The asymptotic solution for the Painleve-2 equation with small parameter is considered. The solution has algebraic behavior before point t∗ and fast oscillating behavior after the point t∗. In the transition layer the behavior of the asymptotic solution is more complicated. The leading term of the asymptotics satisfies the Painleve-1 equation and some elliptic equation with constant coefficient...

Abstract. This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion coefficient functions such as the stochastic Ginzburg-Landau equation and the 3/2-volatility model from mathematical finance. Our analysis of the ...

To cite: Edlin JC, AlfaWali M, Bond A. BMJ Case Rep Published online: [please include Day Month Year] doi:10.1136/bcr-2015209409 DESCRIPTION An 88-year-old woman presented with sudden onset sharp upper abdominal pain associated with anorexia, vomiting and weight loss. Examination revealed a tender palpable mass in the epigastrium without any abnormal blood tests. A CT scan showed a 12 cm cystic...

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.

We discuss a dynamic procedure that makes fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent second moment, namely, with the power index mu in the interval 2<mu<3 , yield a generalized master equation equivalent to the sum of an ordin...

We consider a subset of Markov fluid models where the discrete background process is a Population Continuous Time Markov Chain (PCTMC) – a Markov process capturing interactions between large groups of identically behaved components. We allow the transition and fluid evolution rates to depend on the fluid level. Additionally, we include time-inhomogeneous rate parameters, which can be used to in...

In solving a system of ordinary differential equations by an interval method the approximate solution at any considered moment of time t represents a set (called interval) containing the exact solution at the moment t. The intervals determining the solution of a system are often expanded in the course of time irrespective of the method and step used. The phenomenon of interval expansion, called...