Related papers: The Schwarz Lemma: An Odyssey
I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
This is an introductory document surveying several results in polynomial approximation, known as the Bramble-Hilbert lemma.
An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
We describe two distinct simple, short and self contained proofs of the composition lemma.
We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.
We start with a bijective proof of Schur's theorem due to Alladi and Gordon and describe how a particular iteration of it leads to some very general theorems on colored partitions. These theorems imply a number of important results,…
Diese kurze Einfuehrung in Theorie und Berechnung linearer Rekurrenzen versucht, eine Luecke in der Literatur zu fuellen. Zu diesem Zweck sind viele ausfuehrliche Beispiele angegeben. This short introduction to theory and usage of linear…
Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras E we investigate a natural implication and prove that the implication reduct of E is term equivalent to E. Then we present a…
This article presents an elementary proof of Zorn's Lemma under the Axiom of Choice, simplifying and supplying necessary details in the original proof by Paul R. Halmos in his book, Naive Set Theory. Also provided, is a preamble to Zorn's…
Rejoinder to ``The 2005 Neyman Lecture: Dynamic Indeterminism in Science'' [arXiv:0808.0620]
This lecture has the following sections: Systems and States; Brownian Motion; Segmental Relaxation and the Glass Transition; Dynamics of a Free Chain; Entanglement and Reptation. Appendices cover: Linear response theory, relaxation,…
We propose an explanatory and computational theory of transformative discoveries in science. The theory is derived from a recurring theme found in a diverse range of scientific change, scientific discovery, and knowledge diffusion theories…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
The scattering of massive particles by a Schwarzschild black hole also undergoing a drag force is considered. The latter is modeled as a viscous force acting on the orbital plane, with components proportional to the associated particle…
This note revisits some majorization inequalities for eigenvalues, special attention is given to an elegant theorem of Hiroshima. An extension of the special case of Hiroshima's theorem is presented. Some discussion and open problems are…
A brief comment on the paper hep-th/0508051 (with the title mentioned above) by F. Nasseri.
Some notes and questions about the concept of time are exposed. Particular reference is given to the problem in quantum mechanics, in connection with the indeterminacy principle.