Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization, which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a fami...

Abstract. The concept of Lagrange and Hermite interpolation polynomials can be generalized. The spectral basis of idempotents and nilpotents of a factor ring of polynomials provides a powerful framework for the expression of Lagrange and Hermite interpolation in 1, 2 and higher dimensional spaces. We give a new definition of quantum Lagrange and Hermite interpolation polynomials which works on ...

the isogeometric analysis is increasingly used in various engineering problems. it is based on non-uniform rational b-splines (nurbs) basis function applied for the solution field approximation and the geometry description. one of the major concerns with this method is finding an efficient approach to impose essential boundary conditions, especially for inhomogeneous boundaries. the main contri...

the gravity recovery and climate experiment (grace), twin satellites launched in march 2002, are making detailed measurements of the earth's gravity field. it will yield discoveries about gravity and the earth's natural systems. different sensors and instruments have been placed in the grace satellites to fulfill the primary scientific objective of the mission in mapping the earth’s g...

This thesis proposes a two-stage optimization for solving unit commitment. In the first stage, Lagrangian Relaxation (LR) method is used to solve unit commitment using a sub-gradient algorithm for updating Lagrange multipliers. In the second stage, Particle Swarm Optimization (PSO) is applied to update Lagrange multipliers in the Lagrangian Relaxation method (PSOLR). Lagrange multipliers soluti...

We study homological invariants of smooth families of real quadratic forms as a step towards a “ Lagrange multipliers rule in the large” that intends to describe topology of smooth vector functions in terms of scalar Lagrange functions.

We discuss a few of Erdös’results on Lagrange interpolation, and then focus on some of the rami…cations of the Erdös-Turan Theorem on Mean Convergence of Lagrange interpolation.

In order to decrease the fluid drag on an underwater robot manipulator, an optimal trajectory method based on the variational method is presented. By introducing the adjoint variables, which are Lagrange multipliers, we formulate a Lagrange function under certain constraints related to the target angle, target angular velocity, and dynamic equation of the robot manipulator. The state equation (...