We prove that a divergence-free and C1-robustly transitive vector field has no singularities. Moreover, if the vector field is C4 then the linear Poincaré flow associated to it admits a dominated splitting over M . MSC 2000: primary 37D30, 37D25; secondary 37A99. keywords: Volume-preserving flows; Robust transitivity; Dominated splitting; Ergodicity.

Since the kinetic and potential energy terms of the real-time nonlinear Schrödinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well-known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even ...

A class of splitting iterative methods are considered for solving fuzzy system of linear equations, which covers Jacobi, Gauss Seidel, SOR, SSOR and their block variance proposed. Theoretical analysis showed that for a regular splitting, the corresponding iterative method converge to the unique fuzzy solution for any initial vector and fuzzy right hand side vector. Finally, we illustrate our ap...

A mathematical model of contractile ring-dependent cytokinesis is presented by using both phase-field and immersed-boundary methods in a three-dimensional domain. It is one of the powerful hypotheses that cytokinesis happens driven by the contractile ring; however, there are only few mathematical model following the hypothesis in authors knowledge. I consider a hybrid method to model the phenom...

The stochastic volatility jump diffusion model with jumps in both return and volatility leads to a two-dimensional partial integro-differential equation (PIDE). We exploit a fast exponential time integration scheme to solve this PIDE. After spatial discretization and temporal integration, the solution of the PIDE can be formulated as the action of an exponential of a block Toeplitz matrix on a ...

The Dirac equation serves as the basis for the relativistic description of atoms, nuclei and hadrons. In atoms the relevant potentials felt by the electron are Coulombic vector potentials. A Dirac Hamiltonian with a Coulomb potential exhibits a finestructure spectrum with characteristic two-fold degeneracy. Relativistic mean fields in nuclei generated by meson exchanges , and quark confinement ...

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problem...

Climate warming over the next century is expected to have a large impact on the interactions between pathogens and their animal and human hosts. Vector-borne diseases are particularly sensitive to warming because temperature changes can alter vector development rates, shift their geographical distribution and alter transmission dynamics. For this reason, African trypanosomiasis (sleeping sickne...