Related papers: Correction: Root extraction in one-relator groups …
This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.
We prove a stronger version of a termination theorem appeared in the paper "On existence of log minimal models II". We essentially just get rid of the redundant assumptions so the proof is almost the same as in there. However, we give a…
It has been conjectured that in a braid group, or more generally in a Garside group, applying any sequence of monotone equivalences and word reversings can increase the length of a word by at most a linear factor depending on the group…
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
We give a new simpler proof of a theorem of Jayne and Rogers.
We provide a generalization of the Phragm\'en-Lindel\"of principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in the literature.
It is argued that power contributions of short distance origin naturally arise in the infrared finite coupling approach. A phenomenology of $1/Q^2$ power corrections is sketched.
We confirm recently proposed theorems for the structure of next-to-soft corrections in gauge and gravity theories using diagrammatic techniques, first developed for use in QCD phenomenology. Our aim is to provide a useful alternative…
We exhibit explicit orthogonal decompositions of every multidimensional restricted root space of a real semi-simple Lie algebra. We then show a link between this result and a radiality property of smooth functions on G-homogeneous spaces…
In this short note, we show that a result about words which coincide except in one position given as an exercise in Lothaire's Algebraic Combinatorics on Words is false. Moreover, we derive a modified statement which allows us to fix the…
We show a smoothed version of Goldston-Pintz-Yildirim's sifting argument to detect small gaps between primes, which has a higly flexible error term. Our argument is applicable to high dimensional Selberg sieve situations as well, although…
We provide a corrector theory for the strong approximation of fields inside composites made from two materials with different power law behavior. The correctors are used to develop bounds on the local singularity strength for gradient…
Correction to Annals of Probability 28 (2000) 277--302 [doi:10.1214/aop/1019160120].
In this short note we briefly review some recent developments in understanding discrete torsion. Specifically, we give a short overview of the highlights of a group of recent papers which give the basic understanding of discrete torsion.…
Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately…
A corrector theory for the strong approximation of gradient fields inside periodic composites made from two materials with different power law behavior is provided. Each material component has a distinctly different exponent appearing in…
This paper is withdrawn. The current main theorem can be proved by using a simple field theory. The main theorem is to placed by another theorem, shortly.
We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…
Citations are updated; referred papers are increased. An error right after the eq.~(27) is corrected, and several chages (not serious) are made.
This paper has been removed by the author due to a misstatement in Theorem 1 and a gap in its proof. A corrected and largely extended successor (a joint work with Thomas Bauer and Tomasz Szemberg) can be found under math.AG/0312211,