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This treatment presents most of the methods for solving ordinary differential equations and systematic arrangements of more than 2,000 equations and their solutions. The material is organized so that standard equations can be easily found. Plus, the substantial number and variety of equations promises an exact equation or a sufficiently similar one. 1960 edition.
This softcover book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games. It will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book.
1. 1 A paradigm About one hundred years ago, Maurice Couette, a French physicist, de signed an apparatus consisting of two coaxial cylinders, the space between the cylinders being filled with a viscous fluid and the outer cylinder being rotated at angular velocity O2. The purpose of this experiment was, follow ing an idea of the Austrian physicist Max Margules, to deduce the viscosity of the fluid from measurements of the torque exerted by the fluid on the inner cylinder (the fluid is assumed to adhere to the walls of the cylinders). At least when O is not too large, the fluid flow is nearly laminar and 2 the method of Couette is valuable because the torque is then proportional to 110 , where II is the kinematic viscosity of the fluid. If, however, O is 2 2 increased to a very large value, the flow becomes eventually turbulent. A few years later, Arnulph Mallock designed a similar apparatus but allowed the inner cylinder to rotate with angular velocity 01, while O2 = o. The surprise was that the laminar flow, now known as the Couette flow, was not observable when 0 exceeded a certain "low" critical value Ole, even 1 though, as we shall see in Chapter II, it is a solution of the model equations for any values of 0 and O .
This book was first published in 1991. It considers the concepts and theories relating to mostly aqueous systems of activity coefficients.
The Porphyrin Handbook, Volume 20: Phthalocyanines: Structural Characterization provides information pertinent to every aspect of the chemistry, synthesis, spectroscopy, and structure of phthalocyanines. This book examines the biology and medical implications of porphyrin systems. Organized into one chapter, this volume begins with an overview of the molecular and crystal structures of phthalocyanine and related complexes followed by a database section. This text then examines the crystallographic data that provided many researchers with the foundation to conduct their own research on phthalocyanine crystal structures. This book considers the structural basis for the prediction or calculation of the phthalocyanine physical properties. This book discusses as well the fundamental structure of a phthalocyanine molecule that consists of four isoindole units, circularly linked via azamethine bridges. This book is a valuable resource for research scientists, engineers, and clinicians.