We show that the matter Lagrangian of an ideal fluid equals (up to a sign depending on its definition and chosen signature metric) total energy density fluid, i.e. rest plus internal density.

Represented Coxeter matroids of types Cn and Dn, that is, symplectic and orthogonal matroids arising from totally isotropic subspaces of symplectic or (even-dimensional) orthogonal spaces, may also be represented in buildings of type Cn and Dn, respectively (see [4, Chapter 7]). Indeed, the particular buildings involved are those arising from the flags or oriflammes, respectively, of totally is...

The analytic center cutting plane method (ACCPM) is one of successful methods to solve nondifferentiable optimization problems. In this paper ACCPM is used for the first time in the vehicle routing problem with time windows (VRPTW) to accelerate lagrangian relaxation procedure for the problem. At first the basic cutting plane algorithm and its relationship with column generation method is clari...

The Lagrangian star is a germ of the system ({L1, . . . , Lk}, p̃) of Lagrangian submanifolds in the symplectic manifold (M,ω). We investigate the symplectic group action on Lagrangian stars and construct the basic invariants of such action. The Kashiwara signature for 3-Lagrangian linear stars is generalized to the nonlinear case and the generalized contact classes for Lagrangian stars are cons...

The aim of this paper is to investigate geometrically nonlinear static analysis of axially functionally graded cantilever beam subjected to transversal non follower load. The considered problem is solved by finite element method with total Lagrangian kinematic approach. The material properties of the beam vary along the longitudinal direction according to the power law function. The finite elem...

We develop the foundation of the complex symplectic geometry of Lagrangian subvarieties in a hyperkähler manifold. We establish a characterization, a Chern number inequality, topological and geometrical properties of Lagrangian submanifolds. We discuss a category of Lagrangian subvarieties and its relationship with the theory of Lagrangian intersection. We also introduce and study extensively a...