19,604 results
Search Results
2. A comment about the paper On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation
- Author
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Fábio Natali and Renan H. Martins
- Subjects
Camassa–Holm equation ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Orbital stability ,Space (mathematics) ,01 natural sciences ,Instability ,010101 applied mathematics ,Mathematics - Analysis of PDEs ,Traveling wave ,0101 mathematics ,Analysis ,Energy (signal processing) ,Mathematics - Abstract
We discuss the recent paper by A. Dar\'os and L.K. Arruda (On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation, J. Diff. Equat., 266 (2019), 1946-1968). Our intention is to correct some imperfections left by the authors and present the orbital stability of periodic snoidal waves in the energy space., Comment: 10 pages and 2 figures
- Published
- 2019
3. Multiplayer Rock-Paper-Scissors
- Author
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Charlotte Aten
- Subjects
Pure mathematics ,Class (set theory) ,Algebra and Number Theory ,010102 general mathematics ,0102 computer and information sciences ,Mathematics - Rings and Algebras ,Automorphism ,01 natural sciences ,08A05 (Primary) 05C20, 05C65, 08A35 (Secondary) ,010201 computation theory & mathematics ,Simple (abstract algebra) ,Rings and Algebras (math.RA) ,FOS: Mathematics ,Congruence (manifolds) ,0101 mathematics ,Algebra over a field ,Mathematics - Abstract
We study a class of algebras we regard as generalized Rock-Paper-Scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by hypertournament algebras, count these algebras, study their automorphisms, and determine their congruence lattices. We produce a family of finite simple algebras., Submitted to the special Topical Collection of Algebra Universalis honoring Ralph Freese, Bill Lampe, and JB Nation
- Published
- 2019
4. Notes on Some Recent Papers Concerning $F$-Contractions in $b$-Metric Spaces
- Author
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Stojan Radenović and Zoran Kadelburg
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Numerical Analysis ,Pure mathematics ,Matematik ,$b$-Metric space,$F$-Contraction,$\alpha$-Admissible mappings ,Applied Mathematics ,010102 general mathematics ,Auxiliary function ,Fixed point ,01 natural sciences ,010101 applied mathematics ,Metric space ,Order (group theory) ,F contraction ,0101 mathematics ,Analysis ,Mathematics - Abstract
In several recent papers, attempts have been made to apply Wardowski's method of $F$-contractions in order to obtain fixed point results for single and multivalued mappings in $b$-metric spaces. In this article, it is shown that in most cases the conditions imposed on respective mappings are too strong and that the results can be obtained directly, i.e., without using most of the properties of auxiliary function $F$.
- Published
- 2018
5. A letter concerning Leonetti's paper 'Continuous Projections onto Ideal Convergent Sequences'
- Author
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Tomasz Kania
- Subjects
Mathematics::Functional Analysis ,Applied Mathematics ,010102 general mathematics ,46B20, 46B26 (primary), and 40A35 (secondary) ,Space (mathematics) ,Quotient space (linear algebra) ,01 natural sciences ,Functional Analysis (math.FA) ,010101 applied mathematics ,Combinatorics ,Mathematics - Functional Analysis ,Mathematics (miscellaneous) ,FOS: Mathematics ,Uncountable set ,Ideal (ring theory) ,Family of sets ,0101 mathematics ,Mathematics - Abstract
Leonetti proved that whenever $${\mathcal {I}}$$ is an ideal on $${\mathbb {N}}$$ such that there exists an uncountable family of sets that are not in $${\mathcal {I}}$$ with the property that the intersection of any two distinct members of that family is in $${\mathcal {I}}$$ , then the space $$c_{0,{\mathcal {I}}}$$ of sequences in $$\ell _\infty $$ that converge to 0 along $${\mathcal {I}}$$ is not complemented. We provide a shorter proof of a more general fact that the quotient space $$\ell _\infty / c_{0,{\mathcal {I}}}$$ does not even embed into $$\ell _\infty $$ .
- Published
- 2018
6. Scalings and limits of Landau-de Gennes models for liquid crystals: a comment on some recent analytical papers
- Author
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Jr. Eugene C. Gartland
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Macroscopic model ,FOS: Physical sciences ,Condensed Matter - Soft Condensed Matter ,01 natural sciences ,large-body limit ,liquid crystals ,Liquid crystal ,Condensed Matter::Superconductivity ,QA1-939 ,Statistical physics ,0101 mathematics ,Elasticity (economics) ,Scaling ,Superconductivity ,Physics ,Mesoscopic physics ,010102 general mathematics ,low-temperature limit ,Landau-de Gennes model ,Coherence length ,010101 applied mathematics ,Ferromagnetism ,Modeling and Simulation ,Soft Condensed Matter (cond-mat.soft) ,Analysis ,Mathematics ,Oseen-Frank model - Abstract
Some recent analytical papers have explored limiting behaviors of Landau-deGennes models for liquid crystals in certain extreme ranges of the model parameters: limits of "vanishing elasticity" (in the language of some of these papers) and "low-temperature limits." We use simple scaling analysis to show that these limits are properly interpreted as limits in which geometric length scales (such as the size of the domain containing the liquid crystal material) become large compared to intrinsic length scales (such as correlation lengths or coherence lengths, which determine defect core sizes). This represents the natural passage from a mesoscopic model to a macroscopic model and is analogous to a "London limit" in the Ginzburg-Landau theory of superconductivity or a "large-body limit" in the Landau-Lifshitz theory of ferromagnetism. Known relevant length scales in these parameter regimes (nematic correlation length, biaxial coherence length) can be seen to emerge via balances in equilibrium Euler-Lagrange equations associated with well-scaled Landau-deGennes free-energy functionals., 17 pages; no figures; uses Springer journal LaTeX class file svjour3.cls; uses LaTeX packages mathptmx, amsmath, amssymb, and mathtools. Version 'v2' is an update of the note originally posted Dec 2015. The main change (based upon feedback on the earlier note) is to add consideration of the "low temperature" limit (and to illustrate its relationship to the "large body" limit already discussed)
- Published
- 2018
7. A correction of the decomposability result in a paper by Meyer-Neutsch
- Author
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Vladimir G. Tkachev
- Subjects
Pure mathematics ,Group Theory (math.GR) ,Commutative Algebra (math.AC) ,01 natural sciences ,Griess algebra ,Commutative nonassociative algebras ,Associative bilinear form ,0103 physical sciences ,17A99, 17C27, 20D08 ,FOS: Mathematics ,Metrised algebras ,0101 mathematics ,Commutative property ,Associative property ,Algebra och logik ,Mathematics ,Idempotents ,Algebra and Number Theory ,Mathematics::Rings and Algebras ,010102 general mathematics ,Subalgebra ,Mathematics - Rings and Algebras ,Mathematics - Commutative Algebra ,Algebra and Logic ,Linear map ,Rings and Algebras (math.RA) ,Product (mathematics) ,Idempotence ,010307 mathematical physics ,Indecomposable module ,Mathematics - Group Theory - Abstract
In this short note, it is shown that there is a gap in the proof of Theorem 11 in the paper of Meyer and Neutsch (J. of Algebra, 1993). We prove, nevertheless, that the statement of the theorem is true and fix the proof by using a certain extremal property of idempotents which has an independent interest., 6 pages, submitted 2017
- Published
- 2018
8. On a paper of Berestycki-Hamel-Rossi and its relations to the weak maximum principle at infinity, with applications
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Luciano Mari, Marco Rigoli, and Marco Magliaro
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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.
