25,431 results
Search Results
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
- Full Text
- View/download PDF
5. 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
6. 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
7. 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
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. Corrections and complements to my paper 'On a class of operator monotone functions of several variables'
- Author
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A. R. Mirotin
- Subjects
Discrete mathematics ,General Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,021107 urban & regional planning ,02 engineering and technology ,Finite-rank operator ,Compact operator ,Strongly monotone ,Shift operator ,01 natural sciences ,Semi-elliptic operator ,Algebra ,Pseudo-monotone operator ,Monotone polygon ,Multiplication operator ,0101 mathematics ,Mathematics - Published
- 2017
11. 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
12. Notes on the Paper 'On SS-Quasinormal and S-Quasinormally Embedded Subgroups of Finite Groups' of Shen et al
- Author
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Yuemei Mao, Xiaolan Yi, and Changwen Li
- Subjects
Discrete mathematics ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,Zhàng ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,010307 mathematical physics ,0101 mathematics ,01 natural sciences ,GeneralLiterature_MISCELLANEOUS ,Mathematics - Abstract
We correct an error in the paper of Z. Shen, S. Li, and J. Zhang published in [4]. In addition, we give an answer to a question posed by the authors.
- Published
- 2018
13. Using A4-sized paper to illustrate that is irrational
- Author
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Nick Lord
- Subjects
General Mathematics ,Irrational number ,010102 general mathematics ,0101 mathematics ,01 natural sciences ,Mathematical economics ,Mathematics - Published
- 2017
14. Remark on the paper 'On products of Fourier coefficients of cusp forms'
- Author
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Yuk-Kam Lau, Deyu Zhang, and Yingnan Wang
- Subjects
Cusp (singularity) ,Discrete group ,Mathematics::Number Theory ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Holomorphic function ,02 engineering and technology ,01 natural sciences ,Cusp form ,Combinatorics ,Integer ,Product (mathematics) ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,0101 mathematics ,Fourier series ,Mathematics - Abstract
Let a(n) be the Fourier coefficient of a holomorphic cusp form on some discrete subgroup of \(SL_2({\mathbb R})\). This note is to refine a recent result of Hofmann and Kohnen on the non-positive (resp. non-negative) product of \(a(n)a(n+r)\) for a fixed positive integer r.
- Published
- 2016
15. On Nash’s unique contribution to analysis in just three of his papers
- Author
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Sergiu Klainerman
- Subjects
Applied Mathematics ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,01 natural sciences ,Mathematics - Published
- 2016
16. Addendum to the paper 'Linearly topologized modules over a discrete valuation ring'
- Author
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Patricia Couto G. Mauro and Dinamérico P. Pombo
- Subjects
Discrete mathematics ,General Mathematics ,010102 general mathematics ,Addendum ,0101 mathematics ,01 natural sciences ,Discrete valuation ring ,Linear equation ,Mathematics - Abstract
For any discrete valuation ring R, any R-linear mapping u from an R-module E into an R-module F and any \(y_0\in F\), a necessary and sufficient condition for the solvability of the equation \(u(x)=y_0\) is established, and an application of this result is presented.
- Published
- 2016
17. Derived length of zero entropy groups acting on projective varieties in arbitrary characteristic — A remark to a paper of Dinh-Oguiso-Zhang
- Author
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Sichen Li
- Subjects
Automorphism group ,Pure mathematics ,Computer Science::Information Retrieval ,General Mathematics ,010102 general mathematics ,Zhàng ,Astrophysics::Instrumentation and Methods for Astrophysics ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,01 natural sciences ,0103 physical sciences ,Computer Science::General Literature ,Entropy (information theory) ,010307 mathematical physics ,0101 mathematics ,Algebraically closed field ,Projective test ,Projective variety ,Mathematics - Abstract
Let [Formula: see text] be a projective variety of dimension [Formula: see text] over an algebraically closed field of arbitrary characteristic. We prove a Fujiki–Lieberman type theorem on the structure of the automorphism group of [Formula: see text]. Let [Formula: see text] be a group of zero entropy automorphisms of [Formula: see text] and [Formula: see text] the set of elements in [Formula: see text] which are isotopic to the identity. We show that after replacing [Formula: see text] by a suitable finite-index subgroup, [Formula: see text] is a unipotent group of the derived length at most [Formula: see text]. This result was first proved by Dinh et al. for compact Kähler manifolds.
- Published
- 2020
18. 'Graph Paper' Trace Characterizations of Functions of Finite Energy
- Author
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Robert S. Strichartz
- Subjects
Discrete mathematics ,Plane (geometry) ,General Mathematics ,010102 general mathematics ,Voltage graph ,Mathematics::General Topology ,Graph paper ,01 natural sciences ,Sierpinski triangle ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Sobolev space ,Coxeter graph ,Sierpinski carpet ,0103 physical sciences ,String graph ,FOS: Mathematics ,010307 mathematical physics ,0101 mathematics ,Analysis ,Mathematics - Abstract
We characterize functions of finite energy in the plane in terms of their traces on the lines that make up "graph paper" with squares of side length $mn$ for all $n$, and certain $\12-$order Sobolev norms on the graph paper lines. We also obtain analogous results for functions of finite energy on two classical fractals: the Sierpinski gasket and the Sierpinski carpet.
