Essays in Mathematics and its Applications

​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.