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  Subjects -> MATHEMATICS (Total: 955 journals)
    - APPLIED MATHEMATICS (82 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (706 journals)
    - MATHEMATICS (GENERAL) (43 journals)
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    - PROBABILITIES AND MATH STATISTICS (82 journals)

MATHEMATICS (706 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 27)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 6)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 3)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 5)
Advances in Science and Research (ASR)     Open Access   (Followers: 4)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 5)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 11)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 10)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Advances in Mathematics
  [SJR: 3.261]   [H-I: 65]   [10 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 0001-8708 - ISSN (Online) 1090-2082
   Published by Elsevier Homepage  [3175 journals]
  • Differentiability and Hölder spectra of a class of self-affine
           functions
    • Authors: Pieter C. Allaart
      Pages: 1 - 39
      Abstract: Publication date: 13 April 2018
      Source:Advances in Mathematics, Volume 328
      Author(s): Pieter C. Allaart
      This paper studies a large class of continuous functions f : [ 0 , 1 ] → R d whose range is the attractor of an iterated function system { S 1 , … , S m } consisting of similitudes. This class includes such classical examples as Pólya's space-filling curves, the Riesz–Nagy singular functions and Okamoto's functions. The differentiability of f is completely classified in terms of the contraction ratios of the maps S 1 , … , S m . Generalizing results of Lax (1973) and Okamoto (2006), it is shown that either (i) f is nowhere differentiable; (ii) f is non-differentiable almost everywhere but with uncountably many exceptions; or (iii) f is differentiable almost everywhere but with uncountably many exceptions. The Hausdorff dimension of the exceptional sets in cases (ii) and (iii) above is calculated, and more generally, the complete multifractal spectrum of f is determined.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2018.01.009
      Issue No: Vol. 328 (2018)
       
  • Stratification of free boundary points for a two-phase variational problem
    • Authors: Serena Dipierro; Aram L. Karakhanyan
      Pages: 40 - 81
      Abstract: Publication date: 13 April 2018
      Source:Advances in Mathematics, Volume 328
      Author(s): Serena Dipierro, Aram L. Karakhanyan
      In this paper we prove the local Lipschitz regularity of the minimizers of the two-phase Bernoulli type free boundary problem arising from the minimization of the functional J ( u ) : = ∫ Ω ∇ u p + λ + p χ { u > 0 } + λ − p χ { u ≤ 0 } , 1 < p < ∞ . Here Ω ⊂ R N is a bounded smooth domain and λ ± are positive constants such that λ + p − λ − p > 0 . Furthermore, we show that for p > 1 the free boundary has locally finite perimeter and the set of non-smooth points of the free boundary is of zero ( N − 1 ) -dimensional Hausdorff measure. For this, our approach is new even for the classical case p = 2 .

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2018.01.005
      Issue No: Vol. 328 (2018)
       
  • Monotone, free, and boolean cumulants: A shuffle algebra approach
    • Authors: Kurusch Ebrahimi-Fard; Frédéric Patras
      Pages: 112 - 132
      Abstract: Publication date: 13 April 2018
      Source:Advances in Mathematics, Volume 328
      Author(s): Kurusch Ebrahimi-Fard, Frédéric Patras
      The theory of cumulants is revisited in the “Rota way”, that is, by following a combinatorial Hopf algebra approach. Monotone, free, and boolean cumulants are considered as infinitesimal characters over a particular combinatorial Hopf algebra. The latter is neither commutative nor cocommutative, and has an underlying unshuffle bialgebra structure which gives rise to a shuffle product on its graded dual. The moment-cumulant relations are encoded in terms of shuffle and half-shuffle exponentials. It is then shown how to express concisely monotone, free, and boolean cumulants in terms of each other using the pre-Lie Magnus expansion together with shuffle and half-shuffle logarithms.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2018.01.003
      Issue No: Vol. 328 (2018)
       
