Reflected BSDE with stochastic Lipschitz coefficient

In this paper, we deal with a class of one-dimensional reflected backward stochastic differential equations with stochastic Lipschitz coefficient. We derive the existence and uniqueness of the solutions for those equations via Snell envelope and the fixed point theorem.Comment: 12 pages without figur

Multiscale modelling of fluid and solute transport in soft tissues and microvessels

This study focuses on the movement of particles and extracellular fluid in soft tissues and microvessels. It analyzes modeling applications in biological and physiological fluids at a range of different length scales: from between a few tens to several hundred nanometers, on the endothelial glycocalyx and its effects on interactions between blood and the vessel wall; to a few micrometers, on movement of blood cells in capillaries and transcapillary exchange; to a few millimetres and centimetres, on extracellular matrix deformation and interstitial fluid movement in soft tissues. Interactions between blood cells and capillary wall are discussed when the sizes of the two are of the same order of magnitude, with the glycocalyx on the endothelial and red cell membranes being considered. Exchange of fluid, solutes, and gases by microvessels are highlighted when capillaries have counter-current arrangements. This anatomical feature exists in a number of tissues and is the key in the renal medulla on the urinary concentrating mechanism. The paper also addresses an important phenomenon on the transport of macromolecules. Concentration polarization of hyaluronan on the synovial lining of joint cavities is presented to demonstrate how the mechanism works in principle and how model predictions agree to experimental observations quantitatively

Pointwise Approximation Theorems for Combinations of Bernstein Polynomials With Inner Singularities

We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.Comment: 13 pages, late