- Published
- 2013
- Full Text
- View/download PDF
19. On a paper of Berestycki-Hamel-Rossi and its relations to the weak maximum principle at infinity, with applications
- Author
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Luciano Mari, Marco Rigoli, and Marco Magliaro
- Subjects
Pure mathematics ,Work (thermodynamics) ,Trace (linear algebra) ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Differential operator ,Infinity ,01 natural sciences ,010101 applied mathematics ,Type condition ,Maximum principle ,Bounded function ,Uniqueness ,0101 mathematics ,Mathematics ,media_common - Abstract
The aim of this paper is to study a new equivalent form of the weak maximum principle for a large class of differential operators on Riemannian manifolds. This new form has been inspired by the work of Berestycki, Hamel and Rossi for trace operators, and allows us to shed new light on it and to introduce a new sufficient bounded Khas’minskii type condition for its validity. We show its effectiveness by applying it to obtain some uniqueness results in a geometric setting.
- Published
- 2018
20. NOTES ON THE PAPER 'A CRITERION FOR BOUNDED FUNCTIONS' [BULL. KOREAN MATH. SOC. 53 (2016), NO. 1, 215-225]
- Author
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Jin-Lin Liu and Yi-Ling Cang
- Subjects
Algebra ,General Mathematics ,Bounded function ,010102 general mathematics ,0101 mathematics ,Arithmetic ,01 natural sciences ,Mathematics - Published
- 2016
21. Entropy criteria and stability of extreme shocks: a remark on a paper of Leger and Vasseur
- Author
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Kevin Zumbrun and Benjamin Texier
- Subjects
Conservation law ,Kullback–Leibler divergence ,Standard molar entropy ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Regular polygon ,Min entropy ,Shock strength ,01 natural sciences ,010101 applied mathematics ,Mathematics - Analysis of PDEs ,FOS: Mathematics ,Uniqueness ,0101 mathematics ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
We show that a relative entropy condition recently shown by Leger and Vasseur to imply uniqueness and stable $L^2$ dependence on initial data of Lax 1- or $n$-shock solutions of an $n\times n$ system of hyperbolic conservation laws with convex entropy implies Lopatinski stability in the sense of Majda. This means in particular that Leger and Vasseur's relative entropy condition represents a considerable improvement over the standard entropy condition of decreasing shock strength and increasing entropy along forward Hugoniot curves, which, in a recent example exhibited by Barker, Freist\"uhler and Zumbrun, was shown to fail to imply Lopatinski stability, even for systems with convex entropy. This observation bears also on the parallel question of existence, at least for small $BV$ or $H^s$ perturbations, Comment: to appear in Proceedings of the AMS
- Published
- 2014
22. Some comments on the paper of Khuangsatung and Kangtunyakarn
- Author
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Kanokwan Wongchan
- Subjects
010101 applied mathematics ,Nonlinear system ,Fixed point problem ,General Mathematics ,010102 general mathematics ,Convergence (routing) ,Applied mathematics ,0101 mathematics ,Fixed point ,01 natural sciences ,Mathematics - Abstract
In this paper, we discuss the validity of the result of Khuangsatung and Kangtunyakarn [Existence and convergence theorem for fixed point problem of various nonlinear mappings and variational inequality problems without some assumptions, Filomat 32(1) (2018) 305–309].
- Published
- 2018
23. A Note on a Paper by Wong and Heyde
- Author
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Mikhail Urusov and Aleksandar Mijatović
- Subjects
Statistics and Probability ,Statistics::Theory ,Pure mathematics ,60G44, 60G48, 60H10, 60J60 ,General Mathematics ,Applied probability ,01 natural sciences ,FOS: Economics and business ,010104 statistics & probability ,60G48 ,FOS: Mathematics ,60G44 ,0101 mathematics ,60J60 ,Mathematics ,Local martingales versus true martingales ,010102 general mathematics ,Probability (math.PR) ,stochastic exponential ,Exponential function ,Mathematik ,60H10 ,Statistics, Probability and Uncertainty ,Martingale (probability theory) ,Quantitative Finance - General Finance ,General Finance (q-fin.GN) ,Mathematics - Probability ,Counterexample - Abstract
In this note we re-examine the analysis of the paper "On the martingale property of stochastic exponentials" by B. Wong and C.C. Heyde, Journal of Applied Probability, 41(3):654-664, 2004. Some counterexamples are presented and alternative formulations are discussed., Comment: To appear in Journal of Applied Probability, 11 pages
- Published
- 2011
24. Some comments on the paper: Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014), no. 5, 941–959
- Author
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Michelle Pierri and Donal O'Regan
- Subjects
Discrete mathematics ,Class (set theory) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,General Physics and Astronomy ,Differential systems ,01 natural sciences ,010101 applied mathematics ,Controllability ,Algebra ,0101 mathematics ,Differential (mathematics) ,Mathematics - Abstract
The abstract results and applications presented in “Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014), no. 5, 941–959, are not correct. Moreover, the class of differential control problems studied in [1] is not H-controllable.
