Related papers: Gauss and the Eccentric Halsted
This paper is partly a historical survey of various approaches and methods in the fractional calculus, partly a description of the Kipriyanov extraordinary theory in comparison with the classical one. The significance and outstanding…
We provide a proof to a recent conjecture by Forrester [2014 J. Phys. A: Math. Theor. 47, 065202] regarding the algebraic and arithmetic structure of Meijer G-functions which appear in the expression for probability of all eigenvalues real…
An elementary approach is shown which derives the value of the Gauss sum of a cubic character over a finite field $\mathbb F_{2^s}$ without using Davenport-Hasse's theorem (namely, if $s$ is odd the Gauss sum is -1, and if $s$ is even its…
A recent pair of papers of Armstrong, Loehr, and Warrington and Armstrong, Williams, and the author initiated the systematic study of {\em rational Catalan combinatorics} which is a generalization of Fuss-Catalan combinatorics (which is in…
We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…
Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical…
Let $k$ be a real abelian number field and $p$ an odd prime not dividing $[k:\mathbb{Q}]$. For a natural number $d$, let $E_d$ denote the group of units of $k$ congruent to $1$ modulo $d$, $C_d$ the subgroup of $d$-circular units of $E_d$,…
We give a purely mathematical interpretation and construction of sculptures rendered by one of the authors, known herein as Fels sculptures. We also show that the mathematical framework underlying Ferguson's sculpture, {\it The Ariadne…
The aim of this expository note is to prove that any $1$-subgaussian random vector is dominated in the convex ordering by a universal constant times a standard Gaussian vector. This strengthens Talagrand's celebrated subgaussian comparison…
In this article we provide further evidence for the monstrous proposal of Daniel Allcock, by giving a plausible but still conjectural explanation for the deflation relation in the Coxeter group quotient of the orbifold fundamental group.
We introduce Galois corings, and give a survey of properties that have been obtained so far. The Definition is motivated using descent theory, and we show that classical Galois theory, Hopf-Galois theory and coalgebra Galois theory can be…
Following the paper of J.D. Jackson [arXiv:0708.4249] on a false attribution of discoveries, equations, and methods [Am. J. Phys. 76, 704-719 (2008)] I consider examples, in which some of independent discoverers are forgotten, and in other…
A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made less mysterious by virtue of being generalized through the introduction of an additional parameter.
We consider the commutation relations between the Gauss--Weierstrass semigroup on $\mathbb{R}^{n}$, generated by convolution with the complex Gaussian kernel, and monomial weights. We provide an explicit representation and a sharper…
Proposing a certain category of bialgebroid maps we show that the balanced depth 2 extensions appear as they were the finitary Galois extensions in the context of quantum groupoid actions, i.e., actions by finite bialgebroids, weak…
Herbrand's theorem is often presented as a corollary of Gentzen's sharpened Hauptsatz for the classical sequent calculus. However, the midsequent gives Herbrand's theorem directly only for formulae in prenex normal form. In the Handbook of…
The approximation of the Gaussian cumulative distribution or of the related Mills ratio have a long history starting with Gauss and Laplace and continuing nowadays. Below, we improve an important family of bounds provided recently by…
Brief recollections of two giants of physics, their origins, similarities and differences.
In 1966, the Brazilian physicist Klaus Tausk circulated a preprint from the International Centre for Theoretical Physics, in Trieste, criticizing the theory put forward by Daneri, Loinger & Prosperi on the measurement problem in quantum…
The inverse problem of Galois Theory was developed in the early 1800 s as an approach to understand polynomials and their roots. The inverse Galois problem states whether any finite group can be realized as a Galois group over Q (field of…