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- 2018
9. A note on Lavi’s paper 'A Ganzstellensatz for semi-algebraic sets and a boundedness criterion for rational functions'
- Author
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Tomasz Kowalczyk
- Subjects
Model theory ,Discrete mathematics ,Computer Science::Computer Science and Game Theory ,Algebra and Number Theory ,valuation theory ,010102 general mathematics ,010103 numerical & computational mathematics ,Valuation theory ,Rational function ,01 natural sciences ,Algebra ,model theory ,Real algebraic geometry ,real algebraic geometry ,0101 mathematics ,Algebraic number ,Mathematics - Abstract
This article is intended to indicate and discuss some errors in N. Lavi’s paper “A Ganzstellensatz for semi-algebraic sets and a boundedness criterion for rational functions”.
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- 2018
10. Note on A. Barbour’s paper on Stein’s method for diffusion approximations
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Andrew B. Duncan, Mikołaj Kasprzak, and Sebastian J. Vollmer
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Statistics and Probability ,Pure mathematics ,60B10 ,Statistics & Probability ,Gaussian ,Banach space ,Stein’s method ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,FOS: Mathematics ,60J65 ,60E05 ,0101 mathematics ,QA ,60J60 ,Mathematics ,Semigroup ,0104 Statistics ,010102 general mathematics ,Probability (math.PR) ,Stein's method ,Heavy traffic approximation ,60F17 ,Primary: 60B10, 60F17, Secondary: 60J60, 60J65, 60E05 ,Norm (mathematics) ,symbols ,Stein equation ,Mathematics [G03] [Physical, chemical, mathematical & earth Sciences] ,Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre] ,Statistics, Probability and Uncertainty ,Donsker’s theorem ,Mathematics - Probability ,diffusion approximations - Abstract
In (Barbour, 1990) foundations for diffusion approximation via Stein's method are laid. This paper has been cited more than 130 times and is a cornerstone in the area of Stein's method. A semigroup argument is used therein to solve a Stein equation for Gaussian diffusion approximation. We prove that, contrary to the claim in (Barbour, 1990), the semigroup considered therein is not strongly continuous on the Banach space of continuous, real-valued functions on D[0,1] growing slower than a cubic, equipped with an appropriate norm. We also provide a proof of the exact formulation of the solution to the Stein equation of interest, which does not require the aforementioned strong continuity. This shows that the main results of (Barbour, 1990) hold true., Comment: 8 pages
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- 2017
11. Corrigendum to the paper 'On the K^2 of degenerations of surfaces and the multiple point formula'
- Author
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Alberto Calabri, Ciro Ciliberto, Richard Miranda, and Flaminio Flamini
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Pure mathematics ,deformations, degenerations, enumerative problems, singularities ,deformations ,010102 general mathematics ,Minor (linear algebra) ,Socio-culturale ,01 natural sciences ,degenerations ,Combinatorics ,Multiple point ,Section (fiber bundle) ,Mathematics (miscellaneous) ,0103 physical sciences ,enumerative problems ,Gravitational singularity ,010307 mathematical physics ,Settore MAT/03 - Geometria ,0101 mathematics ,Statistics, Probability and Uncertainty ,singularities ,Mathematics - Abstract
We correct an error in the Multiple Point Formula (7.3) in the paper mentioned in the title. This correction propagates to formulas (7.5), (7.6), (7.23) and (8.18), and it affects minor results in Section 8, where few statements require an extra assumption, but it does not affect the main results of Section 8.
- Published
- 2017
12. Lp-solution for BSDEs with jumps in the case p<2 : Corrections to the paper ‘BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration’
- Author
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Alexandre Popier and Thomas Kruse
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Statistics and Probability ,Generator (computer programming) ,010102 general mathematics ,Monotonic function ,Poisson distribution ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,Stochastic differential equation ,Monotone polygon ,Modeling and Simulation ,Mathematik ,symbols ,Filtration (mathematics) ,Applied mathematics ,Uniqueness ,0101 mathematics ,Brownian motion ,Mathematics - Abstract
In T. Kruse and A. Popier, we established existence and uniqueness of solutions of backward stochastic differential equations in under a monotonicity condition on the generator and in a general filtration. There was a mistake in the case . Here we give a corrected proof. Moreover the quasi-left continuity condition on the filtration is removed.
- Published
- 2017
13. A remark on our paper 'Negative Holomorphic curvature and positive canonical bundle'
- Author
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Shing-Tung Yau and Damin Wu
- Subjects
Statistics and Probability ,Mathematics - Differential Geometry ,Pure mathematics ,Conjecture ,010102 general mathematics ,Holomorphic function ,Curvature ,Mathematical proof ,01 natural sciences ,Canonical bundle ,Continuation ,Differential Geometry (math.DG) ,Argument ,0103 physical sciences ,FOS: Mathematics ,010307 mathematical physics ,Geometry and Topology ,Sectional curvature ,0101 mathematics ,Statistics, Probability and Uncertainty ,Analysis ,Mathematics - Abstract
This is a continuation of our first paper in [WY16]. There are two purposes of this paper: One is to give a proof of the main result in [WY16] without going through the argument depending on numerical effectiveness. The other one is to provide a proof of our conjecture, mentioned in [TY], where the assumption of negative holomorphic sectional curvature is dropped to quasi-negative. We should note that a solution to our conjecture is also provided by Diverio-Trapani [DT]. Both proofs depend on our argument in [WY16]. But our argument here makes use of the argument given by the second author and Cheng in [CY75].