  • Asymptotics of scalar waves on long-range asymptotically Minkowski spaces
    • Authors: Dean Baskin; András Vasy; Jared Wunsch
      Pages: 160 - 216
      Abstract: Publication date: 13 April 2018
      Source:Advances in Mathematics, Volume 328
      Author(s): Dean Baskin, András Vasy, Jared Wunsch
      We show the existence of the full compound asymptotics of solutions to the scalar wave equation on long-range non-trapping Lorentzian manifolds modeled on the radial compactification of Minkowski space. In particular, we show that there is a joint asymptotic expansion at null and timelike infinity for forward solutions of the inhomogeneous equation. In two appendices we show how these results apply to certain spacetimes whose null infinity is modeled on that of the Kerr family. In these cases the leading order logarithmic term in our asymptotic expansions at null infinity is shown to be nonzero.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2018.01.012
      Issue No: Vol. 328 (2018)
       
  • Heat flow for Dirichlet-to-Neumann operator with critical growth
    • Authors: Fei Fang; Zhong Tan
      Pages: 217 - 247
      Abstract: Publication date: 13 April 2018
      Source:Advances in Mathematics, Volume 328
      Author(s): Fei Fang, Zhong Tan
      In this article, we study the heat flow equation for Dirichlet-to-Neumann operator with critical growth. By assuming that the initial value is lower-energy, we obtain the existence, blowup and regularity. On the other hand, a concentration phenomenon of the solution when the time goes to infinity is proved.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2018.01.010
      Issue No: Vol. 328 (2018)
       
  • Convex subshifts, separated Bratteli diagrams, and ideal structure of tame
           separated graph algebras
    • Authors: Pere Ara; Matias Lolk
      Pages: 367 - 435
      Abstract: Publication date: 13 April 2018
      Source:Advances in Mathematics, Volume 328
      Author(s): Pere Ara, Matias Lolk
      We introduce a new class of partial actions of free groups on totally disconnected compact Hausdorff spaces, which we call convex subshifts. These serve as an abstract framework for the partial actions associated with finite separated graphs in much the same way as classical subshifts generalize the edge shift of a finite graph. We define the notion of a finite type convex subshift and show that any such subshift is Kakutani equivalent to the partial action associated with a finite bipartite separated graph. We then study the ideal structure of both the full and the reduced tame graph C*-algebras, O ( E , C ) and O r ( E , C ) , of a separated graph ( E , C ) , and of the abelianized Leavitt path algebra L K ab ( E , C ) as well. These algebras are the (reduced) crossed products with respect to the above-mentioned partial actions, and we prove that there is a lattice isomorphism between the lattice of induced ideals and the lattice of hereditary D ∞ -saturated subsets of a certain infinite separated graph ( F ∞ , D ∞ ) built from ( E , C ) , called the separated Bratteli diagram of ( E , C ) . We finally use these tools to study simplicity and primeness of the tame separated graph algebras.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2018.01.020
      Issue No: Vol. 328 (2018)
       
  • Integral representation for fractional Laplace–Beltrami operators
    • Authors: Diego Alonso-Orán; Antonio Córdoba; Ángel D. Martínez
      Pages: 436 - 445
      Abstract: Publication date: 13 April 2018
      Source:Advances in Mathematics, Volume 328
      Author(s): Diego Alonso-Orán, Antonio Córdoba, Ángel D. Martínez
      In this paper we provide an integral representation of the fractional Laplace–Beltrami operator for general riemannian manifolds which has several interesting applications. We give two different proofs, in two different scenarios, of essentially the same result. The first deals with compact manifolds with or without boundary, while the second approach treats the case of riemannian manifolds without boundary whose Ricci curvature is uniformly bounded below.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2018.01.014
      Issue No: Vol. 328 (2018)
       
