We consider the dynamics when traveling pulses encounter heterogeneities in a three-component reaction diffusion system of one-activator-two-inhibitor type, which typically arises as a qualitative model of a gas-discharge system. We focused on the case where one of the kinetic coefficients changes similar to a smoothed step function, which is basic for more general heterogeneity as in periodic ...

This paper analyzes both the utopian and dystopian aspects of American society in F. Scott Fitzgerald’s (1896-1940) The Great Gatsby (1925). It aims at depicting those through a careful examination settings, particularly East egg Valley Ashes. former represents protagonist’s ideal reality which he dreams becoming famous, wealthy, more satisfied. Yet, climax tragic ending reveal Egg society, suc...

In this paper, we review analytical methods for a rigorous study of the existence and stability of stationary, multiple spots for reaction-diffusion systems. We will consider two classes of reaction-diffusion systems: activator-inhibitor systems (such as the Gierer-Meinhardt system) and activator-substrate systems (such as the Gray-Scott system or the Schnakenberg model). The main ideas are pre...

Mathematics of Domains A dissertation presented to the Faculty of the Graduate School of Arts and Sciences of Brandeis University, Waltham, Massachusetts by Michael A. Bukatin Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types. Scott continuous functions repre...