Related papers: Riemann Integration in the Euclidean Space
Summation formulae are classical tools in analysis: Taylor-MacLaurin, Euler-MacLaurin, Poisson, Vorono\"i, Circle formulae\ldots We will show how, from a single equation - referred to as the mother-equation - it is possible to unify these…
An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds.…
Given a Riemannian metric on the 2-sphere, sweep the 2-sphere out by a continuous one-parameter family of closed curves starting and ending at point curves. Pull the sweepout tight by, in a continuous way, pulling each curve as tight as…
This paper proposes a numerical method based on the Adomian decomposition approach for the time discretization, applied to Euler equations. A recursive property is demonstrated that allows to formulate the method in an appropriate and…
On the infinite dimensional space $E$ of continuous paths from $[0,1]$ to $\mathbb R^n$, $n \ge 3$, endowed with the Wiener measure $\mu$, we construct a surface measure defined on level sets of the $L^2$-norm of $n$-dimensional processes…
In symbolic integration, the Risch--Norman algorithm aims to find closed forms of elementary integrals over differential fields by an ansatz for the integral, which usually is based on heuristic degree bounds. Norman presented an approach…
We present a method for completing a premetric space, in the sense introduced by F. Richman in the context of constructive Mathematics without countable choice.
Optimization under the symplecticity constraint is an approach for solving various problems in quantum physics and scientific computing. Building on the results that this optimization problem can be transformed into an unconstrained problem…
Although the interpretation of complexity in extended theories of gravity is available in the literature, its illustration in $f(R,L_{m},\mathcal{T})$ theory is still ambiguous. The orthogonal decomposition of the Riemann tensor results in…
We describe a method to compute the norm on the cotangent space to the moduli space of Riemann surfaces associated to the Finsler Teichm\"uller metric. Our method involves computing the periods of abelian double covers and is easy to…
In this paper we connect a celebrated theorem of Nyman and Beurling on the equivalence between the Riemann hypothesis and the density of some functional space in $ L^2(0, 1)$ to a trigonometric series considered first by Hardy and…
This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the…
We provide an overview of technics that lead to an Euclidean upper bound on the volume of geodesic balls.
The Euler-MacLaurin summation formula relates a sum of a function to a corresponding integral, with a remainder term. The remainder term has an asymptotic expansion, and for a typical analytic function, it is a divergent (Gevrey-1) series.…
More than thirty years passed since the first discoveries of various aspects of integrability of the symmetry reduced vacuum Einstein equations and electrovacuum Einstein - Maxwell equations were made and gave rise to constructions of…
We use visible point vector identities to examine polylogarithms in the neighbourhood of the Riemann zeta function zeroes. New formulas limiting to the trivial zeroes and to the critical line on the zeta function are given. Similar results…
This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the…
We report on experience with an investigation of the analytic structure of the solution of certain algebraic complex equations. In particular the behavior of their series expansions around the origin is discussed. The investigation imposes…
We outline the history of the idea of deformation of space, which lead to the concept of curvature invariants, as we understand them today, including contributions of E. Bacaloglu and F. Casorati, among others. We pursue the following…
Euler explored the problem of finding three numbers such that the sum or difference of any two of them is a perfect square. He discovered a parametric solution represented by polynomials of degree 18 and identified the smallest of these…