- Published
- 2016
14. 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
15. Erratum for the paper ‘On the chain-level intersection pairing for PL manifolds’
- Author
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J E McClure
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Lemma (mathematics) ,Pure mathematics ,010102 general mathematics ,Partial algebra ,intersection pairing ,01 natural sciences ,Combinatorics ,Chain (algebraic topology) ,Intersection ,18D50 ,Pairing ,0103 physical sciences ,57Q65 ,partial algebra ,010307 mathematical physics ,Geometry and Topology ,0101 mathematics ,General position ,Mathematics ,Sign (mathematics) ,general position - Abstract
Greg Friedman has pointed out that there are sign errors in our paper ‘On the chain-level intersection pairing for PL manifolds’, linked above, and in particular Lemma 10.5(b) (which is a key step in the proof of the main theorem) is not correct as stated. ¶ The purpose of this note is to provide a correction.
- Published
- 2009
16. 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
17. Notes on a paper of Mess
- Author
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Kevin P. Scannell, Jean-Marc Schlenker, Riccardo Benedetti, Thierry Barbot, François Labourie, Lars Andersson, Francesco Bonsante, William M. Goldman, Max-Planck-Institut für Gravitationsphysik ( Albert-Einstein-Institut ) (AEI), Max-Planck-Gesellschaft, Laboratoire d'Analyse non linéaire et Géométrie (LANLG), Avignon Université (AU), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Mathematics - Differential Geometry ,[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] ,Art history ,FOS: Physical sciences ,01 natural sciences ,Mathematics - Geometric Topology ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,Mathematics::Category Theory ,[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] ,0103 physical sciences ,FOS: Mathematics ,0101 mathematics ,Mathematical Physics ,Mathematics ,Mathematical physics ,Computer Science::Cryptography and Security ,010308 nuclear & particles physics ,010102 general mathematics ,Geometric Topology (math.GT) ,Mathematical Physics (math-ph) ,83C80 ,57S25 ,Constant curvature ,Differential Geometry (math.DG) ,[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] ,Geometry and Topology - Abstract
These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata., Comment: 26 pages
- Published
- 2007
18. Note on a paper by A. Granville and K. Soundararajan
- Author
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Jie Wu, 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), and Wu, Jie
- Subjects
Discrete mathematics ,Algebra and Number Theory ,Distribution (number theory) ,010102 general mathematics ,Equal probability ,01 natural sciences ,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] ,Combinatorics ,symbols.namesake ,Results on L(1,χ) ,\chi)$ ,0103 physical sciences ,symbols ,Results on $L(1 ,010307 mathematical physics ,11M20 ,0101 mathematics ,Random variable ,Euler product ,[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT] ,Mathematics - Abstract
In this note, we improve some results of Granville and Soundararajan on the distribution of values of the truncated random Euler product L ( 1 , X ; y ) : = ∏ p ⩽ y ( 1 − X ( p ) / p ) −1 , where the X ( p ) are independent random variables, taking the values ±1 with equal probability p / 2 ( p + 1 ) and 0 with probability 1 / ( p + 1 ) .
- Published
- 2007
19. Addendum to the paper 'A note on weighted Bergman spaces and the Cesàro operator'
- Author
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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
20. ADDITIONS AND CORRECTIONS TO THE PAPER 'ISOTRIVIAL FAMILIES OF CURVES ON AFFINE SURFACES AND CHARACTERIZATION OF THE AFFINE PLANE'
- Author
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M G Zaĭdenberg, Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Institut Fourier (IF ), and Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
- Subjects
Pure mathematics ,Plane curve ,010102 general mathematics ,Geometry ,General Medicine ,Characterization (mathematics) ,16. Peace & justice ,01 natural sciences ,Affine plane ,Affine involution ,Affine geometry of curves ,0103 physical sciences ,010307 mathematical physics ,Affine transformation ,[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
International audience
- Published
- 1992
21. Co-actions, Isometries and isomorphism classes of Hilbert modules
- Author
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Dan Z. Kučerovský
- Subjects
Pure mathematics ,0211 other engineering and technologies ,02 engineering and technology ,Hilbert modules ,01 natural sciences ,Unitary state ,C*-algebraic quantum group ,symbols.namesake ,16T05 ,FOS: Mathematics ,0101 mathematics ,Operator Algebras (math.OA) ,47L80 ,16T20 ,Mathematics ,Original Paper ,021103 operations research ,Algebra and Number Theory ,Functor ,Semigroup ,Mathematics::Operator Algebras ,Computer Science::Information Retrieval ,Operator (physics) ,010102 general mathematics ,Multiplicative function ,Hilbert space ,Mathematics - Operator Algebras ,Operator theory ,Multiplicative unitaries ,Cuntz semigroups ,symbols ,Isomorphism ,Analysis ,47L50 - Abstract
We show that a A-linear map of Hilbert A-modules is induced by a unitary Hilbert module operator if and only if it extends to an ordinary unitary on appropriately defined enveloping Hilbert spaces. Applications to the theory of multiplicative unitaries let us to compute the equivalence classes of Hilbert modules over a class of C*-algebraic quantum groups. We, thus, develop a theory that, for example, could be used to show non-existence of certain co-actions. In particular, we show that the Cuntz semigroup functor takes a co-action to a multiplicative action.
