25,431 results
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2. On Variability and Interdependence of Local Porosity and Local Tortuosity in Porous Materials: a Case Study for Sack Paper
- Author
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Matthias Neumann, Eduardo Machado Charry, Volker Schmidt, and Karin Zojer
- Subjects
Statistics and Probability ,Geodesic ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Copula (linguistics) ,Sinuosity ,01 natural sciences ,Tortuosity ,010104 statistics & probability ,Goodness of fit ,Gumbel distribution ,Joint probability distribution ,0101 mathematics ,Porosity ,Mathematics - Abstract
The variability and interdependence of local porosity and local mean geodesic tortuosity, which is a measure for the sinuosity of shortest transportation paths, is investigated at the example of the microstructure in sack paper. By means of statistical image analysis, these two morphological characteristics are computed for several cutouts of 3D image data obtained by X-ray microcomputed tomography. Considering cutouts of different sizes allows us to study the influence of the sample size on the local variability of the considered characteristics. Moreover, the interdependence between local porosity and local mean geodesic tortuosity is quantified by modeling their joint distribution parametrically using Archimedean copulas. It turns out that the family of Gumbel copulas is an appropriate model type, which is formally validated by a goodness of fit test. Besides mean geodesic tortuosity, we consider further related morphological characteristics, describing the sinuosity of those shortest transportation paths, whose minimum diameter exceeds a predefined threshold. Moreover, we show that the copula approach investigated in this paper can also be used to quantify the negative correlation between local porosity and these modified versions of local mean geodesic tortuosity. Our results elucidate the impact of local porosity on various kinds of morphological characteristics, which are not experimentally accessible and which are important for local air permeance – a key property of sack paper.
- Published
- 2020
3. Note on a paper by Bordellès, Dai, Heyman, Pan and Shparlinski
- Author
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Jie Wu
- Subjects
Combinatorics ,General Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,021107 urban & regional planning ,02 engineering and technology ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
Very recently Bordelles, Dai, Heyman, Pan and Shparlinski studied asymptotic behaviour of the quantity $$\begin{aligned} S_f(x) := \sum _{n\leqslant x} f\left( \left[ \frac{x}{n}\right] \right) , \end{aligned}$$and established some asymptotic formulas for $$S_f(x)$$ under three different types of assumptions on f. In this short note we improve some of their results.
- Published
- 2019
4. An example regarding Kalton's paper 'Isomorphisms between spaces of vector-valued continuous functions'
- Author
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Félix Cabello Sánchez
- Subjects
Pure mathematics ,Mathematics::Functional Analysis ,General Mathematics ,010102 general mathematics ,General Topology (math.GN) ,01 natural sciences ,Functional Analysis (math.FA) ,010101 applied mathematics ,Mathematics - Functional Analysis ,Dimension (vector space) ,46A16, 46E10 ,Metric (mathematics) ,FOS: Mathematics ,0101 mathematics ,Mathematics ,Mathematics - General Topology - Abstract
The paper alluded to in the title contains the following striking result: Let $I$ be the unit interval and $\Delta$ the Cantor set. If $X$ is a quasi Banach space containing no copy of $c_0$ which is isomorphic to a closed subspace of a space with a basis and $C(I, X)$ is linearly homeomorphic to $C(\Delta, X)$, then $X$ is locally convex, i.e., a Banach space. It is shown that Kalton result is sharp by exhibiting non locally convex quasi Banach spaces X with a basis for which $C(I, X)$ and $C(\Delta, X)$ are isomorphic. Our examples are rather specific and actually in all cases X is isomorphic to $C(\Delta, X)$ if $K$ is a metric compactum of finite covering dimension., Comment: 4 pages
- Published
- 2021
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5. On a paper of Erdös and Szekeres
- Author
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Mei-Chu Chang and Jean Bourgain
- Subjects
010101 applied mathematics ,Discrete mathematics ,Set (abstract data type) ,Partial differential equation ,Functional analysis ,General Mathematics ,010102 general mathematics ,0101 mathematics ,01 natural sciences ,Analysis ,Mathematics - Abstract
Propositions 1.1–1.3 stated below contribute to results and certain problems considered in [E-S], on the behavior of products $$\Pi^n_1(1-z^{a_j}),1\leq{a_1}...\leq{a_n}$$ integers. In the discussion below, {a1,..., an} will be either a proportional subset of {1,..., n} or a set of large arithmetic diameter.
- Published
- 2018
6. Correction and notes to the paper 'A classification of Artin–Schreier defect extensions and characterizations of defectless fields'
- Author
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Franz-Viktor Kuhlmann
- Subjects
Discrete mathematics ,Lemma (mathematics) ,14B05 ,General Mathematics ,13A18 ,010102 general mathematics ,12J10 ,Mistake ,Commutative Algebra (math.AC) ,Linearly disjoint ,Mathematics - Commutative Algebra ,01 natural sciences ,Primary 12J10, 13A18, Secondary 12J25, 12L12, 14B05 ,Field extension ,0103 physical sciences ,FOS: Mathematics ,010307 mathematical physics ,0101 mathematics ,12J25 ,12L12 ,Mathematics - Abstract
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. We give an example to show that a separability assumption in one of these results cannot be dropped (doing so had led to the mistake). Further, we discuss recent generalizations of the original classification of defect extensions.
- Published
- 2019
7. Notes on the paper 'A note on pronormal p-subgroups of finite groups'
- Author
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Haoran Yu and Suli Liu
- Subjects
Discrete mathematics ,Lemma (mathematics) ,010505 oceanography ,General Mathematics ,010102 general mathematics ,0101 mathematics ,01 natural sciences ,0105 earth and related environmental sciences ,Mathematics - Abstract
In this short note, we show that Theorem 4.3 of Liu and Yu (Monatshefte Math 195:173–176, 2021) is a consequence of Lemma 2 of Ballester-Bolinches and Esteban-Romero (J Aust Math Soc 75:181–191, 2003).
