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Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

Mathematical Physics · Physics 2020-09-03 Juuso Österman

We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…

Numerical Analysis · Mathematics 2008-09-15 S. A. Belbas

This paper discusses the extension of the Prototype Verification System (PVS) sub-theory for rings, part of the PVS algebra theory, with theorems related to the division algorithm for Euclidean rings and Unique Factorization Domains that…

Logic in Computer Science · Computer Science 2024-04-24 Thaynara Arielly de Lima , Andréia Borges Avelar , André Luiz Galdino , Mauricio Ayala-Rincón

In [Computer Aided Geometric Design 27 (2010), 212-231] the authors present an algorithm to parametrize approximately $\epsilon$-rational curves, and they show in 2 examples that the Hausdorff distance, w.r.t. to the Euclidean distance,…

Algebraic Geometry · Mathematics 2010-04-14 Sonia L. Rueda , Juana Sendra

Linearly repetitive cut and project sets are mathematical models for perfectly ordered quasicrystals. In a previous paper we presented a characterization of linearly repetitive cut and project sets. In this paper we extend the classical…

Dynamical Systems · Mathematics 2015-09-29 Alan Haynes , Henna Koivusalo , James Walton

We say that a metric graph is uniformly bounded if the degrees of all vertices are uniformly bounded and the lengths of edges are pinched between two positive constants; a metric space is approximable by a uniform graph if there is one…

Metric Geometry · Mathematics 2013-06-25 Dmitri Burago , Sergei Ivanov

The inevitable noise in real measurements motivates the problem to continuously quantify the similarity between rigid objects such as periodic time series and proteins given by ordered points and considered up to isometry maintaining…

Computational Geometry · Computer Science 2022-07-19 Vitaliy Kurlin

This paper proposes a hierarchical clustering approach for the segmentation of mobile LiDAR point clouds. We perform the hierarchical clustering on unorganized point clouds based on a proximity matrix. The dissimilarity measure in the…

Computer Vision and Pattern Recognition · Computer Science 2019-06-12 Sheng Xu , Ruisheng Wang , Han Zheng

It was shown in 1994, in Oberguggenberger & Rosinger, that very large classes of nonlinear PDEs have solutions which can be assimilated with usual measurable functions on the Euclidean domains of definition of the respective equations. In…

Analysis of PDEs · Mathematics 2007-05-23 Roumen Anguelov , Elemer E Rosinger

We characterize the uniform limits of Dirichlet polynomials on a right half plane. In the Dirichlet setting, we find approximation results, with respect to the Euclidean distance and {to} the chordal one as well, analogous to classical…

Complex Variables · Mathematics 2016-08-24 Richard Aron , Frédéric Bayart , Paul Gauthier , Manuel Maestre , Vassili Nestoridis

In the quest to produce quantum technology, superconducting networks, working at temperatures just above absolute zero, have arisen as one of the most promising physical implementations. The precise analysis and synthesis of such circuits…

Quantum Physics · Physics 2021-04-20 Adrian Parra-Rodriguez

In this paper, we develop homology groups for digital images based on cubical singular homology theory for topological spaces. Using this homology, we present digital Hurewicz theorem for the fundamental group of digital images. We also…

Algebraic Topology · Mathematics 2020-05-19 Samira Sahar Jamil , Danish Ali

This paper proposes a concise coding of the cells of n-dimensional finite regular grids. It induces a simple, generic and efficient framework for implementing classical digital topology data structures and algorithms. Discrete subsets of…

Discrete Mathematics · Computer Science 2009-06-16 Jacques-Olivier Lachaud

We study the configurations of pixels that occur when two digitized straight lines meet each other.

Graphics · Computer Science 2008-02-03 Donald E. Knuth

We develop a new approach to address some classical questions concerning the size and structure of integer distance sets. Our main result is that any integer distance set in the Euclidean plane is either very sparse or has all but an…

Number Theory · Mathematics 2025-08-26 Rachel Greenfeld , Marina Iliopoulou , Sarah Peluse

To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…

Physics and Society · Physics 2018-04-23 Johann H. Martínez , Mario Chavez

We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and…

Number Theory · Mathematics 2016-12-30 Tommy Hofmann , Claus Fieker

We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm designed for practical use both because of its ability to…

Networking and Internet Architecture · Computer Science 2007-05-23 Fabien Viger , Matthieu Latapy

Piecewise constant image approximations of sequential number of segments or clusters of disconnected pixels are treated. The method of majorizing of optimal approximation sequence by hierarchical sequence of image approximations is…

Computer Vision and Pattern Recognition · Computer Science 2013-10-02 M. Kharinov

We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…

Computational Geometry · Computer Science 2009-09-29 M. H. van Emden , B. Moa