- Published
- 2016
25. Fractional Factorials and Prime Numbers (A Remark on the Paper 'On Prime Values of Some Quadratic Polynomials')
- Author
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A. N. Andrianov
- Subjects
Statistics and Probability ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Prime element ,01 natural sciences ,Prime k-tuple ,Prime (order theory) ,010305 fluids & plasmas ,Combinatorics ,0103 physical sciences ,Prime factor ,Unique prime ,0101 mathematics ,Fibonacci prime ,Prime power ,Sphenic number ,Mathematics - Abstract
Congruences mod p for a prime p and partial products of the numbers 1,…, p − 1 are obtained. Bibliography: 2 titles.
- Published
- 2016
26. Variations on a Theme in Paper Folding
- Author
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Burkard Polster
- Subjects
General Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,Folding (DSP implementation) ,0101 mathematics ,01 natural sciences ,Linguistics ,Theme (narrative) ,Mathematics - Published
- 2004
27. Corrigendum to our paper : How Expressions can code for Automata
- Author
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Sylvain Lombardy, Jacques Sakarovitch, Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), and Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS)
- Subjects
TheoryofComputation_COMPUTATIONBYABSTRACTDEVICES ,Powerset construction ,General Mathematics ,010102 general mathematics ,Continuous automaton ,Timed automaton ,Pushdown automaton ,Büchi automaton ,0102 computer and information sciences ,16. Peace & justice ,Nonlinear Sciences::Cellular Automata and Lattice Gases ,01 natural sciences ,Computer Science Applications ,Algebra ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,Deterministic automaton ,[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering ,Probabilistic automaton ,Two-way deterministic finite automaton ,0101 mathematics ,Algorithm ,Software ,Computer Science::Formal Languages and Automata Theory ,Mathematics - Abstract
International audience; In a previous paper, we have described the construction of an automaton from a rational expression which has the property that the automaton built from an expression which is itself computed from a co-deterministic automaton by the state elimination method is co-deterministic. It turned out that the definition on which the construction is based was inappropriate, and thus the proof of the property was flawed. We give here the correct definition of the broken derived terms of an expression which allow to define the automaton and the detailed full proof of the property.
- Published
- 2010
28. Rebuttal of Donnelly's paper on the spectral gap
- Author
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Antoine Henrot, Mark S. Ashbaugh, Richard S. Laugesen, Department of Mathematics, University of Missouri Columbia, University of Missouri [Columbia] (Mizzou), University of Missouri System-University of Missouri System, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Department of Mathematics [Urbana], University of Illinois at Urbana-Champaign [Urbana], University of Illinois System-University of Illinois System, CORIDA, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est
- Subjects
Discrete mathematics ,Sequence ,Conjecture ,General Mathematics ,010102 general mathematics ,Mathematics::History and Overview ,Mathematics::Spectral Theory ,01 natural sciences ,Domain (mathematical analysis) ,Computer Science::Computers and Society ,010101 applied mathematics ,symbols.namesake ,Physics::Popular Physics ,Dirichlet boundary condition ,Euclidean geometry ,symbols ,Calculus ,Convex body ,Quantitative Biology::Populations and Evolution ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Spectral gap ,0101 mathematics ,Mathematics ,Unit interval - Abstract
The spectral gap conjecture of M. van den Berg [2, formula (65)] asserts that λ2 − λ1 ≥ 3π for all convex euclidean domains of diameter 1, where λ1 and λ2 denote the first two eigenvalues of the Dirichlet Laplacian. Notice that equality holds for the 1-dimensional unit interval, which can be regarded also as a degenerate n-dimensional rectangular box. The gap estimate is conjectured to hold more generally for Schrodinger operators with convex potentials, under Dirichlet boundary conditions; see the work of S.-T. Yau and collaborators [9, 11]. This Schrodinger gap conjecture was proved some time ago in 1 dimension by R. Lavine [8], and more recently in all dimensions by B. Andrews and J. Clutterbuck [1]. The proof in this journal by H. Donnelly [3] of the original gap conjecture in 2 dimensions (for the Dirichlet Laplacian with zero potential) is not correct. The Editors of Mathematische Zeitschrift have asked us to describe the flaws in the proof, in order to clarify the state of the literature. Donnelly’s approach to the problem is a natural one: first perform a shape optimization to rule out a non-degenerate minimizing domain, and then analyze the spectral gap for a sequence of domains degenerating to an interval, with the help of results by D. Jerison [5]. (For some history on this approach, and on the gap conjecture more generally, see the report on the AIM meeting “Low Eigenvalues of Laplace and Schrodinger Operators” [10], especially page 12 of the open problems list.) The error lies in the proof of the shape optimization step, as we now explain. Donnelly wishes to prove that no minimizing domain can exist for
- Published
- 2011
29. On Dyakonov’s paper 'Equivalent normos on Lipschitz-type spaces of homorphic functions'
- Author
-
Miroslav Pavlović
- Subjects
010101 applied mathematics ,Pure mathematics ,Unit circle ,General Mathematics ,010102 general mathematics ,Holomorphic function ,0101 mathematics ,Type (model theory) ,Lipschitz continuity ,01 natural sciences ,Complex plane ,Unit disk ,Mathematics - Published
- 1999
30. Addendum to the paper 'A note on weighted Bergman spaces and the Cesàro operator'
- Author
-
Stevo Stević and Der-Chen Chang
- Subjects
Pure mathematics ,010308 nuclear & particles physics ,General Mathematics ,Operator (physics) ,010102 general mathematics ,Mathematical analysis ,Weighted Bergman space ,Addendum ,01 natural sciences ,Bergman space ,0103 physical sciences ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,46E15 ,0101 mathematics ,polydisk ,Cesàro operator ,Mathematics ,Bergman kernel ,47B38 - Abstract
Let H(Dn) be the space of holomorphic functions on the unit polydisk Dn, and let , where p, q> 0, α = (α1,…,αn) with αj > -1, j =1,..., n, be the class of all measurable functions f defined on Dn such thatwhere Mp(f,r) denote the p-integral means of the function f. Denote the weighted Bergman space on . We provide a characterization for a function f being in . Using the characterization we prove the following result: Let p> 1, then the Cesàro operator is bounded on the space .
