In this paper, we introduce the concept of ordinary smooth topology on a set X by considering the gradation of openness of ordinary subsets of X . And we obtain the result [Corollary 2.13] : An ordinary smooth topology is fully determined its decomposition in classical topologies. Also we introduce the notion of ordinary smooth [resp. strong and weak] continuity and study some its properties. A...

My typical working week shows just how varied mental health nursing can be. As a GP liaison nurse specialising in mental health, I work from the surgery, hospitals, clinics and other agencies, depending on where the surgery's patients are referred.

1 Initial Value Problem We are given a right hand side function f(t, y) with f : [t0, T ]×Rn → Rn and an initial value y0 ∈ Rn. We want to find a function y(t) with y : [t0, T ] → Rn such that y′(t) exists, is continuous and satisfies the initial value problem y′(t) = f (t, y(t)) , y(t0) = y0. (1) We assume that f(t, y) satisfies a Lipschitz condition with respect to y (at least for y with |y −...

Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential equations. We give several families of differential systems which illustrate how the integrability of the system passes through the solutions of a linear diff...

Abstract We extend the Eruguin result exposed in the paper ”Construction of the whole set of ordinary differential equations with a given integral curve” published in 1952 and construct a differential system in R which admits a given set of the partial integrals, in particular we study the case when theses functions are polynomials. We construct a non-Darboux integrable planar polynomial system...

Most physical processes are modeled by differential equations. First order ordinary differential equations, also known as dynamical systems, arise in a wide range of applications, including population dynamics, mechanical systems, planetary motion, ecology, chemical diffusion, etc., etc. See [19, 72,ODES] for additional material and applications. The goal of this chapter is to study and solve i...

The DI methods for directly solving a system ofa general higher order ODEs are discussed. The convergence of the constant stepsize and constant order formulation of the DI methods is proven first before the convergencefor the variable order and stepsize case.

lut 009 meteorite was found during a trip to lut desert of iran in march,2012, at 30°20.38' n, 59°09.04' e. chemical compositions of equilibrated olivine (fa19.3 ± 0.5) and orthopyroxene (fs16.7 ± 0.6) show that the meteorite sample belongs to h group of ordinary chondrites, while the texture (chondrule petrography and plagioclase size) suggests a petrologic type of 4. the lut 009 has...