Related papers: Divisibility Theory and Complexity of Algorithms i…
New version of my 1998 article. The method of proof of the main results follows the original, but there are many simplifications/streamlining of arguments, especially Lemma 3.6 (new Lemma 3.7). Fixed small error in proof of lower bound for…
The Comments are devoted to the paper ``Solutions of Multitime Reaction-Diffusion PDE'' (Mathematics, vol. 10 (2022), 3623), in which main results are misleading and can be derived in a simple way from those obtained earlier. Moreover, it…
Correction to Annals of Probability 29 (2001) 1612--1624 [doi:10.1214/aop/1015345764].
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
There is a mathematical error in the first version of this paper. A new corrected version will be posted when the error is fixed, possibly with a modified title.
This paper has been withdrawn by the author, because a better treatment is given in the author's Phd. thesis (Sections 3.4.6 and 4.4), now available on the arxiv.
This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).
The goal of this modern presentation, followed by an English translation from the German, is to make available some parts of Lie's very systematic mathematical thought which deserve to join the contemporary literature, and above all also,…
This note complements our paper "Categoricity-like properties in the first order realm" (Journal for the Philosophy of Mathematics, 2024).
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…
This paper has been withdrawn, not because of any errors (that we know of), but because rather than presenting our material as a series of 3 papers, as we originally intended, we have now combined them into one long paper, which is "A…
The recent theory of fractional $h$-difference equations introduced in [N. R. O. Bastos, R. A. C. Ferreira, D. F. M. Torres: Discrete-time fractional variational problems, Signal Process. 91 (2011), no. 3, 513--524], is enriched with useful…
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
The content of this preprint together with additional material appears now in 0706.2154.
In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…
A didactic introduction, dated by 1999, to the ideas of the papers arXiv:q-bio/0701050 and arXiv:0704.0034
This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), goo.gl/pZWA6X.
This is an introduction to small divisors problems. The material treated in this book was brought together for a PhD course I tought at the University of Pisa in the spring of 1999. Here is a Table of Contents: Part I One Dimensional Small…
Translation of the paper "Interpolation of linear spaces and maximum estimates for solutions to parabolic equations" published in Russian in the collected volume "Partial differential equations", Akad. Nauk SSSR, Sibirsk. Otdel., Inst.…
We reply to Dukelsky, et al. regarding the article: L. A. Wu, M. S. Byrd and D. A. Lidar, Phys. Rev. Lett. 89, 057904 (2002).