Related papers: A proof of the butterfly theorem using the scale f…
We present a new, elementary, dynamical proof of the prime number theorem.
We present in this work a new and simple proof of the false centre theorem.
This document presents an alternative proof of Sylvester's theorem stating that "the product of $n$ consecutive numbers strictly greater than $n$ is divisible by a prime strictly greater than $n$". In addition, the paper proposes stronger…
As a first application of a very old theorem, known as Herschel's theorem, we provide direct elementary proofs of several explicit expressions for some numbers and polynomials that are known in combinatorics. The second application deals…
An technically interesting proof of a known theorem.
Butterfly algorithms are an effective multilevel technique to compress discretizations of integral operators with highly oscillatory kernel functions. The particular version of the butterfly algorithm considered here realizes the transfer…
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
Motivated by the theory of trapezoidal words, whose sequences of cardinality of factors by length are symmetric, we introduce a bivariate variant of this symmetry. We show that this symmetry characterizes Christoffel words, and establish…
In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…
Recently, a factorization theorem was proposed for partonic flavor evolution as defined by the net flavor of the Winner-Take-All axis of a jet. We validate the factorization theorem through explicit calculation at two-loop order, and in the…
The factorisation of scattering amplitude is described by the Weinberg theorem. In this talk, we will show the universality of the theorem at the next leading correction of the soft expansion. For that we will derive the soft operator by…
This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…
We present a short, elementary proof not involving Fourier transforms of the theorem of Cram\'er and Wold that a Borel probability measure is determined by its values on half-spaces.
A proof is given of Rosenthal's \(\ell_1\) theorem.
The paper gives a unified and simple proof of both theorems and Cousin's theorem.
We describe some of the basic properties of the 2-category of 2-term complexes in an abelian category, using butterflies as morphisms.
Stirling's formula is a powerful asymptotic approximation of the factorial function. Many well-known proofs of this formula are grounded in integral calculus. In this paper, we present an alternative proof of Stirling's formula using only…
A scientometric analysis has been performed on selected physics journals to estimate the presence of simulation and modeling in physics literature in the past fifty years. Correlations between the observed trends and several social and…
Using a sums of squares formula for two variable polynomials with no zeros on the bidisk, we are able to give a new proof of a representation for distinguished varieties. For distinguished varieties with no singularities on the two-torus,…