Related papers: Divisibility Theory and Complexity of Algorithms i…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
In the paper are proved theorems, which amplify the results of my paper "On the difference equation of Poincare type (Part 3)", Max-Plank-Institut fuer Mathematik, Bonn, Preprint Series, 2004, 09, 1-34.
This is the original paper appeared in the book "Elliptic and Parabolic Methods in Geometry (Minneapolis, MN,1994), A K Peters, Wellesley, MA, (1996)" (p.1-16), except with a few minor modifications as described at the end of the paper (on…
The contents are divided into two papers "The Monotone Cumulants" (arXiv:0907.4896) and "Conditionally monotone independence" (arXiv:0907.5473).
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
It has been pointed out by counterexamples in a 2013 paper in the IEEE Transactions on Computers [1], that there is an error in the previously ibid.\ in 2005 published paper [2] on the construction of valid digit selection tables for SRT…
This is about the paper by Thawhat Changphas and Nawamin Phaipong in Quasigroups and Related Systems 22 (2014), 193--200.
An error in the author's paper (Functiones et Approximatio, 37 . pp. 203-211) is corrected.
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
The thesis was defended by the author in University of Angers (France). It consists of four parts. The fist part (in French) is introductory and is devoted to relation between quantum groups, integrable systems and statistical models. In…
We abstract and generalize homotopical monadicity statements, placing in a single conceptual framework a range of old and recent recognition and characterization principles in iterated loop space theory in classical, equivariant, and…
This is the text of an article that I wrote and disseminated in September 1981, except that I've updated the references, corrected a few misprints, and added a table of contents, some footnotes, and an addendum. The original article gave a…
This is a position paper written as an introduction to the special volume on quantum algorithms I edited for the journal Mathematical Structures in Computer Science (Volume 20 - Special Issue 06 (Quantum Algorithms), 2010).
This invited chapter in the Handbook of Quantum Logic and Quantum Structures consists of two parts: 1. A substantially updated version of quant-ph/0402130 by the same authors, which initiated the area of categorical quantum mechanics, but…
The normal form theorem, proved in R. Laver, On the left distributive law and the freeness of an algebra of elementary embeddings, Advances in Mathematics 91 (1992), 209-231, for the free algebra $\Cal A$ on one generator $x$ satisfying the…
Draft version of an article prepared for the Encyclopedia of Mathematical Physics, Elsevier, to appear in 2006.
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
This habilitation thesis is cumulative and, therefore, is collecting and connecting research that I (together with several co-authors) have conducted over the last few years. Thus, the absolute core of the work is formed by the ten…
This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006).
This paper has been withdrawn by the corresponding author because the newest version is now published in Journal of Discrete Algorithms.