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"This monograph provides a mathematical proof that, for distances of the order of 10 AU, space is Euclidean. This result is, of course, not surprising for such small cosmic scales. But it is good to finally have a mathematical confirmation in this sense. This book shed some light on the dynamics of N point masses that move in spaces of non-zero constant curvature according to an attraction law that naturally extends classical Newtonian gravitation beyond the flat (Euclidean) space. This extension is given by the cotangent potential, proposed by the German mathematician Ernest Schering in 1870. He was the first to obtain this analytic expression of a law suggested decades earlier for a 2-body problem in hyperbolic space by Janos Bolyai and, independently, by Nikolai Lobachevsky. As Newton's idea of gravitation was to introduce a force inversely proportional to the area of a sphere the same radius as the Euclidean distance between the bodies, Bolyai and Lobachevsky thought of a similar definition using the hyperbolic distance in hyperbolic space. The recent generalization we gave to the cotangent potential to any number N of bodies, led to the discovery of some interesting properties. This new research reveals certain connections among at least five branches of mathematics, classical dynamics, non-Euclidean geometry, geometric topology, Lie groups, and the theory of polytopes."

"This book of general analytical chemistry, as opposed to instrumental analysis or separation methods, in aqueous solutions is focuses on fundamentals, which is an area too often overlooked in the literature. Explanations abound of the chemical and physical principles of different operations of chemical analysis in aqueous solutions. Once these principle are firmly established, numerous examples of applications are also given."

"Evolutionary foundations of equilibria in irrational markets proves traditional economic equilibria continue to occur despite natural selection in irrational markets. It covers a wide sampling of equilibria under various scenarios, and each chapter addresses the results of these models at an aggregate level. The text is supplemented with charts and figures to drive home key findings and proofs."

"Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.Several features make this book unique. The first is the systematic use of bordered matrix methods in the numerical computation and continuation of various bifurcations. The second is a detailed treatment of bialternate matrix products and their Jordan structure. Govaerts discusses their use in the numerical methods for Hopf and related bifurcations. A third feature is a unified treatment of singularity theory, with and without a distinguished bifurcation parameter, from a numerical point of view. Finally, numerical methods for symmetry-breaking bifurcations are discussed in detail, up to the fundamental cases covered by the equivariant branching lemma."

"In the usual nash equilibrium of strategic noncooperative games, the mixed strategies of all the players are assumed to be stochastically independent...."