- Published
- 2005
31. A study on fractional COVID‐19 disease model by using Hermite wavelets
- Author
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Shaher Momani, Ranbir Kumar, Samir Hadid, and Sunil Kumar
- Subjects
General Mathematics ,coronavirus ,Value (computer science) ,Derivative ,34a34 ,01 natural sciences ,Caputo derivative ,convergence analysis ,Wavelet ,Special Issue Paper ,operational matrix ,Applied mathematics ,0101 mathematics ,26a33 ,Hermite wavelets ,Mathematics ,Hermite polynomials ,Collocation ,Special Issue Papers ,Basis (linear algebra) ,010102 general mathematics ,General Engineering ,34a08 ,010101 applied mathematics ,Algebraic equation ,Scheme (mathematics) ,60g22 ,mathematical model - Abstract
The preeminent target of present study is to reveal the speed characteristic of ongoing outbreak COVID-19 due to novel coronavirus. On January 2020, the novel coronavirus infection (COVID-19) detected in India, and the total statistic of cases continuously increased to 7 128 268 cases including 109 285 deceases to October 2020, where 860 601 cases are active in India. In this study, we use the Hermite wavelets basis in order to solve the COVID-19 model with time- arbitrary Caputo derivative. The discussed framework is based upon Hermite wavelets. The operational matrix incorporated with the collocation scheme is used in order to transform arbitrary-order problem into algebraic equations. The corrector scheme is also used for solving the COVID-19 model for distinct value of arbitrary order. Also, authors have investigated the various behaviors of the arbitrary-order COVID-19 system and procured developments are matched with exiting developments by various techniques. The various illustrations of susceptible, exposed, infected, and recovered individuals are given for its behaviors at the various value of fractional order. In addition, the proposed model has been also supported by some numerical simulations and wavelet-based results.
- Published
- 2021
32. A note on Saleh's paper ‘Almost continuity implies closure continuity’
- Author
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Julian Dontchev and Takashi Noiri
- Subjects
Pure mathematics ,Continuous function ,General Mathematics ,010102 general mathematics ,General Topology (math.GN) ,Closure (topology) ,Topology (electrical circuits) ,01 natural sciences ,010101 applied mathematics ,54C08 ,FOS: Mathematics ,0101 mathematics ,Mathematics - General Topology ,Mathematics - Abstract
Recently, Saleh claimed to have solved `a long standing open question' in Topology; namely, he proved that every almost continuous function is closure continuous (= $\theta$-continuous). Unfortunately, this problem was settled long time ago and even a better result is known., Comment: 2 pages, to appear in "Glasgow Math. J."
- Published
- 1998
33. Biased Adjusted Poisson Ridge Estimators-Method and Application
- Author
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Pär Sjölander, Muhammad Qasim, Muhammad Amin, B. M. Golam Kibria, and Kristofer Månsson
- Subjects
Mean squared error ,General Mathematics ,Maximum likelihood ,General Physics and Astronomy ,Regression estimator ,Poisson distribution ,Modified almost unbiased ridge estimators ,01 natural sciences ,symbols.namesake ,0103 physical sciences ,Statistics ,Poisson regression ,0101 mathematics ,Mathematics ,010308 nuclear & particles physics ,010102 general mathematics ,Estimator ,Mean square error ,General Chemistry ,Ridge (differential geometry) ,Poisson ridge regression ,Multicollinearity ,Maximum likelihood estimator ,symbols ,General Earth and Planetary Sciences ,General Agricultural and Biological Sciences ,Research Paper - Abstract
Månsson and Shukur (Econ Model 28:1475–1481, 2011) proposed a Poisson ridge regression estimator (PRRE) to reduce the negative effects of multicollinearity. However, a weakness of the PRRE is its relatively large bias. Therefore, as a remedy, Türkan and Özel (J Appl Stat 43:1892–1905, 2016) examined the performance of almost unbiased ridge estimators for the Poisson regression model. These estimators will not only reduce the consequences of multicollinearity but also decrease the bias of PRRE and thus perform more efficiently. The aim of this paper is twofold. Firstly, to derive the mean square error properties of the Modified Almost Unbiased PRRE (MAUPRRE) and Almost Unbiased PRRE (AUPRRE) and then propose new ridge estimators for MAUPRRE and AUPRRE. Secondly, to compare the performance of the MAUPRRE with the AUPRRE, PRRE and maximum likelihood estimator. Using both simulation study and real-world dataset from the Swedish football league, it is evidenced that one of the proposed, MAUPRRE ($$ \hat{k}_{q4} $$ k ^ q 4 ) performed better than the rest in the presence of high to strong (0.80–0.99) multicollinearity situation.
