Suchergebnisse

The derivation of the Boltzmann function f(r, c, t) from the Liouville density DN is shown to be equivalent to a transition from Γ space to µ space. In this formulation, the collision is left in all its generality. This enables one to define a most probable distribution function even when the collision term is not set to zero.

This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.

AbstractStructuralism in philosophy of mathematics has largely focused on arithmetic, algebra, and basic analysis. Some have doubted whether distinctively structural working methods have any impact in other fields such as differential equations. We show narrowly construed structuralism as offered by Benacerraf has no practical role in differential equations. But Dedekind's approach to the continuum already did not fit that narrow sense, and little of mathematics today does. We draw on one calculus textbook, one celebrated analysis textbook, and a monograph on the Navier–Stokes equation to show structural methods like Dedekind's have long been central to differential equations, and have philosophically respectable ontology and epistemology.

"Structural Equation Modelling (SEM) is a relatively recently developed statistical technique based upon factor analysis and multiple regression. This review will cover four of the most widely used (in psychology departments) packages, looking in particular at their suitability for use in a teaching environment, rather than an in depth look at their technical capabilities: LISREL 8.20, EQS 5.6, AMOS 3.6, SEPath. The four programs reviewed were all tested running Windows 95, on a 166 MHz Pentium, with 32 MB RAM." (author's abstract)