- Published
- 2023
22. (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
23. A note on the Albert–Kelly paper 'the closure of a class of colimits'
- Author
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Robert Paré and G. M. Kelly
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Class (set theory) ,Pure mathematics ,Algebra and Number Theory ,Functor ,010102 general mathematics ,Closure (topology) ,0102 computer and information sciences ,Type (model theory) ,01 natural sciences ,010201 computation theory & mathematics ,Calculus ,0101 mathematics ,Special case ,Mathematics - Abstract
In the preceding article “The closure of a class of colimits” by M.H. Albert and G.M. Kelly, the authors were unable, except in one special case, to answer the following question. Let an indexing type ψ for colimits be such that every category admitting all ∅-indexed colimits for ∅ in some class Φ also admits ψ-indexed colimits; need a functor which preserves all Φ-indexed colimits also preserve ψ-indexed ones? Without settling the question, the present authors give two more positive results in this direction, including an affirmative answer when Φ-indexed colimits are conical.
- Full Text
- View/download PDF
24. Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
- Author
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Feng Qi and Chuan-Jun Huang
- Subjects
Pure mathematics ,Binomial (polynomial) ,Determinant ,33B15 ,11A25 ,01 natural sciences ,Inversion (discrete mathematics) ,11B65 ,symbols.namesake ,Beta function ,Identity ,Gauss hypergeometric function ,Differentiable function ,0101 mathematics ,Hypergeometric function ,Secondary 05A10 ,Mathematics ,Original Paper ,Algebra and Number Theory ,Applied Mathematics ,010102 general mathematics ,Gauss ,Sum ,Primary 33C05 ,Binomial inversion formula ,Polygamma function ,010101 applied mathematics ,Derivative formula for a ratio of two differential functions ,Computational Mathematics ,symbols ,Partial derivative ,Geometry and Topology ,Analysis - Abstract
In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial derivatives, polygamma functions, the Gauss hypergeometric function, and a determinant. These results generalize known ones in combinatorics. This preprint has been formally published as "Feng Qi and Chuan-Jun Huang, Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales Serie A Matematicas, Vol. 114, Paper No. 191, 9 pages (2020); available online at https://doi.org/10.1007/s13398-020-00927-y."
- Published
- 2020
25. Improving the performance of deep learning models using statistical features: The case study of COVID‐19 forecasting
- Author
-
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
26. Pure discrete spectrum and regular model sets in d-dimensional unimodular substitution tilings
- Author
-
Dong-il Lee, Jeong Yup Lee, and Shigeki Akiyama
- Subjects
Substitution tiling ,01 natural sciences ,Biochemistry ,Discrete spectrum ,Inorganic Chemistry ,Combinatorics ,Pisot family substitution tilings ,Structural Biology ,Euclidean geometry ,General Materials Science ,0101 mathematics ,Physical and Theoretical Chemistry ,Algebraic number ,Meyer sets ,Eigenvalues and eigenvectors ,Mathematics ,regular model sets ,010102 general mathematics ,Multiplicity (mathematics) ,Condensed Matter Physics ,Research Papers ,010101 applied mathematics ,Unimodular matrix ,Regular model ,rigidity ,pure discrete spectrum - Abstract
The equivalence between pure discrete spectrum and regular model sets in d-dimensional unimodular substitution tilings is discussed., Primitive substitution tilings on whose expansion maps are unimodular are considered. It is assumed that all the eigenvalues of the expansion maps are algebraic conjugates with the same multiplicity. In this case, a cut-and-project scheme can be constructed with a Euclidean internal space. Under some additional condition, it is shown that if the substitution tiling has pure discrete spectrum, then the corresponding representative point sets are regular model sets in that cut-and-project scheme.
- Published
- 2020
27. $q$-difference equations for homogeneous $q$-difference operators and their applications
- Author
-
Sama Arjika
- Subjects
Pure mathematics ,Algebra and Number Theory ,Applied Mathematics ,010102 general mathematics ,Short paper ,01 natural sciences ,010101 applied mathematics ,Homogeneous ,Mathematics - Classical Analysis and ODEs ,Hahn polynomials ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,05A30, 33D15, 33D45, 05A40, 11B65 ,0101 mathematics ,Analysis ,Mathematics - Abstract
In this short paper, we show how to deduce several types of generating functions from Srivastava {\it et al} [Appl. Set-Valued Anal. Optim. {\bf 1} (2019), pp. 187-201.] by the method of $q$-difference equations. Moreover, we build relations between transformation formulas and homogeneous $q$-difference equations., 10
- Published
- 2020
28. Padovan numbers which are palindromic concatenations of two distinct repdigits
- Author
-
Mahadi Ddamulira, Taboka P. Chalebgwa, McMaster University (CANADA), Graz University of Technology [Graz] (TU Graz), and Max Planck Institute for Software Systems (MPI-SWS)
- Subjects
Baker–Davenport reduction method ,Original Paper ,11D61 ,TheoryofComputation_COMPUTATIONBYABSTRACTDEVICES ,Algebra and Number Theory ,Applied Mathematics ,Padovan numbers ,010102 general mathematics ,11J86 ,Palindrome ,11B39 ,01 natural sciences ,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] ,Baker's method ,010101 applied mathematics ,Combinatorics ,Computational Mathematics ,Linear forms in logarithms ,Repdigits ,Geometry and Topology ,0101 mathematics ,Analysis ,Mathematics - Abstract
In this paper we determine all Padovan numbers that are palindromic concatenations of two distinct repdigits.
