In this paper, we study a multi-symplectic scheme for three dimensional Maxwell’s equations in a simple medium. This is a system of PDEs with multi-symplectic structures. We prove that this multi-symplectic scheme preserves the discrete version of local and global energy conservation law and the discrete divergence. Furthermore, we extend the discussion to several dispersion properties of the m...

The aim of this paper is to discuss an important discourse, as most literatures highlighted the dimension partial flag in a certain manner, according fixed definition that does not include all possible cases. In present existence two different cases flags varieties groups and explained wholly. addition we will proceed by calculating dimensions for given after pertaining signature these are stud...

The automorphism group of a locally conformal symplectic structure is studied. It is shown that this group possesses essential features of the symplectomorphism group. By using a special type of cohomology the flux and Calabi homomorphisms are introduced. The main theorem states that the kernels of these homomorphisms are simple groups, for the precise statement see chapter 7. Some of the metho...

Let K be the field of real or complex numbers. Let (X ∼= K, ω) be a symplectic affine space. We study the group of polynomial symplectomorphisms of X. We show that for an arbitrary k ∈ N the group of polynomial symplectomorphisms acts k-transitively on X. Moreover, if 2 l 2n− 2 then elements of this group can be characterized by polynomial automorphisms which preserve the symplectic type of all...

We present a method to construct symplecticity-preserving renormalization group maps by using the Liouville operator, and obtain correctly reduced symplectic maps describing their long-time behavior even when a resonant island chain appears. There has been a long history to study an asymptotic solution of Hamiltonian flows by means of singular perturbation methods such as the averaging method a...

Given a symplectic space, equipped with a line bundle and a Hamiltonian group action satisfying certain compatibility conditions, it is a basic question to understand the decomposition of the quantization space in irreducible representations of the group. We derive weight multiplicity formulas for the quantization space in terms of data at the fixed points on the symplectic space, which apply t...

In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient Wr = {(x, y, z, t)|xy − z + t = 0}/μr(a,−a, 1, 0), r ≥ 1, which we call orbi-conifolds. The related orbifold symplectic conifold transition and orbifold symplectic flops are constructed. Let X and Y be two symplectic orbifolds connected by such a flop. We study orbifold Gromov-Witten invariants of...