Let us consider the di erential equation

Let X be the solution of an Itô di erential equation with jumps over R. Under some auxiliary assumptions on the parameters of the equation, we characterize the support of the law of X in the Skorohod space D as the closure of the set of solutions to piecewise ordinary di erential equations. This gives an analogue in the Poisson space to the classical Stroock–Varadhan support theorem. c © 2000 P...

In this paper, we study the existence and stability of traveling waves in lattice dynamical systems, in particular, in lattice ordinary di erential equations (lattice ODE's) and in coupled map lattices (CML's). Instead of employing the moving coordinate approach as for partial di erential equations, we construct a local coordinate system around a traveling wave solution of a lattice ODE, analog...

We address the enumeration of q-coloured planar maps counted by the number of edges and the number of monochromatic edges. We prove that the associated generating function is di erentially algebraic, that is, satis es a non-trivial polynomial di erential equation with respect to the edge variable. We give explicitly a di erential system that characterizes this series. We then prove a similar re...

We consider the construction of geometric integrators in the class of RKMK methods. Any di erential equation in the form of an in nitesimal generator on a homogeneous space is shown to be locally equivalent to a di erential equation on the Lie algebra corresponding to the Lie group acting on the homogenous space. This way we obtain a distinction between the coordinate-free phrasing of the di er...

In this article we consider derive a macroscopic model for root length density evolution, starting from a discrete mesh of roots, using homogenization. In the microscopic model each roots grows vertically according to an ordinary di erential equation. The roots growth rates depend on the spatial repartition of nutrient in the soil, which also evolves in time, leading to a fully coupled nonlinea...

© 2008 Pappu et al. The Rockefeller University Press $30.00 J. Exp. Med. Vol. 205 No. 5 1049-1062 www.jem.org/cgi/doi/ 1049 10.1084/jem.20071364 After activation, CD4 + Th cells diff erentiate into distinct eff ector subsets that are characterized by their unique cytokine expression and immunoregulatory function ( 1, 2 ). A novel Th subset — termed Th IL-17 , Th17, or infl ammatory Th — has bee...

"In this paper we investigate the existence of solutions initial value problems (IVP for short), partial hyperbolic functional and neutral differential inclusions fractional order involving Caputo derivative with finite delay by using nonlinear alternative Frigon type multivalued admissible contraction in Frechet spaces."

In this paper we present a numerical method for fuzzy differential equation of fractional order under gH-fractional Caputo differentiability. The main idea of this method is to approximate the solution of fuzzy fractional differential equation (FFDE) by an implicit method as corrector and explicit method as predictor. This method is tested on numerical examples.

The derivative of an ideal in a number ring is defined and the relation between the ideal derivative and the arithmetic derivative of a number in Z is discussed. Some simple ideal di↵erential equations are also studied. Further, the definition of the ideal derivative is extended to the derivative of a fractional ideal in a number ring. Again, the relation between the fractional ideal derivative...