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The main purpose of this paper is to study a concrete example of $\delta$-Koszul algebras, which is related to three questions raised by Green and Marcos in [3].

We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.

This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…

In what follows, essentially two things will be accomplished: Firstly, it will be proven that a version of the Arzel\`a--Ascoli theorem and the Fr\'echet--Kolmogorov theorem are equivalent to the axiom of countable choice for subsets of…

We extend two results of Ruzsa and Vu on the additive complements of primes

We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.

We commend the authors for an exciting paper which provides a strong contribution to the emerging field of probabilistic numerics (PN). Below, we discuss aspects of prior modelling which need to be considered thoroughly in future work.

This is a reply to the comment to a letter by D. Mandal, K. Klymko and M. R. DeWeese published as Phys. Rev. Lett. 119, 258001 (2017).

The essential elements in my way of fitting the kappa reviewed. A number of incorrect claims made by Takamatsu are clarified and corrected.

A Comment on Frank Wilczek's paper "Quantum Time Crystals" (Phys. Rev. Lett. 109, 160401 (2012); arXiv:1202.2539).

Results of the work of S. Bruce [{\it Nuovo Cimento} {\bf 110}B (1995) 115] are compared with those of recent papers of D. V. Ahluwalia and myself, devoted to describing neutral particles of spin $j=1/2$ and $j=1$.

The contributions of Lucio Russo to the mathematics of percolation and disordered systems are outlined. The context of his work is explained, and its ongoing impact on current work is described and amplified.

Some comments are made on the usefulness or otherwise of the concept of `expanding space' in cosmology. These notes are an expanded version of material first published in 2001 but not previously available online except at…

A response to commenter Ke Lan's comment on our paper published in Nature Communications (2023)14:5782 by J. Yan et al

This article introduces and studies Minkowski Bisectors, Minkowski Cells, and Lattice Coverings.

This manuscript (hep-th/9906140v1) is incomplete. Please read instead S. D. G{\l}azek, T. Mas{\l}owski, Renormalized Poincar\'e algebra for effective particles in quantum field theory, Phys.Rev. D65 (2002) 065011, (hep-th/0110185).

In this note, we revisit certain results from a previous work of the second author concerning $z$-ideals of semirings. We demonstrate that the assumption of the semiring being a bzi-semiring can be dispensed with. Additionally, we propose a…

Claims by Kroha and Zawadowski in cond-mat/0105026 on inadequate approximations and an incorrect statement in cond-mat/0102150 are shown to be based on oversimplified estimates and a false quotation.

We exhibit how the Rasiowa-Sikorski Lemma simplifies, in a sense, proofs of results that make use of the technique known as back-and-forth, often resulting in not very illustrative arguments. The first two sections seek to show one simple…

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).