We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variasional...

One of the well-known problems in evolutionary search for solving optimization problem is the premature convergence. The general constrained optimization techniques such as hybrid evolutionary programming, two{phase evolutionary programming, and Evolian algorithms are not safe from the same problem in the rst phase. To overcome this problem, we apply the sharing function to the Evolian algorith...

We discuss how the Lagrange multiplier method of nonequilibrium steady state statistical mechanics can be applied to describe the electronic transport in a quantum wire. We describe the theoretical scheme using a tight-binding model. The Hamiltonian of the wire is extended via a Lagrange multiplier to "open" the quantum system and to drive current through it. The diagonalization of the extended...

A novel procedure to reduce by four the order of Euler–Lagrange equations associated to n-th order variational problems involving single variable integrals is presented. In preparation, a new formula for the commutator of two C∞symmetries is established. The method is based on a pair of variational C∞-symmetries whose commutators satisfy a certain solvability condition. It allows one to recover...

Abstract We prove that the heavy symmetric top (Lagrange, 1788) linearizes on a two–dimensional non– compact algebraic group – the generalized Jacobian of an elliptic curve with two points identified. This leads to a transparent description of its complex and real invariant level sets. We deduce, by making use of a Baker–Akhiezer function, simple explicit formulae for the general solution of th...

valid for f 2 Lp(IR ) and an arbitrary nite sequence of points in IR, is discussed. The linear functional f 7! R f was introduced by Micchelli [M80] in connection with Kergin interpolation. This functional also naturally occurs in other multivariate generalisations of Lagrange interpolation, including Hakopian interpolation, and the Lagrange maps of Section 5. For each of these schemes, (1) imp...

Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained m...

We propose a natural Fedosov type quantization of generalized Lagrange models and gravity theories with metrics lifted on tangent bundle, or extended to higher dimension, following some stated geometric/ physical conditions (for instance, nonholonomic and/or conformal transforms to some physically important metrics or mapping into a gauge model). Such generalized Lagrange transforms define cano...