Related papers: Karl Stein (1913-2000)
Considered one of the founding fathers of integral geometry, Luis Santal\'o has contributed to various areas of mathematics. His work has applications in number theory, in the theory of differential equations, in stochastic geometry, in…
We identify a class of "semi-modular" forms invariant on special subgroups of $GL_2(\mathbb Z)$, which includes classical modular forms together with complementary classes of functions that are also nice in a specific sense. We define an…
A possible influence of Klein's Erlangen program on physical theories is investigated. While some connections are found, it is concluded that Lie's theory of transformation groups and Lie algebras have had a much larger impact. In this…
We are concerned with the invariants of Steiner chains consisting of four circles. In particular, we compute the invariant moments of curvatures in Steiner 4-chains and give two applications of the obtained formulas. Specifically, we…
We present an adaptation of Stein's method of normal approximation to the study of both discrete- and continuous-time dynamical systems. We obtain new correlation-decay conditions on dynamical systems for a multivariate central limit…
After some brief biographical notes, Wolfgang Pauli's main contributions to general relativity, quantum theory, quantum field theory, and elementary particle physics are reviewed. A detailed description is given how Pauli descovered -…
We introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete distributions on the real line. Our approach rests on a new…
"Symmetry" was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in physics of the 21st century. As used today, there are a variety of interpretations of this term, which…
These pages contain a short overview on the state of the art of efficient numerical analysis methods that solve systems of multivariate polynomial equations. We focus on the work of Steve Smale who initiated this research framework, and on…
The Stone-von Neumann Theorem is a fundamental result which unified the competing quantum mechanical models of matrix mechanics and wave mechanics. It's mechanism of proof ultimately involved the study of unitary group representations on a…
The application of classical methods of statistical mechanics, originally developed by Ludwig Boltzmann in gas dynamics, to the description of social phenomena is a successful story that we try to outline in this paper. On one hand, it is…
The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in…
This article reviews the biography of the Swiss mathematician Marcel Grossmann (1878-1936) and his contributions to the emergence of the general theory of relativity. The first part is his biography, while the second part reviews his…
A short scientific biography is given of physicist Paul Wesson (1949-2015), who published over 300 works encompassing the fields of astrobiology, astrophysics, geophysics, cosmology, and relativity; and who was particularly associated with…
This is an expository paper about the Borel complexity of structure and classification theorems. It sorts several classical problems relative to known benchmarks of complexity. As a corollary various problems proposed by people such as von…
Einstein is usually revered as the father of special and general relativity. In this article I demonstrate that he is also the father of Solid State Physics, or even his broader version known as Condensed Matter Physics (including liquids).…
Leo Breiman was a highly creative, influential researcher with a down-to-earth personal style and an insistence on working on important real world problems and producing useful solutions. This paper is a short review of Breiman's extensive…
Although Planck's constant h is currently regarded as the elementary quantum of action appearing in quantum theory, it can also be interpreted as the multiplicative scale factor setting the scale of classical zero-point radiation appearing…
We establish a link between the two functional approaches: a mesoscopic field theory developed recently by A.Ciach and G.Stell [A. Ciach and G. Stell, J. Mol. Liq. 87 (2000) 253] for the study of ionic models and an exact statistical field…
Published between 1760 and 1770, Bielfeld's writings prove that scholars of the time were acquainted with the concepts of both political arithmetic and German statistik, long before they merged into a new discipline at the beginning the…