Essays in Mathematics and its Applications: In Honor of Stephen Smales 80th Birthday 2012 edition

Marc Notes: This volume is dedicated to Stephen Smale on the occasion of his 80th birthday. Smale has done pioneering work in differential topology, globalanalysis, dynamical systems, nonlinear functional analysis, numerical analysis, and theory of computation and machine learning. Table of Contents: Preface.- Transitivity and Topological Mixing for C1 Diffeomorphisms.- Recent Results on the Size of Critical Sets.- The FoxLi operator as a Test and a Spur for WienerHopf Theory.- Kahler Metrics with Cone Singularities along a Divisor.- The Space of Framed functions is Contractible.- Quantum Gravity via Manifold Positivity.- Parabolic Explosions in Families of Complex Polynomials.- Super Stable Kahlerian Horseshoe?.- A Smooth Multivariate Interpolation Algorithm.- Bifurcations of Solutions of the 2-Dimensional Navier-Stokes System.- Arnold Diffusion by Variational Methods.- Turning Washington's Heuristics in Favor of Vandiver's Conjecture.- Schwartzman Cycles and Ergodic Solenoids.- An Additive Functional equation in Orthogonality Spaces.- Exotic Heat PDEs. II.- Topology at a Scale in Metric Spaces.- Functions and Associated Series and Integrals.- Gyrations: The Missing Link Between Classical Mechanics with its Underlying Euclidean Geometry and Relativistic Mechanics with its Underlying Hyperbolic Geometry."Jacket Description/Back: The volume is dedicated to Stephen Smale on the occasion of his 80th birthday. Besides his startling 1960 result of the proof of the Poincare conjecture for all dimensions greater than or equal to five, Smale s ground breaking contributions invarious fields in Mathematics have marked the second part of the 20th century and beyond. Stephen Smale has done pioneering work in differential topology, global analysis, dynamical systems, nonlinear functional analysis, numerical analysis, theory of computation and machine learning as well as applications in the physical and biological sciences and economics. In sum, Stephen Smale has manifestly broken the barriers among the different fields of mathematics and dispelled some remaining prejudices. He is indeed a universal mathematician. Smale has been honored with several prizes and honorary degrees including, among others, the Fields Medal(1966), The Veblen Prize (1966), the National Medal of Science (1996) and theWolf Prize (2006/2007)."

Contributor Bio:  Pardalos, Panos M Panos M. Pardalos is one of the leading experts in global optimization and control theory. V. Yatsenko's research is connected with control of bilinear systems, nonlinear estimation, control of quantum systems, and globabl optimization problems. Both Pardalos and Yatsenko have authored numerous publications including books and well-known scientific journals. Contributor Bio:  Rassias, Themistocles M Rassias, National Technical University of Athens, Greece.