- Published
- 2020
34. Algebraic bounds on the Rayleigh–Bénard attractor
- Author
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Michael S. Jolly, Edriss S. Titi, Yu Cao, Jared P. Whitehead, Jolly, Michael S [0000-0002-7158-0933], Titi, Edriss S [0000-0002-5004-1746], Apollo - University of Cambridge Repository, Jolly, MS [0000-0002-7158-0933], and Titi, ES [0000-0002-5004-1746]
- Subjects
Paper ,General Mathematics ,General Physics and Astronomy ,global attractor ,Enstrophy ,01 natural sciences ,76F35 ,Attractor ,Periodic boundary conditions ,Boundary value problem ,0101 mathematics ,Algebraic number ,Rayleigh–Bénard convection ,math.AP ,Mathematical Physics ,Mathematics ,Rayleigh-Benard convection ,Plane (geometry) ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Statistical and Nonlinear Physics ,76E06 ,Nonlinear Sciences::Chaotic Dynamics ,010101 applied mathematics ,34D06 ,Homogeneous space ,Affine space ,synchronization ,35Q35 - Abstract
Funder: John Simon Guggenheim Memorial Foundation; doi: https://doi.org/10.13039/100005851, Funder: Einstein Visiting Fellow Program, The Rayleigh–Bénard system with stress-free boundary conditions is shown to have a global attractor in each affine space where velocity has fixed spatial average. The physical problem is shown to be equivalent to one with periodic boundary conditions and certain symmetries. This enables a Gronwall estimate on enstrophy. That estimate is then used to bound the L 2 norm of the temperature gradient on the global attractor, which, in turn, is used to find a bounding region for the attractor in the enstrophy–palinstrophy plane. All final bounds are algebraic in the viscosity and thermal diffusivity, a significant improvement over previously established estimates. The sharpness of the bounds are tested with numerical simulations.
- Published
- 2021
35. Improving the performance of deep learning models using statistical features: The case study of COVID‐19 forecasting
- Author
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Hossein Abbasimehr, Reza Paki, and Aram Bahrini
- Subjects
2019-20 coronavirus outbreak ,Coronavirus disease 2019 (COVID-19) ,62‐07 ,General Mathematics ,Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ,Context (language use) ,97r40 ,Machine learning ,computer.software_genre ,01 natural sciences ,Convolutional neural network ,Special Issue Paper ,0101 mathematics ,Combined method ,Mathematics ,Special Issue Papers ,business.industry ,Deep learning ,010102 general mathematics ,General Engineering ,deep learning ,COVID‐19 pandemic ,010101 applied mathematics ,hybrid methods ,Memory model ,Artificial intelligence ,business ,computer ,statistical features - Abstract
COVID-19 pandemic has affected all aspects of people's lives and disrupted the economy. Forecasting the number of cases infected with this virus can help authorities make accurate decisions on the interventions that must be implemented to control the pandemic. Investigation of the studies on COVID-19 forecasting indicates that various techniques such as statistical, mathematical, and machine and deep learning have been utilized. Although deep learning models have shown promising results in this context, their performance can be improved using auxiliary features. Therefore, in this study, we propose two hybrid deep learning methods that utilize the statistical features as auxiliary inputs and associate them with their main input. Specifically, we design a hybrid method of the multihead attention mechanism and the statistical features (ATT_FE) and a combined method of convolutional neural network and the statistical features (CNN_FE) and apply them to COVID-19 data of 10 countries with the highest number of confirmed cases. The results of experiments indicate that the hybrid models outperform their conventional counterparts in terms of performance measures. The experiments also demonstrate the superiority of the hybrid ATT_FE method over the long short-term memory model.
- Published
- 2021
36. Remarks on E. A. Rahmanov's paper 'on the asymptotics of the ratio of orthogonal polynomials'
- Author
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Paul Nevai and Attila Máté
- Subjects
Discrete mathematics ,Mathematics(all) ,Numerical Analysis ,Statement (logic) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Algebra ,Orthogonal polynomials ,0101 mathematics ,Analysis ,Mathematics ,Counterexample - Abstract
It is pointed out that the proof of the basic result of Rahmanov's paper has a serious gap. It is documented by original sources that a statement he relied on in the proof contains a misprint, and it is shown by a counterexample that this statement (with the misprint) is, in fact, false. A somewhat weaker statement is proved true.