  • Rough bilinear singular integrals
    • Authors: Loukas Grafakos; Danqing He; Petr Honzík
      Pages: 54 - 78
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): Loukas Grafakos, Danqing He, Petr Honzík
      We study the rough bilinear singular integral, introduced by Coifman and Meyer [8], T Ω ( f , g ) ( x ) = p.v. ∫ R n ∫ R n ( y , z ) − 2 n Ω ( ( y , z ) / ( y , z ) ) f ( x − y ) g ( x − z ) d y d z , when Ω is a function in L q ( S 2 n − 1 ) with vanishing integral and 2 ≤ q ≤ ∞ . When q = ∞ we obtain boundedness for T Ω from L p 1 ( R n ) × L p 2 ( R n ) to L p ( R n ) when 1 < p 1 , p 2 < ∞ and 1 / p = 1 / p 1 + 1 / p 2 . For q = 2 we obtain that T Ω is bounded from L 2 ( R n ) × L 2 ( R n ) to L 1 ( R n ) . For q between 2 and infinity we obtain the analogous boundedness on a set of indices around the point ( 1 / 2 , 1 / 2 , 1 ) . To obtain our results we ...
      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2017.12.013
      Issue No: Vol. 326 (2018)
       
  • Donaldson–Thomas invariants of 2-dimensional sheaves inside
           threefolds and modular forms
    • Authors: Amin Gholampour; Artan Sheshmani
      Pages: 79 - 107
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): Amin Gholampour, Artan Sheshmani
      Motivated by the S-duality conjecture, we study the Donaldson–Thomas invariants of the 2-dimensional Gieseker stable sheaves on a threefold. These sheaves are supported on the fibers of a nonsingular threefold X fibered over a nonsingular curve. In the case where X is a K3 fibration, we express these invariants in terms of the Euler characteristic of the Hilbert scheme of points on the K3 fiber and the Noether–Lefschetz numbers of the fibration. We prove that a certain generating function of these invariants is a vector modular form of weight − 3 / 2 as predicted in S-duality.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2017.12.015
      Issue No: Vol. 326 (2018)
       
  • On stability of Abrikosov vortex lattices
    • Authors: Israel Michael Sigal; Tim Tzaneteas
      Pages: 108 - 199
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): Israel Michael Sigal, Tim Tzaneteas
      The Ginzburg–Landau equations play a key role in superconductivity and particle physics. They inspired many imitations in other areas of physics. These equations have two remarkable classes of solutions – vortices and (Abrikosov) vortex lattices. For the standard cylindrical geometry, the existence theory for these solutions, as well as the stability theory of vortices are well developed. The latter is done within the context of the time-dependent Ginzburg–Landau equations – the Gorkov–Eliashberg–Schmid equations of superconductivity – and the abelian Higgs model of particle physics. We study stability of Abrikosov vortex lattices under finite energy perturbations satisfying a natural parity condition (both defined precisely in the text) for the dynamics given by the Gorkov–Eliashberg–Schmid equations. For magnetic fields close to the second critical magnetic field and for arbitrary lattice shapes, we prove that there exist two functions on the space of lattices, such that Abrikosov vortex lattice solutions are asymptotically stable, provided the superconductor is of Type II and these functions are positive, and unstable, for superconductors of Type I, or if one of these functions is negative.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2017.11.031
      Issue No: Vol. 326 (2018)
       
  • Auslander–Gorenstein algebras and precluster tilting
    • Authors: Osamu Iyama; Øyvind Solberg
      Pages: 200 - 240
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): Osamu Iyama, Øyvind Solberg
      We generalize the notions of n-cluster tilting subcategories and τ-selfinjective algebras into n-precluster tilting subcategories and τ n -selfinjective algebras, where we show that a subcategory naturally associated to n-precluster tilting subcategories has a higher Auslander–Reiten theory. Furthermore, we give a bijection between n-precluster tilting subcategories and n-minimal Auslander–Gorenstein algebras, which is a higher dimensional analog of Auslander–Solberg correspondence [8] as well as a Gorenstein analog of n-Auslander correspondence [22]. The Auslander–Reiten theory associated to an n-precluster tilting subcategory is used to classify the n-minimal Auslander–Gorenstein algebras into four disjoint classes. Our method is based on relative homological algebra due to Auslander–Solberg.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2017.11.025
      Issue No: Vol. 326 (2018)
       
