The problem of computing quantum mechanical propagators can be recast as a computation Wilson line operator for parallel transport by flat connection acting on vector bundle wavefunctions. In this picture the base manifold is an odd dimensional symplectic geometry, or quite generically contact that viewed "phase-spacetime", while fibers are Hilbert spaces. This approach enjoys "quantum Darboux ...

In this article, a two prey - one predator model has been studied where species are competitive in nature and also uses toxic substances for own existence. Biologically well posedness of the system shown through positivity boundedness solutions. Existence criterion stability analysis non-negative equilibrium points have discussed. The sufficient conditions existence Hopf bifurcation switches in...

We give effective bilipschitz bounds on the change in metric between thick parts of a cusped hyperbolic 3-manifold and its long Dehn fillings. In thin manifold, we complex length short closed geodesic. These results quantify filling theorem Brock Bromberg, extend previous authors from finite volume 3-manifolds to any tame 3-manifold. To prove main results, assemble tools Kleinian group theory i...

We construct examples of nonresolvable generalized «-manifolds, n > 6 , with arbitrary resolution obstruction, homotopy equivalent to any simply connected, closed «-manifold. We further investigate the structure of generalized manifolds and present a program for understanding their topology. By a generalized n-manifold we will mean a finite-dimensional absolute neighborhood retract X such that ...

We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures. In this article we explain how to normalize tight contact structures with respect to a fixed triangulation. Using t...

Abstract A diffusive phytoplankton–zooplankton model with nonlinear harvesting is considered in this paper. Firstly, using the as parameter, we get existence and stability of positive steady state, also investigate spatially homogeneous inhomogeneous periodic solutions. Then, by applying normal form theory center manifold theorem, give direction Hopf bifurcation from state. In addition, prove B...