- Published
- 1982
37. Epidemics with carriers: A note on a paper of Dietz
- Author
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F. Downton
- Subjects
Statistics and Probability ,Entire population ,education.field_of_study ,General Mathematics ,010102 general mathematics ,Population ,01 natural sciences ,Short interval ,010104 statistics & probability ,0101 mathematics ,Statistics, Probability and Uncertainty ,education ,Demography ,Mathematics - Abstract
In a recent paper Weiss (1965) has suggested a simple model for a carrier-borne epidemic such as typhoid. He considers a population (of size m) of susceptibles into which a number (k) of carriers is introduced. These carriers exhibit no overt symptoms and are only detectable by the discovery of infected persons. He supposed that after the initial introduction of the carriers, the population remains entirely closed and no new carriers arise. The epidemic then progresses until either all the carriers have been traced and isolated or until the entire population has succumbed to the disease.
- Published
- 1967
38. (CMMSE2018 paper) Solving the random Pielou logistic equation with the random variable transformation technique: Theory and applications
- Author
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Ana Navarro-Quiles, M.-D. Roselló, José Vicente Romero, and Juan Carlos Cortés
- Subjects
education.field_of_study ,Differential equation ,Stochastic process ,General Mathematics ,Computation ,010102 general mathematics ,Population ,General Engineering ,Probability density function ,01 natural sciences ,010101 applied mathematics ,Transformation (function) ,Applied mathematics ,0101 mathematics ,Logistic function ,education ,Random variable ,Mathematics - Abstract
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples, the first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data.
- Full Text
- View/download PDF
39. Special Ulrich bundles on regular Weierstrass fibrations
- Author
-
Joan Pons-Llopis and Rosa M. Miró-Roig
- Subjects
Pure mathematics ,Class (set theory) ,Mathematics::Commutative Algebra ,General Mathematics ,010102 general mathematics ,Short paper ,Elliptic surfaces ,Ulrich bundles ,01 natural sciences ,Mathematics::Algebraic Geometry ,Simple (abstract algebra) ,0103 physical sciences ,Weierstrass fibrations ,Rank (graph theory) ,010307 mathematical physics ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
The main goal of this short paper is to prove the existence of rank 2 simple and special Ulrich bundles on a wide class of elliptic surfaces: namely, on regular Weierstrass fibrations \(\pi : S\rightarrow \mathbb {P}^1\). Alongside we also show the existence of rank 2 weakly Ulrich sheaves on arbitrary Weierstrass fibrations \(S\rightarrow C_0\) and we deal with the (non-)existence of rank one Ulrich bundles on them.
- Published
- 2019
40. On the Characterizations of Wave Front Sets in Terms of the Short-Time Fourier Transform
- Author
-
Stevan Pilipović and Bojan Prangoski
- Subjects
Wavefront ,General Mathematics ,010102 general mathematics ,Short paper ,Mathematical analysis ,Short-time Fourier transform ,02 engineering and technology ,01 natural sciences ,Sobolev space ,symbols.namesake ,020303 mechanical engineering & transports ,Fourier transform ,0203 mechanical engineering ,symbols ,0101 mathematics ,Mathematics - Abstract
© 2019, Pleiades Publishing, Ltd. It is well known that the classical and Sobolev wave fronts were extended to nonequivalent global versions by the use of the short-time Fourier transform. In this very short paper, we give complete characterizations of the former wave front sets in terms of the short-time Fourier transform.
- Published
- 2019
41. Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization
- Author
-
Sander Gribling, Monique Laurent, David de Laat, Econometrics and Operations Research, and Research Group: Operations Research
- Subjects
Optimization problem ,General Mathematics ,Quantum correlation ,Dimension (graph theory) ,quantum graph parameters ,FOS: Physical sciences ,Quantum entanglement ,90C22 ,Squashed entanglement ,01 natural sciences ,90C26 ,81P40 ,81P45 ,0103 physical sciences ,polynomial optimization ,FOS: Mathematics ,0101 mathematics ,010306 general physics ,Mathematics - Optimization and Control ,Mathematics ,Discrete mathematics ,Semidefinite programming ,Quantum Physics ,Quantum discord ,Full Length Paper ,quantum correlations ,010102 general mathematics ,90C30 ,TheoryofComputation_GENERAL ,16. Peace & justice ,entanglement dimension ,05C15 ,Optimization and Control (math.OC) ,Quantum graph ,Quantum Physics (quant-ph) ,Software - Abstract
In this paper we study bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a bipartite correlation. This hierarchy converges to a new parameter: the minimal average entanglement dimension, which measures the amount of entanglement needed to reproduce a quantum correlation when access to shared randomness is free. For synchronous correlations, we show a correspondence between the minimal entanglement dimension and the completely positive semidefinite rank of an associated matrix. We then study optimization over the set of synchronous correlations by investigating quantum graph parameters. We unify existing bounds on the quantum chromatic number and the quantum stability number by placing them in the framework of tracial optimization. In particular, we show that the projective packing number, the projective rank, and the tracial rank arise naturally when considering tracial analogues of the Lasserre hierarchy for the stability and chromatic number of a graph. We also introduce semidefinite programming hierarchies converging to the commuting quantum chromatic number and commuting quantum stability number., Comment: 26 pages