  • Poincaré duality with cap products in intersection homology
    • Authors: David Chataur; Martintxo Saralegi-Aranguren; Daniel Tanré
      Pages: 314 - 351
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): David Chataur, Martintxo Saralegi-Aranguren, Daniel Tanré
      For having a Poincaré duality via a cap product between the intersection homology of a paracompact oriented pseudomanifold and the cohomology given by the dual complex, G. Friedman and J. E. McClure need a coefficient field or an additional hypothesis on the torsion. In this work, by using the classical geometric process of blowing-up, adapted to a simplicial setting, we build a cochain complex which gives a Poincaré duality via a cap product with intersection homology, for any commutative ring of coefficients. We prove also the topological invariance of the blown-up intersection cohomology with compact supports in the case of a paracompact pseudomanifold with no codimension one strata. This work is written with general perversities, defined on each stratum and not only in function of the codimension of strata. It contains also a tame intersection homology, suitable for large perversities.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2017.12.017
      Issue No: Vol. 326 (2018)
       
  • Chern forms of singular metrics on vector bundles
    • Authors: Richard Lärkäng; Hossein Raufi; Jean Ruppenthal; Martin Sera
      Pages: 465 - 489
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): Richard Lärkäng, Hossein Raufi, Jean Ruppenthal, Martin Sera
      We study singular hermitian metrics on holomorphic vector bundles, following Berndtsson–Păun. Previous work by Raufi has shown that for such metrics, it is in general not possible to define the curvature as a current with measure coefficients. In this paper we show that despite this, under appropriate codimension restrictions on the singular set of the metric, it is still possible to define Chern forms as closed currents of order 0 with locally finite mass, which represent the Chern classes of the vector bundle.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2017.12.009
      Issue No: Vol. 326 (2018)
       
  • On the global behavior of solutions of the
           Maxwell–Klein–Gordon equations
    • Authors: Shiwu Yang
      Pages: 490 - 520
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): Shiwu Yang
      It is known that the Maxwell–Klein–Gordon equations in R 3 + 1 admit global solutions with finite energy data. In this paper, we present a new approach to study the asymptotic behavior of these global solutions. We show the quantitative energy flux decay of the solutions with data merely bounded in some weighted energy space. We also establish an integrated local energy decay and a hierarchy of r-weighted energy decay. The results in particular hold in the presence of large total charge. This is the first result to give a complete and precise description of the global behavior of large nonlinear charged scalar fields.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2018.01.006
      Issue No: Vol. 326 (2018)
       
  • Busemann's intersection inequality in hyperbolic and spherical spaces
    • Authors: Susanna Dann; Jaegil Kim; Vladyslav Yaskin
      Pages: 521 - 560
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): Susanna Dann, Jaegil Kim, Vladyslav Yaskin
      Busemann's intersection inequality asserts that the only maximizers of the integral ∫ S n − 1 K ∩ ξ ⊥ n d ξ among all convex bodies of a fixed volume in R n are centered ellipsoids. We study this question in the hyperbolic and spherical spaces, as well as general measure spaces.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2018.01.008
      Issue No: Vol. 326 (2018)
       
  • Computable torsion abelian groups
    • Authors: Alexander G. Melnikov; Keng Meng Ng
      Pages: 864 - 907
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Alexander G. Melnikov, Keng Meng Ng
      We prove that c.c. torsion abelian groups can be described by a Π 4 0 -predicate that describes the failure of a brute-force diagonalisation attempt on such groups. We show that there is no simpler description since their index set is Π 4 0 -complete. The results can be viewed as a solution to a 60 year-old problem of Mal'cev in the case of torsion abelian groups. We prove that a computable torsion abelian group has one or infinitely many computable copies, up to computable isomorphism. The result confirms a conjecture of Goncharov from the early 1980s for the case of torsion abelian groups.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2017.12.011
      Issue No: Vol. 325 (2018)
       
  • A remark on Gromov–Witten invariants of quintic threefold
    • Authors: Longting
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): Longting Wu
      The purpose of the article is to give a proof of a conjecture of Maulik and Pandharipande for genus 2 and 3. As a result, it gives a way to determine Gromov–Witten invariants of the quintic threefold for genus 2 and 3.