- Published
- 2020
29. 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
30. 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
31. Real-time Prediction of the Daily Incidence of COVID-19 in 215 Countries and Territories Using Machine Learning: Model Development and Validation
- Author
-
Chi Pui Pang, Cuilian Li, Xinjian Chen, Haoyu Chen, Yuanyuan Peng, and Yibiao Rong
- Subjects
Mean squared error ,Computer applications to medicine. Medical informatics ,digital health ,R858-859.7 ,Google Trends ,Health Informatics ,daily incidence ,Machine learning ,computer.software_genre ,01 natural sciences ,Spearman's rank correlation coefficient ,infodemiology ,Infodemiology ,Machine Learning ,03 medical and health sciences ,symbols.namesake ,infoveillance ,0302 clinical medicine ,prevention ,Range (statistics) ,real-time prediction ,Humans ,030212 general & internal medicine ,0101 mathematics ,Cluster analysis ,digital public health ,Mathematics ,Original Paper ,model ,business.industry ,SARS-CoV-2 ,Incidence ,010102 general mathematics ,COVID-19 ,Reproducibility of Results ,prediction ,Pearson product-moment correlation coefficient ,Random forest ,Infoveillance ,symbols ,surveillance ,Artificial intelligence ,Public aspects of medicine ,RA1-1270 ,business ,computer ,policy - Abstract
Background Advanced prediction of the daily incidence of COVID-19 can aid policy making on the prevention of disease spread, which can profoundly affect people's livelihood. In previous studies, predictions were investigated for single or several countries and territories. Objective We aimed to develop models that can be applied for real-time prediction of COVID-19 activity in all individual countries and territories worldwide. Methods Data of the previous daily incidence and infoveillance data (search volume data via Google Trends) from 215 individual countries and territories were collected. A random forest regression algorithm was used to train models to predict the daily new confirmed cases 7 days ahead. Several methods were used to optimize the models, including clustering the countries and territories, selecting features according to the importance scores, performing multiple-step forecasting, and upgrading the models at regular intervals. The performance of the models was assessed using the mean absolute error (MAE), root mean square error (RMSE), Pearson correlation coefficient, and Spearman correlation coefficient. Results Our models can accurately predict the daily new confirmed cases of COVID-19 in most countries and territories. Of the 215 countries and territories under study, 198 (92.1%) had MAEs 0.8. For the 215 countries and territories, the mean MAE was 5.42 (range 0.26-15.32), the mean RMSE was 9.27 (range 1.81-24.40), the mean Pearson correlation coefficient was 0.89 (range 0.08-0.99), and the mean Spearman correlation coefficient was 0.84 (range 0.2-1.00). Conclusions By integrating previous incidence and Google Trends data, our machine learning algorithm was able to predict the incidence of COVID-19 in most individual countries and territories accurately 7 days ahead.
- Published
- 2021
32. The implementation of the unified transform to the nonlinear Schr\'odinger equation with periodic initial conditions
- Author
-
Bernard Deconinck, Jonatan Lenells, Athanassios S. Fokas, Lenells, J. [0000-0001-6191-7769], Apollo - University of Cambridge Repository, Apollo-University Of Cambridge Repository, and Lenells, J [0000-0001-6191-7769]
- Subjects
Integrable system ,Inverse scattering ,35Q55, 37K15, 35G30 ,FOS: Physical sciences ,Finite-gap solution ,Unified transform method ,01 natural sciences ,010305 fluids & plasmas ,35G30 ,Matrix (mathematics) ,Riemann–Hilbert problem ,Mathematics - Analysis of PDEs ,Fokas method ,0103 physical sciences ,FOS: Mathematics ,Applied mathematics ,Initial value problem ,Integrable evolution equation ,Boundary value problem ,0101 mathematics ,10. No inequality ,Korteweg–de Vries equation ,Mathematical Physics ,Mathematics ,Original Paper ,Partial differential equation ,Inverse scattering transform ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,010102 general mathematics ,Statistical and Nonlinear Physics ,Linearizable boundary condition ,35Q55 ,Nonlinear system ,Periodic solution ,37K15 ,Exactly Solvable and Integrable Systems (nlin.SI) ,Analysis of PDEs (math.AP) - Abstract
The unified transform method (UTM) provides a novel approach to the analysis of initial-boundary value problems for linear as well as for a particular class of nonlinear partial differential equations called integrable. If the latter equations are formulated in two dimensions (either one space and one time, or two space dimensions), the UTM expresses the solution in terms of a matrix Riemann-Hilbert (RH) problem with explicit dependence on the independent variables. For nonlinear integrable evolution equations, such as the celebrated nonlinear Schr\"odinger (NLS) equation, the associated jump matrices are computed in terms of the initial conditions and all boundary values. The unknown boundary values are characterized in terms of the initial datum and the given boundary conditions via the analysis of the so-called global relation. In general, this analysis involves the solution of certain nonlinear equations. In certain cases, called linearizable, it is possible to bypass this nonlinear step. In these cases, the UTM solves the given initial-boundary value problem with the same level of efficiency as the well-known inverse scattering transform solves the initial value problem on the infinite line. We show here that the initial-boundary value problem on a finite interval with $x$-periodic boundary conditions (which can alternatively be viewed as the initial value problem on a circle), belongs to the linearizable class. Indeed, by employing certain transformations of the associated RH problem and by using the global relation, the relevant jump matrices can be expressed explicitly in terms of the so-called scattering data, which are computed in terms of the initial datum. Details are given for NLS, but similar considerations are valid for other well-known integrable evolution equations, including the Korteweg-de Vries (KdV) and modified KdV equations., Comment: 14 pages, includes announcements of results in arXiv:2103.04728
- Published
- 2021
33. Fractional Hermite-Hadamard type inequalities for co-ordinated prequasiinvex functions
- Author
-
Badreddine Meftah and Abdourazek Souahi
- Subjects
Hermite polynomials ,Inequality ,Mathematics::General Mathematics ,media_common.quotation_subject ,lcsh:Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,Mathematics::Classical Analysis and ODEs ,021107 urban & regional planning ,Probability and statistics ,02 engineering and technology ,Type (model theory) ,lcsh:QA1-939 ,01 natural sciences ,Mathematics::Numerical Analysis ,Algebra ,In this paper, the concept of co-ordinated prequasiinvex is introduced, some fractional Hermite-Hadamard type inequalities for functions whose modulus of the mixed derivatives lies in this novel class of functions are established ,Hadamard transform ,26A51 ,0101 mathematics ,lcsh:Probabilities. Mathematical statistics ,lcsh:QA273-280 ,General Economics, Econometrics and Finance ,Mathematics ,media_common - Abstract
Some new Ostrowski’s inequalities for functions whose n-th derivatives are h-convex are established.
- Published
- 2019
34. Selling reduction versus Niggli reduction for crystallographic lattices
- Author
-
Lawrence C. Andrews, Herbert J. Bernstein, and Nicholas K. Sauter
- Subjects
Discrete mathematics ,Delaunay triangulation ,media_common.quotation_subject ,010102 general mathematics ,Delone ,Niggli ,010403 inorganic & nuclear chemistry ,Condensed Matter Physics ,01 natural sciences ,Biochemistry ,Research Papers ,0104 chemical sciences ,Inorganic Chemistry ,Reduction (complexity) ,unit-cell reduction ,Selling ,Structural Biology ,Simple (abstract algebra) ,General Materials Science ,Simplicity ,0101 mathematics ,Physical and Theoretical Chemistry ,Mathematics ,media_common ,Delaunay - Abstract
The unit-cell reduction described by Selling and used by Delone (Delaunay) is explained in a simple form., The unit-cell reduction described by Selling and used by Delone (whose early publications were under the spelling Delaunay) is explained in a simple form. The transformations needed to implement the reduction are listed. The simplicity of this reduction contrasts with the complexity of Niggli reduction.