- Published
- 2018
42. A case study of Covid-19 epidemic in India via new generalised Caputo type fractional derivatives
- Author
-
Pushpendra Kumar and Vedat Suat Erturk
- Subjects
Covid‐19 epidemic ,General Mathematics ,Banach space ,Fixed-point theorem ,new generalised Caputo non‐integer order derivative ,01 natural sciences ,92c60 ,Special Issue Paper ,Applied mathematics ,Uniform boundedness ,Uniqueness ,0101 mathematics ,26a33 ,Mathematics ,Special Issue Papers ,fixed point theory ,010102 general mathematics ,34c60 ,General Engineering ,Equicontinuity ,Fractional calculus ,010101 applied mathematics ,Norm (mathematics) ,92d30 ,Predictor‐Corrector scheme ,Epidemic model ,mathematical model - Abstract
The first symptomatic infected individuals of coronavirus (Covid-19) was confirmed in December 2020 in the city of Wuhan, China. In India, the first reported case of Covid-19 was confirmed on 30 January 2020. Today, coronavirus has been spread out all over the world. In this manuscript, we studied the coronavirus epidemic model with a true data of India by using Predictor-Corrector scheme. For the proposed model of Covid-19, the numerical and graphical simulations are performed in a framework of the new generalised Caputo sense non-integer order derivative. We analysed the existence and uniqueness of solution of the given fractional model by the definition of Chebyshev norm, Banach space, Schauder's second fixed point theorem, Arzel's-Ascoli theorem, uniform boundedness, equicontinuity and Weissinger's fixed point theorem. A new analysis of the given model with the true data is given to analyse the dynamics of the model in fractional sense. Graphical simulations show the structure of the given classes of the non-linear model with respect to the time variable. We investigated that the mentioned method is copiously strong and smooth to implement on the systems of non-linear fractional differential equation systems. The stability results for the projected algorithm is also performed with the applications of some important lemmas. The present study gives the applicability of this new generalised version of Caputo type non-integer operator in mathematical epidemiology. We compared that the fractional order results are more credible to the integer order results.
- Published
- 2020
43. Note on a Paper by Robinson
- Author
-
J. A. Todd
- Subjects
General Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,01 natural sciences ,Mathematical economics ,Mathematics - Abstract
In a recent paper Robinson has obtained an explicit formula for the expression of an invariant matrix of an invariant matrix as a direct sum of invariant matrices. The object of the present note is to show that this formula may be deduced from known properties of Schur functions, with the aid of a result which the author has proved elsewhere.
- Published
- 1950
44. Derived Non-archimedean analytic Hilbert space
- Author
-
Mauro Porta, Jorge António, Institut de Recherche Mathématique Avancée (IRMA), and Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Pure mathematics ,Fiber (mathematics) ,General Mathematics ,010102 general mathematics ,Short paper ,Formal scheme ,Hilbert space ,Space (mathematics) ,01 natural sciences ,symbols.namesake ,Mathematics - Algebraic Geometry ,Mathematics::Category Theory ,0103 physical sciences ,Localization theorem ,FOS: Mathematics ,symbols ,010307 mathematical physics ,[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] ,0101 mathematics ,Algebraic Geometry (math.AG) ,Quotient ,Mathematics - Abstract
In this short paper we combine the representability theorem introduced in [17, 18] with the theory of derived formal models introduced in [2] to prove the existence representability of the derived Hilbert space RHilb(X) for a separated k-analytic space X. Such representability results relies on a localization theorem stating that if X is a quasi-compact and quasi-separated formal scheme, then the \infty-category Coh^+(X^rig) of almost perfect complexes over the generic fiber can be realized as a Verdier quotient of the \infty-category Coh^+(X). Along the way, we prove several results concerning the the \infty-categories of formal models for almost perfect modules on derived k-analytic spaces., 28 pages
- Published
- 2019
45. On sums of squares of primes and a k-th power of prime
- Author
-
Zhixin Liu and Rui Zhang
- Subjects
Discrete mathematics ,010505 oceanography ,General Mathematics ,010102 general mathematics ,Short paper ,Sander ,01 natural sciences ,Prime (order theory) ,Power (physics) ,Integer ,Congruence (manifolds) ,0101 mathematics ,0105 earth and related environmental sciences ,Mathematics - Abstract
In this short paper, we consider the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of two squares of primes and a k-th power of prime for any integer $$k \ge 3$$ . Our results improve the recent results due to Brudern (in: Sander, Steuding, Steuding (eds) From arithmetic to zeta-functions, Springer, Cham 2016). The similar method can be also applied to some related questions in this direction, and this can improve the previous results.
