In this paper we show how to lift Lagrangian immersions in $\mathbb{C} P^{n-1}$ produce cones ^n$, and use process several families of examples special cones. Moreover cones, isotopic the Harvey-Lawson trivial whose projections are with few transverse double points.

We study singularities of Lagrangian mean curvature flow in C when the initial condition is a zero-Maslov class Lagrangian. We start by showing that, in this setting, singularities are unavoidable. More precisely, we construct Lagrangians with arbitrarily small Lagrangian angle and Lagrangians which are Hamiltonian isotopic to a plane that, nevertheless, develop finite time singularities under ...

Anomalous sector of chiral Lagrangian is calculated in a gauge invariant, nonlocal, dynamical quark model. The Wess-Zumino term is proved coming from two kinds of sources, one is independent of and another dependent on dynamical quark self energy Σ(k2). p6 and more higher order anomalous sectors come only from Σ(k2) dependent source. After some cancellation, standard Wess-Zumino action is obtai...