- Published
- 2019
35. Second-order work in barodesy
- Author
-
Gertraud Medicus, Dimitrios Kolymbas, and Barbara Schneider-Muntau
- Subjects
Work (thermodynamics) ,Barodesy ,Second-order work ,010102 general mathematics ,Constitutive equation ,0211 other engineering and technologies ,Finite element simulations ,02 engineering and technology ,Mechanics ,Constitutive model ,Geotechnical Engineering and Engineering Geology ,01 natural sciences ,Finite element method ,Stress (mechanics) ,Solid mechanics ,Earth and Planetary Sciences (miscellaneous) ,Boundary value problem ,Limit (mathematics) ,0101 mathematics ,Shear band ,021101 geological & geomatics engineering ,Mathematics ,Research Paper - Abstract
Second-order work analyses, based on elasto-plastic models, have been frequently carried out leading to the result that failure may occur before the limit yield condition is encountered. In this article, second-order work investigations are carried out with barodesy regarding standard element tests and finite element applications. In barodesy, it was shown—like in hypoplasticity and elasto-plasticity—that second-order work may vanish at stress states inside the critical limit surface. For boundary value problems, an end-to-end shear band of vanishing second-order work marks situations, where failure is imminent.
- Published
- 2018
36. Convex plumbings in closed hyperbolic 4-manifolds
- Author
-
Leone Slavich, Bruno Martelli, Stefano Riolo, Martelli B., Riolo S., and Slavich L.
- Subjects
Pure mathematics ,Mathematics::Dynamical Systems ,Hyperbolic geometry ,Hyperbolic 4-manifold ,Intersection form ,Plumbing ,Algebraic geometry ,01 natural sciences ,Mathematics - Geometric Topology ,Simple (abstract algebra) ,Hyperbolic set ,0103 physical sciences ,FOS: Mathematics ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics ,Original Paper ,010102 general mathematics ,Regular polygon ,Geometric Topology (math.GT) ,Submanifold ,Mathematics::Geometric Topology ,57M50 ,Differential geometry ,010307 mathematical physics ,Geometry and Topology ,Mathematics::Differential Geometry - Abstract
We show that every plumbing of disc bundles over surfaces whose genera satisfy a simple inequality may be embedded as a convex submanifold in some closed hyperbolic four-manifold. In particular its interior has a geometrically finite hyperbolic structure that covers a closed hyperbolic four-manifold., 18 pages, 11 figures
- Published
- 2021
37. Surface bundles over surfaces: new inequalities between signature, simplicial volume and Euler characteristic
- Author
-
Michelle Bucher, Caterina Campagnolo, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), and École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Surface (mathematics) ,Pure mathematics ,Hyperbolic geometry ,0102 computer and information sciences ,Algebraic geometry ,Signature ,01 natural sciences ,symbols.namesake ,Mathematics - Geometric Topology ,Mathematics::Algebraic Geometry ,Simplicial volume ,Euler characteristic ,[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] ,FOS: Mathematics ,Secondary 57R22 ,0101 mathematics ,[MATH]Mathematics [math] ,ddc:510 ,Mathematics::Symplectic Geometry ,Mathematics ,Projective geometry ,Surface bundle ,Original Paper ,010102 general mathematics ,Geometric Topology (math.GT) ,55R10, 57R22 ,Primary 55R10 ,16. Peace & justice ,Differential geometry ,010201 computation theory & mathematics ,symbols ,Geometry and Topology ,Signature (topology) - Abstract
We present three new inequalities tying the signature, the simplicial volume and the Euler characteristic of surface bundles over surfaces. Two of them are true for any surface bundle, while the third holds on a specific family of surface bundles, namely the ones that arise through a ramified covering. These are the main known examples of bundles with non-zero signature., 14 pages. Simplified the proof of Proposition 1.2. This is the final version, accepted in Geometriae Dedicata
- Published
- 2021
38. 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
39. The Daugavet equation in Banach spaces with alternatively convex-smooth duals
- Author
-
Paweł Wójcik
- Subjects
Pure mathematics ,Mathematics::Functional Analysis ,010102 general mathematics ,Short paper ,Banach space ,Regular polygon ,Daugavet equation ,010103 numerical & computational mathematics ,Characterization (mathematics) ,01 natural sciences ,Linear subspace ,acs spaces ,46B20 ,affine subspaces ,47A62 ,luacs spaces ,Dual polyhedron ,Affine transformation ,0101 mathematics ,Invariant (mathematics) ,Mathematics - Abstract
This short paper gives a necessary and sufficient condition for the Daugavet equation $\|I+T\|=1+\|T\|$ . A new characterization of the solution of the Daugavet equation in terms of invariant affine subspaces is given. We also study the notions of alternatively convex or smooth (acs) and locally uniformly alternatively convex or smooth (luacs).
