Related papers: Peripheral elements in reduced Alexander modules: …
We correct a mistake in a lemma in the paper cited in the title and show that it did not affect any of the other results of the paper. To this end we prove results on linearly disjoint field extensions that do not seem to be commonly known.…
This note is an addendum to the paper ''Mahler's method in several variables and finite automata''. It strengthens part (i) of Theorem 1.1 of the aforementioned paper.
In the first section of the present work, we introduce the concept of pseudocomplementation for semirings and show semiring version of some known results in lattice theory. We also introduce semirings with pc-functions and prove some…
We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.
The Response [J. Chem. Phys. 160, 187102 (2024)] of Inoue and coworkers to my Comment [J. Chem. Phys. 160, 187101 (2024)] on their original paper [J. Chem. Phys. 159, 054105 (2023)] clarifies some points put forward in my Comment, but also…
In this paper, we collect the fundamental basic properties of jet modules in algebraic geometry and related properties of differential operators. We claim no originality but we want to provide a reference work for own research and the…
This paper reviews the state of the art and discusses very recent mathematical developments in the field of adaptive boundary element methods. This includes an overview of available a posteriori error estimates as well as a state-of-the-art…
We prove some basic results about irreducible components of varieties of modules for an arbitrary finitely generated associative algebra. Our work generalizes results of Kac and Schofield on representations of quivers, but our methods are…
Many problems in science and engineering can be rigorously recast into minimizing a suitable energy functional. We have been developing efficient and flexible solution strategies to tackle various minimization problems by employing finite…
We reply to the recent comment cond-mat/9810097 on our original Letter `Roughening Transition of Interfaces in Disordered Systems', Phys. Rev. Lett. 81, 1469 (1998).
We completely determine all lower-modular elements of the lattice of all semigroup varieties. As a corollary, we show that a lower-modular element of this lattice is modular.
It is known, since works of Burde and de Rham, that one can detect the roots of the Alexander polynomial of a knot by the study of the representations of the knot group into the group of the invertible upper triangular $2x2$ matrices. In…
We reply to the comments on our previous paper Physical Review Letters, Vol. 129, 087001 (2022), raised by Th\'eo S\'epulcre, Serge Florens, and Izak Snyman in arXiv:2210.00742.
We comment on the paper `UCN anomalous losses and the UCN capture cross section on material defects' by A. Serebrov et al., Phys. Lett. A 335 (2005) 327 - 336. Data presented do not originate from these authors alone but were taken in…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
Paper withdrawn due to errors. Revised version may or may not appear in the future.
In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with the set of element orders and two orders (the order of group and the set of element orders). Some related topics, and…
A geometric interpretation of the equinoctial elements is given with a connection to orthogonal rotations and attitude dynamics in Euclidean 3-space. An identification is made between the equinoctial elements and classic Rodrigues…
Our paper arXiv:2101.11629 contains a technical error which changes some of the conclusions. We thank Streltsov, Pedernales, and Plenio for bringing the essence of this error to our attention. Here we explain the error, examine its…
We give a survey of some recent papers by the authors and Masaaki Wada relating the twisted Alexander polynomial with a partial order on the set of prime knots. We also give examples and pose open problems.