Since their Newtonian inception, differential equations have been a fundamental tool for modeling the natural world. As the name suggests, these equations involve the derivatives of dependent variables (e.g. viral load, species densities, genotypic frequencies) with respect to independent variables (e.g. time, space). When the independent variable is scalar, the differential equation is called ...

Web search engines have become the dominant tools for finding information on the Internet. Due to their popularity, users apply them to a wide range of search needs, from simple look-ups to rather complex information tasks. This paper presents the results of a study that investigated the characteristics of these complex information needs in the context of Web search engines. The aim of the stud...

subject to the constraint that q(0) and q(h) are constant. Standard ODE theory provides existence and uniqueness of the corresponding initial value problem because the derivatives q~(t) of the evolution curves q(t) are the integral curves of the corresponding Lagrangian vector field XE. Given two nearby ql, q2 6 Q, does there exist a unique evolution curve q(t) such that q(0) = q~ and q(h) = q2...