- Published
- 2018
46. Improved bounds for solutions of ϕ-Laplacians
- Author
-
Jorge Huentutripay and Waldo Arriagada
- Subjects
Pure mathematics ,Harnack inequality ,General Mathematics ,lcsh:T57-57.97 ,010102 general mathematics ,Short paper ,Sense (electronics) ,01 natural sciences ,\(\phi\)-Laplacian ,Orlicz-Sobolev space ,lcsh:Applied mathematics. Quantitative methods ,0101 mathematics ,Parametric statistics ,Mathematics ,Harnack's inequality - Abstract
In this short paper we prove a parametric version of the Harnack inequality for \(\phi\)-Laplacian equations. In this sense, the estimates are optimal and represent an improvement of previous bounds for this kind of operators.
- Published
- 2018
47. On some previous results for the Drazin inverse of block matrices
- Author
-
Jelena Višnjić
- Subjects
Combinatorics ,General Mathematics ,010102 general mathematics ,Drazin inverse ,Short paper ,Block (permutation group theory) ,Block matrix ,010103 numerical & computational mathematics ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
This short paper is motivated by the paper of Bu et al. [C. Bu, C. Feng, P. Dong, A note on computational formulas for the Drazin inverse of certain block matrices, J. Appl. Math. Comput.(38) (2012) 631-640], where the authors gave additive formula for Drazin inverse for matrices under new conditions, and two representations under some specific conditions. Here is shown that the additive formula is not valid for all matrices which satisfy given conditions. Also, here is proved that the representations which were given in mentioned paper do not extend the results given by Hartwig et al. [R. Hartwig, X. Li, Y. Wei, Representations for the Drazin inverse of a 2 _ 2 block matrix, SIAM J. Matrix. Anal. Appl. (27)(2006) 757-771 ], in fact they are equivalent.
- Published
- 2016
48. U(X) as a ring for metric spaces X
- Author
-
Javier Cabello Sánchez
- Subjects
Ring (mathematics) ,021103 operations research ,General Mathematics ,010102 general mathematics ,Short paper ,0211 other engineering and technologies ,02 engineering and technology ,Function (mathematics) ,Space (mathematics) ,01 natural sciences ,Combinatorics ,Uniform continuity ,Metric space ,Bounded function ,0101 mathematics ,Mathematics - Abstract
In this short paper, we will show that the space of real valued uniformly continuous functions defined on a metric space (X,d) is a ring if and only if every subset A ? X has one of the following properties: ? A is Bourbaki-bounded, i.e., every uniformly continuous function on X is bounded on A. ? A contains an infinite uniformly isolated subset, i.e., there exist ? > 0 and an infinite subset F ? A such that d(a,x) ? ? for every a ? F, x ? X n \{a}.
- Published
- 2017
49. Self-contracted curves in spaces with weak lower curvature bound
- Author
-
Shin-ichi Ohta, Vladimir Zolotov, and Nina Lebedeva
- Subjects
Pure mathematics ,Class (set theory) ,General Mathematics ,Flag (linear algebra) ,010102 general mathematics ,Metric Geometry (math.MG) ,Paper based ,Curvature ,01 natural sciences ,Angle condition ,010101 applied mathematics ,Metric space ,51F99 ,Mathematics - Metric Geometry ,Bounded function ,FOS: Mathematics ,Mathematics::Differential Geometry ,0101 mathematics ,Snowflake ,Mathematics - Abstract
We show that bounded self-contracted curves are rectifiable in metric spaces with weak lower curvature bound in a sense we introduce in this article. This class of spaces is wide and includes, for example, finite-dimensional Alexandrov spaces of curvature bounded below and Berwald spaces of nonnegative flag curvature. (To be more precise, our condition is regarded as a strengthened doubling condition and holds also for a certain class of metric spaces with upper curvature bound.) We also provide the non-embeddability of large snowflakes into (balls in) metric spaces in the same class. We follow the strategy of the last author's previous paper based on the small rough angle condition, where spaces with upper curvature bound are considered. The results in this article show that such a strategy applies to spaces with lower curvature bound as well., Comment: A goofy mistake in formulations of Theorem 2 and 4 is fixed
- Published
- 2019
- Full Text
- View/download PDF
50. Tikhonov regularization of a second order dynamical system with Hessian driven damping
- Author
-
Szilárd László, Radu Ioan Boţ, and Ernö Robert Csetnek
- Subjects
Hessian matrix ,General Mathematics ,0211 other engineering and technologies ,Dynamical Systems (math.DS) ,02 engineering and technology ,Dynamical system ,01 natural sciences ,Hessian-driven damping ,90C26 ,Tikhonov regularization ,symbols.namesake ,34G25, 47J25, 47H05, 90C26, 90C30, 65K10 ,Convergence (routing) ,FOS: Mathematics ,Applied mathematics ,0101 mathematics ,Mathematics - Dynamical Systems ,Mathematics - Optimization and Control ,Mathematics ,65K10 ,021103 operations research ,Full Length Paper ,47J25 ,47H05 ,010102 general mathematics ,Hilbert space ,90C30 ,Function (mathematics) ,Convex optimization ,Optimization and Control (math.OC) ,Second order dynamical system ,34G25 ,symbols ,Fast convergence methods ,Convex function ,Software - Abstract
We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm.
- Published
- 2020
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