Related papers: Divisibility Theory and Complexity of Algorithms i…
Association of some integers n >= 54 to divisibility classes in the Shevelev article of 2007 is corrected.
Further formulas are presented involving quantum mechanics, thermodynamics, and integrable systems. Modifications of dispersionless theory are developed.
This version has been withdrawn. The new and final version is on ArXiv 1103.4878
We comment on a recent paper by D'Abramo [Chaos, Solitons & Fractals, 25 (2005) 29], focusing on the author's statement that an algorithm can produce a list of strings containing at least one string whose algorithmic complexity is greater…
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in…
An error in the paper [J. Math. Phys. 43, 6343 (2002); math-ph/0207009] is corrected. Further explanation is given.
I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and…
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
This paper corrects an error in a proof in the original version of the paper published in 1998 in the Oxford Quarterly. The main theorem remains the same: The geometric realization of the partially ordered set of proper free factors in a…
This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The…
This is the paper "Niels Henrik Abel and the birth of fractional calculus", Podlubny, I., Magin, R. L., Trymorush I., Fractional Calculus and Applied Analysis, vol.20, no.5, pp.1068-1075, 2017 (https://doi.org/10.1515/fca-2017-0057) with…
With regard to the recently published article, ``Y.-Q. Wang, et al., Physical mechanism of equiprobable exclusion network with heterogeneous interactions in phase transitions: Analytical analyses of steady state evolving from initial state,…
In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…
This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of…
In the note an error in Low and Lapsley's article ("Optimization Flow Control, I: Basic Algorithm and Convergence", IEEE/ACM Transactions on Networking, 7(6), pp. 861-874, 1999) is pointed out. Because of this error the proof of the Theorem…
Withdrawn paper because the results are published in math.AT/0308054 and math.AT/0308063.
This is the first draft of a set of lecture notes developed for one-half of a seminar on two approaches to the notion of "Abelian", namely those of universal algebra, and of category theory. The half pertaining to the universal-algebraic…
This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in…
This is a corrected version of our paper published in Osaka Journal of Mathematics 51(2014), 673-693. We correct Theorem~1.1, Proposition~3.3 and their proofs.
An improved (streamlined and extended) version of this paper is available as math.RA/0203010, which however omits some details. We recommend the later version unless details are essential.