In this paper, we prove a Morse index theorem for the index form of regular Lagrangian system with selfadjoint boundary condition.

After reducing a system of higher-order regular Lagrangian into first-order singular Lagrangian using constrained auxiliary description, the Hamilton-Jacobi function is constructed. Besides, the quantization of the system is investigated using the canonical path integral approximation.

This article explains how to construct immersed Lagrangian submanifolds in C2 that are asymptotic at large distance from the origin to a given braid in the 3–sphere. The self-intersections of the Lagrangians are related to the crossings of the braid. These Lagrangians are then used to construct immersed Lagrangians in the vector bundle O(−1)⊕ O(−1) over the Riemann sphere which are asymptotic a...

this paper presents results of applying a new approach on 2d inversion of magnetotelluric (mt) data in order to enhance resolution and stability of the inversion results. due to non-linearity and limited coverage of data acquisition in an mt field campaign, minimizing the error by linearization of the problem in least squares inversion usually leads to an ill-posed problem. in general, an inver...