- Published
- 2018
40. On the space of Laplace transformable distributions
- Author
-
Andreas Debrouwere, Eduard A. Nigsch, and Mathematics-TW
- Subjects
Pure mathematics ,Laplace transform ,Astrophysics::High Energy Astrophysical Phenomena ,Open set ,Predual ,Space (mathematics) ,Ultrabornological (PLS)-spaces ,01 natural sciences ,Primary 46F05 ,FOS: Mathematics ,0101 mathematics ,46A13 ,Mathematics ,Original Paper ,Algebra and Number Theory ,Applied Mathematics ,010102 general mathematics ,Short-time Fourier transform ,Regular polygon ,Secondary 81S30 ,Functional Analysis (math.FA) ,Primary 46F05, 46A13, Secondary 81S30 ,Mathematics - Functional Analysis ,010101 applied mathematics ,Computational Mathematics ,Mathematics and Statistics ,Distributions ,Geometry and Topology ,Analysis - Abstract
We show that the space $\mathcal{S}'(\Gamma)$ of Laplace transformable distributions, where $\Gamma \subseteq \mathbb{R}^d$ is a non-empty convex open set, is an ultrabornological (PLS)-space. Moreover, we determine an explicit topological predual of $\mathcal{S}'(\Gamma)$., Comment: 10 pages
- Published
- 2020
41. Fractional-order susceptible-infected model: definition and applications to the study of COVID-19 main protease
- Author
-
Gissell Estrada-Rodriguez, Ernesto Estrada, and Luciano Abadias
- Subjects
Protease ,Coronavirus disease 2019 (COVID-19) ,Applied Mathematics ,medicine.medical_treatment ,Molecular Networks (q-bio.MN) ,010102 general mathematics ,Survey Paper ,A protein ,medicine.disease_cause ,01 natural sciences ,Upper and lower bounds ,Interaction network ,FOS: Biological sciences ,0103 physical sciences ,medicine ,Quantitative Biology - Molecular Networks ,Adjacency matrix ,0101 mathematics ,Binding site ,Biological system ,010301 acoustics ,Analysis ,Mathematics ,Coronavirus - Abstract
We propose a model for the transmission of perturbations across the amino acids of a protein represented as an interaction network. The dynamics consists of a Susceptible-Infected (SI) model based on the Caputo fractional-order derivative. We find an upper bound to the analytical solution of this model which represents the worse-case scenario on the propagation of perturbations across a protein residue network. This upper bound is expressed in terms of Mittag-Leffler functions of the adjacency matrix of the network of inter-amino acids interactions. We then apply this model to the analysis of the propagation of perturbations produced by inhibitors of the main protease of SARS CoV-2. We find that the perturbations produced by strong inhibitors of the protease are propagated far away from the binding site, confirming the long-range nature of intra-protein communication. On the contrary, the weakest inhibitors only transmit their perturbations across a close environment around the binding site. These findings may help to the design of drug candidates against this new coronavirus., 21 pages, 2 figures
- Published
- 2020
42. 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
43. Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
- Author
-
Gerhard Schindl, Alessandro Oliaro, David Jornet, and Chiara Boiti
- Subjects
Pure mathematics ,Weight matrices, ultradifferentiable functions, sequence spaces, nuclear spaces ,Weight matrices ,nuclear spaces ,Hermite functions ,01 natural sciences ,NO ,Schauder basis ,Nuclear spaces ,Matrix (mathematics) ,Ultradifferentiable functions ,FOS: Mathematics ,PE1_9 ,PE1_8 ,0101 mathematics ,Mathematics ,Original Paper ,weight matrices, ultradifferentiable functions, sequence spaces, nuclear spaces ,Algebra and Number Theory ,Functional analysis ,010102 general mathematics ,46A04, 46A45, 26E10 ,Operator theory ,Sequence spaces ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,010101 applied mathematics ,46A45 ,weight matrices ,ultradifferentiable functions ,sequence spaces ,MATEMATICA APLICADA ,46A04 ,Analysis ,26E10 - Abstract
[EN] We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results for spaces defined by weight functions, Open access funding provided by Universita degli Studi di Ferrara within the CRUI-CARE Agreement
- Published
- 2020
44. The r-Hunter-Saxton equation, smooth and singular solutions and their approximation
- Author
-
Colin J. Cotter, Tristan Pryer, Jacob Deasy, Cotter, Colin J [0000-0001-7962-8324], Apollo - University of Cambridge Repository, and Engineering & Physical Science Research Council (EPSRC)
- Subjects
Paper ,singular solutions ,GEODESIC-FLOW ,Work (thermodynamics) ,General Mathematics ,Mathematics, Applied ,HYPERBOLIC VARIATIONAL EQUATION ,Mathematics::Analysis of PDEs ,General Physics and Astronomy ,FOS: Physical sciences ,01 natural sciences ,Piecewise linear function ,37K06 ,Mathematics - Analysis of PDEs ,0102 Applied Mathematics ,37K05 ,FOS: Mathematics ,Hunter–Saxton equation ,Applied mathematics ,Initial value problem ,Lie symmetries ,0101 mathematics ,nlin.SI ,math.AP ,Mathematical Physics ,Mathematics ,Science & Technology ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,Physics ,Applied Mathematics ,010102 general mathematics ,4901 Applied Mathematics ,4904 Pure Mathematics ,Statistical and Nonlinear Physics ,Action (physics) ,Symmetry (physics) ,Physics, Mathematical ,010101 applied mathematics ,35Q53 ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,nonlinear PDEs ,Physical Sciences ,49 Mathematical Sciences ,37K58 ,Exactly Solvable and Integrable Systems (nlin.SI) ,Analysis of PDEs (math.AP) - Abstract
In this work we introduce the r-Hunter-Saxton equation, a generalisation of the Hunter-Saxton equation arising as extremals of an action principle posed in L_r. We characterise solutions to the Cauchy problem, quantifying the blow-up time and studying various symmetry reductions. We construct piecewise linear functions and show that they are weak solutions to the r-Hunter-Saxton equation., Revised after referee comments
- Published
- 2019
45. A Constraint on Chern Classes of Strictly Pseudoconvex CR Manifolds
- Author
-
Yuya Takeuchi
- Subjects
Mathematics - Differential Geometry ,Pure mathematics ,Chern class ,Mathematics::Complex Variables ,Mathematics - Complex Variables ,010102 general mathematics ,Short paper ,Dimension (graph theory) ,01 natural sciences ,Mathematics::Geometric Topology ,Constraint (information theory) ,Differential Geometry (math.DG) ,Mathematics - Symplectic Geometry ,FOS: Mathematics ,Symplectic Geometry (math.SG) ,Geometry and Topology ,Complex Variables (math.CV) ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematical Physics ,Analysis ,Mathematics ,32V15 (Primary), 32T15, 32V05, 57R17 (Secondary) - Abstract
This short paper gives a constraint on Chern classes of closed strictly pseudoconvex CR manifolds (or equivalently, closed holomorphically fillable contact manifolds) of dimension at least five. We also see that our result is ''optimal'' through some examples.