      PubDate: 2018-02-05T06:56:50Z
       
  • A generalization of Schur functions: Applications to Nevanlinna functions,
           orthogonal polynomials, random walks and unitary and open quantum walks
    • Authors: F.A.
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): F.A. Grünbaum, L. Velázquez
      Recent work on return properties of quantum walks (the quantum analogue of random walks) has identified their generating functions of first returns as Schur functions. This is connected with a representation of Schur functions in terms of the operators governing the evolution of quantum walks, i.e. the unitary operators on Hilbert spaces. In this paper we propose a generalization of Schur functions by extending the above operator representation to arbitrary closed operators on Banach spaces. Such generalized ‘Schur functions’ meet the formal structure of first return generating functions, thus we call them FR-functions. We derive some general properties of FR-functions, among them a simple relation with an operator version of Stieltjes functions which generalizes the renewal equation already known for random and quantum walks. We also prove that FR-functions satisfy splitting properties which extend useful factorizations of Schur functions. When specialized to self-adjoint operators on Hilbert spaces, we show that FR-functions become Nevanlinna functions. This allows us to obtain properties of Nevanlinna functions which, as far as we know, seem to be new. The FR-function structure leads to a new operator representation of Nevanlinna functions in terms of self-adjoint operators, whose spectral measures provide also new integral representations of such functions. This allows us to characterize each Nevanlinna function by a measure on the real line, which we refer to as ‘the measure of the Nevanlinna function’. In contrast to standard operator and integral representations of Nevanlinna functions, these new ones are exact analogues of those already known for Schur functions. The above results are also the source of a very simple ‘Schur algorithm’ for Nevanlinna functions based on interpolations at points on the real line, which we refer to as the ‘Schur algorithm on the real line’. The paper is completed with several applications of FR-functions to orthogonal polynomials and random and quantum walks which illustrate their wide interest: an analogue for orthogonal polynomials on the real line of the Khrushchev formula for orthogonal polynomials on the unit circle, and the use of FR-functions to study recurrence in random walks, quantum walks and open quantum walks. These applications provide numerous explicit examples of FR-functions, clarifying the meaning of these functions –as first return generating functions– and their splittings –which become recurrence splitting rules. They also show that these new tools, despite being extensions of very classical ones, play an important role in the study of physical problems of a highly topical nature.

      PubDate: 2018-02-05T06:56:50Z
       
  • A trichotomy theorem for transformation groups of locally symmetric
           manifolds and topological rigidity
    • Authors: Sylvain Cappell; Alexander Lubotzky; Shmuel Weinberger
      Abstract: Publication date: Available online 19 January 2018
      Source:Advances in Mathematics
      Author(s): Sylvain Cappell, Alexander Lubotzky, Shmuel Weinberger
      Let M be a locally symmetric irreducible closed manifold of dimension ≥3. A result of Borel [6] combined with Mostow rigidity imply that there exists a finite group G = G ( M ) such that any finite subgroup of Homeo + ( M ) is isomorphic to a subgroup of G. Borel [6] asked if there exist M's with G ( M ) trivial and if the number of conjugacy classes of finite subgroups of Homeo + ( M ) is finite. We answer both questions: (1) For every finite group G there exist M's with G ( M ) = G , and (2) the number of maximal subgroups of Homeo + ( M ) can be either one, countably many or continuum and we determine (at least for dim ⁡ M ≠ 4 ) when each case occurs. Our detailed analysis of (2) also gives a complete characterization of the topological local rigidity and topological strong rigidity (for dim M ≠ 4 ) of proper discontinuous actions of uniform lattices in semisimple Lie groups on the associated symmetric spaces.

