We construct super Hamiltonian integrable systems within the theory of supersymmetric Poisson vertex algebras (SUSY PVAs). provide a powerful tool for understanding SUSY PVAs called master formula. attach some Lie superalgebraic data to generalized W-algebra and show that it is equipped with two compatible PVA brackets. reformulate these brackets in terms odd differential operators obtain bi-Ha...

A section of a Hamiltonian system is hypersurface in the phase space system, usually representing set one-sided constraints (e. g., boundary, an obstacle or admissible states). In this paper we give local classification results for all typical singularities sections regular (non-singular) systems, problem equivalent to systems with constraints. particular, complete list exact normal forms funct...

in this paper energy bands and berry curvature of graphene was studied. desired hamiltonian regarding the next-nearest neighbors obtained by tight binding model. by using the second quantization approach, the transformation matrix is calculated and the hamiltonian of system is diagonalized. with this hamiltonian, the band structure and wave function can be calculated. by using calculated wave f...