- Published
- 2021
8. An unpublished paper ‘Über einige durch unendliche Reihen definirte Functionen eines complexen Argumentes’ by Adolf Hurwitz
- Author
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Nicola Oswald
- Subjects
History ,Pure mathematics ,General Mathematics ,010102 general mathematics ,01 natural sciences ,Algebra ,symbols.namesake ,Continuation ,0103 physical sciences ,Functional equation ,symbols ,010307 mathematical physics ,0101 mathematics ,Dirichlet series ,Meromorphic function ,Mathematics - Abstract
In 1903, Epstein published his proof of meromorphic continuation and a functional equation for Dirichlet series associated with quadratic forms, now called Epstein zeta-functions. However, already in 1889 (or even earlier) Hurwitz was aware of these results as his mathematical diaries and some unpublished notes (in an almost final form) found in his estate at the ETH Zurich show. In this article we present and analyze Hurwitz's notes and compare his reasoning with Epstein's paper in detail.
- Published
- 2017
9. Scientific heritage of L.D. Faddeev. Survey of papers
- Author
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M. A. Semenov-Tian-Shansky, I. Ya. Aref'eva, Evgeny Sklyanin, A. Yu. Alekseev, Samson L. Shatashvili, F. A. Smirnov, Leon A. Takhtajan, Euler International Mathematical Institute [St. Petersburg], Stony Brook University [SUNY] (SBU), State University of New York (SUNY), University of Geneva [Switzerland], Steklov Mathematical Institute [Moscow] (SMI), Russian Academy of Sciences [Moscow] (RAS), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), University of York [York, UK], Université Pierre et Marie Curie - Paris 6 (UPMC), Institut des Hautes Etudes Scientifiques (IHES), IHES, Trinity College Dublin, Institute for Information Transmission Problems, The work of Semenov-Tian-Shansky was supported by the Presidium of the Russian Academy of Sciences programme no. 02 'Non-linear dynamics: fundamental problems and applications' (grant no. PRAS-18-02). Sklyanin worked as a Royal Society Leverhulme Trust Senior Research Fellow. The work of Shatashvili was supported by the Simons Foundation under the programme 'Targeted Grants to Institutes' (The Hamilton Mathematics Institute)., Université de Genève = University of Geneva (UNIGE), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), and Institut des Hautes Études Scientifiques (IHES)
- Subjects
Inverse scattering problem ,Scattering theory ,General Mathematics ,Yang-Baxter equation ,Inverse scattering method ,Quantum groups ,01 natural sciences ,AMS 2010 Mathematics Subject Classification. Primary 01A70, 16T25, 17B37, 35J10, 35P25,35Q53, 35Q55, 37K15, 58B32, 58J52, 70S15, 81-03, 81R50, 81S40, 81T10, 81T13, 81T50, 81T70,81U40, 82B23, 82C23 ,Eigenfunction expansion ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,Quantization of gauge fields ,Korteweg-de Vries equation ,0103 physical sciences ,Schrodinger operator ,0101 mathematics ,Korteweg–de Vries equation ,Mathematics ,Mathematical physics ,Quantum anomalies ,010308 nuclear & particles physics ,Yang–Baxter equation ,Faddeev-Popov ghosts ,010102 general mathematics ,Algebraic Bethe ansatz ,Quantum dilogarithm ,Complete integrability ,Quantum inverse problem method - Abstract
International audience; This survey was written by students of L. D. Faddeev under the editorship of L. A. Takhtajan. Sections 1.1, 1.2, 2–4, and 6 were written by Takhtajan, §§1.3 and 1.4 by F. A. Smirnov, §§5.1 and 5.2 by E. K. Sklyanin, §§5.3–5.6 by Sklyanin, Smirnov, and Takhtajan, §7.1 by M. A. Semenov- Tian-Shansky, §§7.2–7.6 by Takhtajan and S. L. Shatashvili, §7.7 by A. Yu. Alekseev and Shatashvili, and §8 by I. Ya. Aref'eva.
- Published
- 2017
10. On A.Ya. Khinchin's paper ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ (1926): A translation with introduction and commentary
- Author
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Lukas M. Verburgt and Olga Hoppe-Kondrikova
- Subjects
History ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Victory ,Ignorance ,06 humanities and the arts ,0603 philosophy, ethics and religion ,01 natural sciences ,Epistemology ,Subject matter ,Formalism (philosophy of mathematics) ,Intuitionism ,060302 philosophy ,Calculus ,Ideology ,0101 mathematics ,Communism ,media_common ,Mathematics - Abstract
The translation into English of Aleksandr Yakovlevich Khinchin's (1894–1959) 1926 paper entitled ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ is made available for the first time. Here, Khinchin presented the famous foundational debate between L.E.J. Brouwer and David Hilbert of the 1920s in terms of a search for a mathematics with content. His main aim seems to have been to make intuitionism ideologically acceptable to his audience at the Communist Academy by means of the claim that insofar as Brouwer's intuitionism had a clear ‘subject matter’ and Hilbert's new program was a concession to intuitionism, the alleged victory of intuitionism not only implied the defeat of ‘empty’ formalism, but also showed the compatibility and affinity of Marxism with the newest developments in modern mathematics. This introduction provides a tentative exploration of the issue of what was tactical (or due to ideological pressure) and what was real scientific interest (or due to ignorance) (or what was both) in Khinchin's 1926 paper in the form of a detailed commentary, especially, on the tactical side of his presentation of the positions of Brouwer and Hilbert.
- Published
- 2016
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