Related papers: Frederick William Gehring, Life and Mathematics
This is an overview of the life and works of Pavel Florensky, an important and singular figure of the period rightly described as the \emph{Silver Age of Russian mathematics}, with a substantial overlap with the \emph{Silver Age of Russian…
Associated Legendre functions of fractional degree appear in the solution of boundary value problems in wedges or in toroidal geometries, and elsewhere in applied mathematics. In the classical case when the degree is half an odd integer,…
We review Euler's work on spherical geometry. After an introduction concerning the general place that trigonometric formulae occupy in geometry, we start by the two memoirs of Euler on spherical trigonometry, in which he establishes the…
Gunnar Nordstrom constructed the first relativistic theory of gravitation formulated in terms of interactions with a scalar field. It was an important precursor to Einstein's general theory of relativity a couple of years later. He was also…
Erd\H{o}s first conjectured that infinitely often we have $\varphi(n) = \sigma(m)$, where $\varphi$ is the Euler totient function and $\sigma$ is the sum of divisor function. This was proven true by Ford, Luca and Pomerance in 2010. We ask…
Let $(R, \mathcal{M})$ be a local ring over a field $k$ with $k = R/\mathcal M$ and $J$ an ideal in $R$ such that $A =R/J$ is an Artinian Gorenstein (AG) $k$-algebra. In 1989, A. Iarrobino introduced the symmetric decomposition of the…
This is a list of corrections for the book: J. Noguchi and T. Ochiai, Geometric Function Theory in Several Complex Variables, xi + 282 pp., Math.\ Monographs Vol.\ {\bf 80}, Amer.\ Math.\ Soc., Providence, 1990. The authors hope that this…
Based on the distinction between the covariant and contravariant metric tensor components in the framework of the affine geometry approach and also on the choice of the contravariant components, it was shown that a wide variety of third,…
Information geometry provides differential geometric concepts like a Riemannian metric, connections and covariant derivatives on spaces of probability distributions. We discuss here how these concepts apply to quantum field theories in the…
We dicuss some curious aspects of the Rogers dilogarithm and the functional relations in integrable systems in two dimensions. This is for the proceedings of the XX1 Differential Geometry Methods in Theoretical Physics, Tianjin, China, 5-9…
In this paper, in order to improve the spatial accuracy, the exponential integrator Fourier Galerkin method (EIFG) is proposed for solving semilinear parabolic equations in rectangular domains. In this proposed method, the spatial…
Joel Scherk (1946--1980) was an important early contributor to the development of string theory. Together with various collaborators, he made numerous profound and influential contributions to the subject throughout the decade of the 1970s.…
We consider a large class of physical fields $u$ written as double inverse Fourier transforms of some functions $F$ of two complex variables. Such integrals occur very often in practice, especially in diffraction theory. Our aim is to…
Jarnik's identity plays a major role in classical simultaneous approximation to two real numbers. O. German [2] has shown a generalization to the weighted setting in which the identity has to be replaced by two inequalities. His methods…
We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be…
The American physicist Robert Dicke (1916-1997) is primarily known for his important contributions to gravitation, cosmology, and microwave physics. Much less known is his work in geophysics and related areas of the earth sciences in which…
We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…
Beginning from the resolution of Dirichlet L function, using the inner product formula of infinite-dimensional vectors in the complex space, the author proved the world's baffling problem--Generalized Riemann hypothesis.
H. Weyl's proposal of 1918 for generalizing Riemannian geometry by local scale gauge (later called {\em Weyl geometry}) was motivated by mathematical, philosophical and physical considerations. It was the starting point of his unified field…
K\"ahler's geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U($N)\otimes$U($N)$…