      PubDate: 2018-02-05T06:56:50Z
      DOI: 10.1016/j.aim.2017.06.010
       
  • The Goldman–Turaev Lie bialgebra in genus zero and the
           Kashiwara–Vergne problem
    • Authors: Anton Alekseev; Nariya Kawazumi; Yusuke Kuno; Florian Naef
      Pages: 1 - 53
      Abstract: Publication date: 21 February 2018
      Source:Advances in Mathematics, Volume 326
      Author(s): Anton Alekseev, Nariya Kawazumi, Yusuke Kuno, Florian Naef
      In this paper, we describe a surprising link between the theory of the Goldman–Turaev Lie bialgebra on surfaces of genus zero and the Kashiwara–Vergne (KV) problem in Lie theory. Let Σ be an oriented 2-dimensional manifold with non-empty boundary and K a field of characteristic zero. The Goldman–Turaev Lie bialgebra is defined by the Goldman bracket { − , − } and Turaev cobracket δ on the K -span of homotopy classes of free loops on Σ. Applying an expansion θ : K π → K 〈 x 1 , … , x n 〉 yields an algebraic description of the operations { − , − } and δ in terms of non-commutative variables x 1 , … , x n . If Σ is a surface of genus g = 0 the lowest degree parts { − , − } − 1 and δ − 1 are canonically defined (and independent of θ). They define a Lie bialgebra structure on the space of cyclic words which was introduced and studied by Schedler [31]. It was conjectured by the second and the third authors that one can define an expansion θ such that { − , − } = { − , − } − 1 and δ = δ − 1 . The main result of this paper states that for surfaces of genus zero constructing such an expansion is essentially equivalent to the KV problem. In [24], Massuyeau constructed such expansions using the Kontsevich integral. In order to prove this result, we show that the Turaev cobracket δ can be constructed in terms of the double bracket (upgrading the Goldman bracket) and the non-commutative divergence cocycle which plays the central role in the KV theory. Among other things, this observation gives a new topological interpretation of the KV problem and allows to extend it to surfaces with arbitrary number of boundary components (and of arbitrary genus, see [2]).

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.12.005
      Issue No: Vol. 326 (2017)
       
  • Local Sobolev constant estimate for integral Ricci curvature bounds
    • Authors: Xianzhe Dai; Guofang Wei; Zhenlei Zhang
      Pages: 1 - 33
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Xianzhe Dai, Guofang Wei, Zhenlei Zhang
      We obtain a local Sobolev constant estimate for integral Ricci curvature, which enables us to extend several important tools such as the maximal principle, the gradient estimate, the heat kernel estimate and the L 2 Hessian estimate to manifolds with integral Ricci lower bounds, without the non-collapsing conditions.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.024
      Issue No: Vol. 325 (2017)
       
  • Finite time blow up in the hyperbolic Boussinesq system
    • Authors: Alexander Kiselev; Changhui Tan
      Pages: 34 - 55
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Alexander Kiselev, Changhui Tan
      In recent work of Luo and Hou [10], a new scenario for finite time blow up in solutions of 3D Euler equation has been proposed. The scenario involves a ring of hyperbolic points of the flow located at the boundary of a cylinder. In this paper, we propose a two dimensional model that we call “hyperbolic Boussinesq system”. This model is designed to provide insight into the hyperbolic point blow up scenario. The model features an incompressible velocity vector field, a simplified Biot–Savart law, and a simplified term modeling buoyancy. We prove that finite time blow up happens for a natural class of initial data.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.019
      Issue No: Vol. 325 (2017)
       