- Published
- 2018
46. A note on gonality of curves on general hypersurfaces
- Author
-
Flaminio Flamini, Paola Supino, Ciro Ciliberto, Francesco Bastianelli, Bastianelli, Francesco, Ciliberto, Ciro, Flamini, Flaminio, and Supino, Paola
- Subjects
Series (mathematics) ,Degree (graph theory) ,family of curves ,General Mathematics ,010102 general mathematics ,Short paper ,Birational geometry ,gonality of curves, projective hypersurfaces ,01 natural sciences ,Hypersurfaces ,Combinatorics ,Mathematics::Algebraic Geometry ,Hypersurface ,Product (mathematics) ,0103 physical sciences ,Hypersurfaces, family of curves, gonality ,010307 mathematical physics ,gonality ,Settore MAT/03 - Geometria ,0101 mathematics ,Mathematics - Abstract
This short paper concerns the existence of curves with low gonality on smooth hypersurfaces $$X\subset \mathbb {P}^{n+1}$$ . After reviewing a series of results on this topic, we report on a recent progress we achieved as a product of the Workshop Birational geometry of surfaces, held at University of Rome “Tor Vergata” on January 11th–15th, 2016. In particular, we obtained that if $$X\subset \mathbb {P}^{n+1}$$ is a very general hypersurface of degree $$d\geqslant 2n+2$$ , the least gonality of a curve $$C\subset X$$ passing through a general point of X is $$\mathrm {gon}(C)=d-\left\lfloor \frac{\sqrt{16n+1}-1}{2}\right\rfloor $$ , apart from some exceptions we list.
- Published
- 2018
47. On Beilinson’s equivalence for p-adic cohomology
- Author
-
Daniel Caro, Tomoyuki Abe, Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo (UTokyo), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), and Normandie Université (NU)-Normandie Université (NU)
- Subjects
Pure mathematics ,Derived category ,Functor ,Holonomic ,General Mathematics ,010102 general mathematics ,Short paper ,General Physics and Astronomy ,Unipotent ,01 natural sciences ,Cohomology ,Mathematics::K-Theory and Homology ,Mathematics::Category Theory ,0103 physical sciences ,010307 mathematical physics ,[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] ,0101 mathematics ,Equivalence (formal languages) ,Mathematics::Representation Theory ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
In this short paper, we construct a unipotent nearby cycle functor and show a p-adic analogue of Beilinson’s equivalence comparing two derived categories: the derived category of holonomic arithmetic $${\mathcal {D}}$$ -modules and the derived category of arithmetic $${\mathcal {D}}$$ -modules whose cohomologies are holonomic.
- Published
- 2018
48. Global strong solutions to the 3D full compressible Navier-Stokes system with vacuum in a bounded domain
- Author
-
Fucai Li and Jishan Fan
- Subjects
Applied Mathematics ,010102 general mathematics ,Short paper ,Mathematical analysis ,Nuclear Theory ,Mathematics::Analysis of PDEs ,01 natural sciences ,Domain (mathematical analysis) ,010101 applied mathematics ,Strong solutions ,Viscosity ,Mathematics - Analysis of PDEs ,Bounded function ,FOS: Mathematics ,Compressibility ,Navier stokes ,0101 mathematics ,Analysis of PDEs (math.AP) ,Mathematics ,35Q30, 35Q35, 76N10 - Abstract
In this short paper we establish the global well-posedness of strong solutions to the 3D full compressible Navier–Stokes system with vacuum in a bounded domain Ω ⊂ R 3 by the bootstrap argument provided that the viscosity coefficients λ and μ satisfy that 7 λ > 9 μ and the initial data ρ 0 and u 0 satisfy that ‖ ρ 0 ‖ L ∞ ( Ω ) and ‖ ρ 0 | u 0 | 5 ‖ L 1 ( Ω ) are sufficiently small.
- Published
- 2017
49. Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups
- Author
-
Durvudkhan Suragan, Michael Ruzhansky, and Nurgissa Yessirkegenov
- Subjects
Pure mathematics ,Inequality ,media_common.quotation_subject ,Short paper ,Mathematics::Analysis of PDEs ,HARDY-TYPE INEQUALITIES ,01 natural sciences ,Stratified Lie group ,RELLICH ,Hardy inequality ,FOS: Mathematics ,0101 mathematics ,HEISENBERG-GROUP ,media_common ,Mathematics ,Mathematics::Functional Analysis ,Sobolev type inequality ,Applied Mathematics ,Caffarelli-Kohn-Nirenberg inequality ,010102 general mathematics ,Lie group ,Type inequality ,Functional Analysis (math.FA) ,010101 applied mathematics ,Sobolev space ,Mathematics - Functional Analysis ,Mathematics and Statistics ,22E30, 43A80 ,UNCERTAINTY INEQUALITIES ,Nirenberg and Matthaei experiment ,Analysis - Abstract
In this short paper, we establish a range of Caffarelli-Kohn-Nirenberg and weighted $L^{p}$-Sobolev type inequalities on stratified Lie groups. All inequalities are obtained with sharp constants. Moreover, the equivalence of the Sobolev type inequality and Hardy inequality is shown in the $L^{2}$-case., to appear in NoDEA
- Published
- 2017
50. A fast algorithm for the gas station problem
- Author
-
Demetres Christofides and Kleitos Papadopoulos
- Subjects
FOS: Computer and information sciences ,010102 general mathematics ,Short paper ,0102 computer and information sciences ,01 natural sciences ,Fast algorithm ,Graph ,Computer Science Applications ,Theoretical Computer Science ,Vertex (geometry) ,Combinatorics ,90B06, 90C35, 68Q25 ,010201 computation theory & mathematics ,Fuel cost ,Signal Processing ,Computer Science - Data Structures and Algorithms ,FOS: Mathematics ,Mathematics - Combinatorics ,Data Structures and Algorithms (cs.DS) ,Combinatorics (math.CO) ,0101 mathematics ,Information Systems ,Mathematics - Abstract
In the gas station problem we want to find the cheapest path between two vertices of an n-vertex graph. Our car has a specific fuel capacity and at each vertex we can fill our car with gas, with the fuel cost depending on the vertex. Furthermore, we are allowed at most Δ stops for refuelling. In this short paper we provide an algorithm solving the problem in O ( Δ n 2 + n 2 log n ) steps improving an earlier result by Khuller, Malekian and Mestre.
- Published
- 2017
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