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We provide some guidance and examples to clear up common misconceptions about special relativity. These misconceptions often come from trying to express the truths of special relativity in Newtonian terms rather than in terms more natural…

General Relativity and Quantum Cosmology · Physics 2026-05-22 David Garfinkle

Several widely-used textbooks lead the reader to believe that solving a linear system of equations Ax = b by multiplying the vector b by a computed inverse inv(A) is inaccurate. Virtually all other textbooks on numerical analysis and…

Numerical Analysis · Computer Science 2012-01-31 Alex Druinsky , Sivan Toledo

We show that the celebrated 1956 Lax-Richtmyer linear theorem in Numerical Analysis - often called the Fundamental Theorem of Numerical Analysis - is in fact wrong. Here "wrong" does not mean that its statement is false mathematically, but…

Analysis of PDEs · Mathematics 2007-05-23 Elemer E Rosinger

This article complements recent results of the papers [J. Math. Phys. 41 (2000), 480; 45 (2004), 336] on the symmetry classification of second-order ordinary difference equations and meshes, as well as the Lagrangian formalism and…

Exactly Solvable and Integrable Systems · Physics 2008-04-24 Vladimir Dorodnitsyn

Samuely et al. (cond-mat/0503153) make the strong claim that our letter is 'contradicting several established experimental results'. As we will show below this is not justified and the claims from are based on a misinterpretation of our…

Superconductivity · Physics 2007-05-23 J. Kortus , O. V. Dolgov , R. K. Kremer , A. A. Golubov

It is demonstrated that remarks and criticism in work [1] (arXiv:1005.2436 nucl-th) have resulted from inattentive reading of work [2] (Phys. Rev.C 81, 035501 (2010)) or just some misunderstanding and do not influence conclusions of work…

Nuclear Experiment · Physics 2010-06-04 A. S. Barabash

A series of monte carlo studies were performed to compare the behavior of some alternative procedures for reasoning under uncertainty. The behavior of several Bayesian, linear model and default reasoning procedures were examined in the…

Artificial Intelligence · Computer Science 2013-03-26 Paul E. Lehner , Azar Sadigh

In this note, we shall point out that all ``numerically calculations'' and figures in \cite{CaFrLeVa-23} are wrong because these calculations are based on some incorrect formulas. Furthermore, by pointing out several serious errors in…

Spectral Theory · Mathematics 2023-12-29 Genqian Liu

We investigate the journal impact factor, focusing on the applied mathematics category. We discuss impact factor manipulation and demonstrate that the impact factor gives an inaccurate view of journal quality, which is poorly correlated…

History and Overview · Mathematics 2014-01-29 Douglas N. Arnold , Kristine K. Fowler

This study presents an abelian group approach to analyzing inconsistency in pairwise comparisons. However, it wrongly assumes that an inconsistency indicator can take values in any abelian linearly ordered group. The followup publication…

Discrete Mathematics · Computer Science 2017-12-27 W. W. Koczkodaj , J. Szybowski , E. Wajch

Whilst an abundance of techniques have recently been proposed to generate counterfactual explanations for the predictions of opaque black-box systems, markedly less attention has been paid to exploring the uncertainty of these generated…

Machine Learning · Computer Science 2021-07-22 Eoin Delaney , Derek Greene , Mark T. Keane

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several…

Artificial Intelligence · Computer Science 2017-05-01 Jiri Mazurek

Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…

Discrete Mathematics · Computer Science 2014-06-27 Timo Jolivet , Jarkko Kari

There are many physical processes that have inherent discontinuities in their mathematical formulations. This paper is motivated by the specific case of collisions between two rigid or deformable bodies and the intrinsic nature of that…

Machine Learning · Computer Science 2023-06-22 Daniel Johnson , Ronald Fedkiw

An argument is given to associate integrable nonintegrable transition of discrete maps with the transition of Lawvere's fixed point theorem to its own contrapositive. We show that the classical description of nonlinear maps is neither…

Dynamical Systems · Mathematics 2016-02-29 S. Saito , N. Saitoh , T. Hatanaka , Y. Wakimoto , T. Yumibayashi

We prove that a real number a greater than or equal to 2 is the irrationality exponent of some computable real number if and only if a is the upper limit of a computable sequence of rational numbers. Thus, there are computable real numbers…

Number Theory · Mathematics 2014-10-07 Verónica Becher , Yann Bugeaud , Theodore A. Slaman

We present a derivation of the cosmological distance-redshift relation up to second order in perturbation theory. In addition, we find the observed redshift and the lensing magnification to second order. We do not require that the density…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-23 Obinna Umeh , Chris Clarkson , Roy Maartens

This is a non-standard paper, containing some problems, mainly in model theory, which I have, in various degrees, been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me,…

Logic · Mathematics 2007-05-23 Saharon Shelah

I review recent results on conformal field theories in four dimensions and quantum field theories interpolating between conformal fixed points, supersymmetric and non-supersymmetric. The talk is structured in three parts: i) central…

High Energy Physics - Theory · Physics 2007-05-23 D. Anselmi

We consider identification and inference about a counterfactual outcome mean when there is unmeasured confounding using tools from proximal causal inference (Miao et al. [2018], Tchetgen Tchetgen et al. [2020]). Proximal causal inference…

Methodology · Statistics 2023-10-03 Jeffrey Zhang , Wei Li , Wang Miao , Eric Tchetgen Tchetgen