In this paper we use a class of stochastic functional Kolmogorov-type model with jumps to describe the evolutions of population dynamics. By constructing a special Lyapunov function, we show that the stochastic functional differential equation associated with our model admits a unique global solution in the positive orthant, and, by the exponential martingale inequality with jumps, we dis...

A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...

We assessed parameters of advanced diffusion weighted imaging (DWI) models for the prediction of the tumor growth rate in 55 head and neck squamous cell carcinoma (HNSCC) patients. The DWI acquisition used single-shot spin-echo echo-planar imaging with 12 b-values (0-2000). We calculated 14 DWI parameters using mono-exponential, bi-exponential, tri-exponential, stretched exponential and diffusi...

We consider the influence of impulsive perturbations of a linear impulsive equation in a Banach space on the existence of bounded solutions and the exponential stability of the equation.