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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…

广义相对论与量子宇宙学 · 物理学 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…

数值分析 · 计算机科学 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…

偏微分方程分析 · 数学 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…

可精确求解与可积系统 · 物理学 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…

超导电性 · 物理学 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…

核实验 · 物理学 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…

人工智能 · 计算机科学 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…

谱理论 · 数学 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…

历史与综述 · 数学 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…

离散数学 · 计算机科学 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…

机器学习 · 计算机科学 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…

人工智能 · 计算机科学 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…

离散数学 · 计算机科学 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…

机器学习 · 计算机科学 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…

动力系统 · 数学 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…

数论 · 数学 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…

宇宙学与河外天体物理 · 物理学 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,…

逻辑 · 数学 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…

高能物理 - 理论 · 物理学 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…

统计方法学 · 统计学 2023-10-03 Jeffrey Zhang , Wei Li , Wang Miao , Eric Tchetgen Tchetgen