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The aim of this paper, triggered by some discussions in the astrophysics community raised by astro-ph/0508529, is to introduce the issue of `fits' from a probabilistic perspective (also known as Bayesian), with special attention to the…

Data Analysis, Statistics and Probability · Physics 2007-05-23 G. D'Agostini

The paper contains critical comments to the paper mentioned in the title from the mathematical point of view

Mathematical Physics · Physics 2007-05-23 Hellmut Baumgaertel

Recently published formulas for the calculation of radial part of overlap integrals (E.Oztekin, M.Yavuz, S.Atalay, Theor.Cmem.Acc., (2001), 106, 264) are critically analyzed. It is demonstrated that the presented in this work formulas are…

Chemical Physics · Physics 2007-05-23 I. I. Guseinov

In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.

Complex Variables · Mathematics 2020-12-29 Sudip Saha

This is an erratum to 'On the quantitative distribution of polynomial nilsequences' [GT]. The proof of Theorem 8.6 of that paper, which claims a distribution result for multiparameter polynomial sequences on nilmanifolds, was incorrect. We…

Number Theory · Mathematics 2015-08-17 Ben Green , Terence Tao

This paper deals with the use of numerical methods based on random root sampling techniques to solve some theoretical problems arising in the analysis of polynomials. These methods are proved to be practical and give solutions where…

Numerical Analysis · Mathematics 2025-04-15 Yousra Gati , Vladimir Petrov Kostov , Mohamed Chaouki Tarchi

This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…

Probability · Mathematics 2019-08-28 Wenpin Tang , Fengmin Tang

This paper is in response to a recent comment by Bellissard [arXiv:1704.02644] on the paper [Phys. Rev. Lett. 118, 130201 (2017)]. It is explained that the issues raised in the comment have already been discussed in the paper and do not…

Quantum Physics · Physics 2017-05-22 Carl M. Bender , Dorje C. Brody , Markus P. Müller

This paper focuses on incidences over finite fields, extending to higher degrees a result by Vinh \cite{VINH20111177} on the number of point-line incidences in the plane $\mathbb{F}^2$, where $\mathbb{F}$ is a finite field. Specifically, we…

Information Theory · Computer Science 2023-12-21 Itzhak Tamo

We prove that the previously established inequality of different metrics for algebraic polynomials is sharp in the sense of order.

Classical Analysis and ODEs · Mathematics 2016-07-06 Roman Veprintsev

In this brief note we connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.

Number Theory · Mathematics 2017-02-24 H. Gopalakrishna Gadiyar , R. Padma

This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.

Number Theory · Mathematics 2008-08-13 Stephan Baier , Liangyi Zhao

We prove Pach-Sharir type incidence theorems for a class of curves in R^n and surfaces in R^3, which we call pseudoflats. In particular, our results apply to a wide class of generic irreducible real algebraic sets of bounded degree.

Combinatorics · Mathematics 2007-05-23 Izabella Laba , Jozsef Solymosi

This paper is a corrigendum to the article 'On the ideal theorem for number fields`. The main result of this paper proves to be untrue and is replaced by an estimate of a weighted sum with an improved error term.

Number Theory · Mathematics 2020-06-25 Olivier Bordellès

In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lata{\l}a on bounds on moments of such sums. We also give a new…

Probability · Mathematics 2007-05-23 Paweł Hitczenko , Stephen Montgomery-Smith

In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…

q-alg · Mathematics 2008-02-03 Charilaos Aneziris

This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).

Statistics Theory · Mathematics 2021-02-01 Tobias Fissler , Johanna F. Ziegel

It is noted that some results of the author's research papers cited in the comprehensive review paper "The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets" by G. H. Jones et al. (2018) have been factually misrepresented. The…

Earth and Planetary Astrophysics · Physics 2019-08-30 Zdenek Sekanina

The problem "A general characterization of uniqueness polynomial for non-critically injective polynomials" has been remained open since the last two decades. In this paper, we explore this open problem. To this end, we initiate a new…

Complex Variables · Mathematics 2025-02-11 Pratap Basak , Sanjay Mallick

No abstract available, since this is a Comment on a published article (cf. title)

Optics · Physics 2015-02-23 L. Gil , G. L. Lippi