  • Multiple elliptic gamma functions associated to cones
    • Authors: Jacob Winding
      Pages: 56 - 86
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Jacob Winding
      We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, associated to good rational cones. We explain how good cones are related to collections of S L r ( Z ) -elements and prove that the generalized multiple sine and multiple elliptic gamma functions enjoy infinite product representations and modular properties determined by the cone. This generalizes the modular properties of the elliptic gamma function studied by Felder and Varchenko, and the results about the usual multiple sine and elliptic gamma functions found by Narukawa.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.022
      Issue No: Vol. 325 (2017)
       
  • Rigorous effective bounds on the Hausdorff dimension of continued fraction
           Cantor sets: A hundred decimal digits for the dimension of E2
    • Authors: O. Jenkinson; M. Pollicott
      Pages: 87 - 115
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): O. Jenkinson, M. Pollicott
      We prove that the algorithm of [19] for approximating the Hausdorff dimension of dynamically defined Cantor sets, using periodic points of the underlying dynamical system, can be used to establish completely rigorous high accuracy bounds on the dimension. The effectiveness of these rigorous estimates is illustrated for Cantor sets consisting of continued fraction expansions with restricted digits. For example the Hausdorff dimension of the set E 2 (of those reals whose continued fraction expansion only contains digits 1 and 2) can be rigorously approximated, with an accuracy of over 100 decimal places, using points of period up to 25. The method for establishing rigorous dimension bounds involves the holomorphic extension of mappings associated to the allowed continued fraction digits, an appropriate disc which is contracted by these mappings, and an associated transfer operator acting on the Hilbert Hardy space of analytic functions on this disc. We introduce methods for rigorously bounding the approximation numbers for the transfer operators, showing that this leads to effective estimates on the Taylor coefficients of the associated determinant, and hence to explicit bounds on the Hausdorff dimension.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.028
      Issue No: Vol. 325 (2017)
       
  • Gap-labelling conjecture with nonzero magnetic field
    • Authors: Moulay Tahar Benameur; Varghese Mathai
      Pages: 116 - 164
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Moulay Tahar Benameur, Varghese Mathai
      Given a constant magnetic field on Euclidean space R p determined by a skew-symmetric ( p × p ) matrix Θ, and a Z p -invariant probability measure μ on the disorder set Σ which is by hypothesis a Cantor set, where the action is assumed to be minimal, the corresponding Integrated Density of States of any self-adjoint operator affiliated to the twisted crossed product algebra C ( Σ ) ⋊ σ Z p , where σ is the multiplier on Z p associated to Θ, takes on values on spectral gaps in the magnetic gap-labelling group. The magnetic frequency group is defined as an explicit countable subgroup of R involving Pfaffians of Θ and its sub-matrices. We conjecture that the magnetic gap labelling group is a subgroup of the magnetic frequency group. We give evidence for the validity of our conjecture in 2D, 3D, the Jordan block diagonal case and the periodic case in all dimensions.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.030
      Issue No: Vol. 325 (2017)
       
  • The limit of the Hermitian–Yang–Mills flow on reflexive
           sheaves
    • Authors: Jiayu Li; Chuanjing Zhang; Xi Zhang
      Pages: 165 - 214
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Jiayu Li, Chuanjing Zhang, Xi Zhang
      In this paper, we study the asymptotic behavior of the Hermitian–Yang–Mills flow on a reflexive sheaf. We prove that the limiting reflexive sheaf is isomorphic to the double dual of the graded sheaf associated to the Harder–Narasimhan–Seshadri filtration, this answers a question by Bando and Siu.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.029
      Issue No: Vol. 325 (2017)
       
  • A Lindelöf group with non-Lindelöf square
    • Authors: Yinhe Peng; Liuzhen Wu
      Pages: 215 - 242
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Yinhe Peng, Liuzhen Wu
      We show that the Lindelöf property of a topological group is not inherited by its square, thus solving an old problem from [2]. Our construction introduces a new method to this area of mathematics and is of independent interest as it may have some further applications. Our method builds on ideas of [11] and techniques from [20] and give us also an optimal result about the partition properties on ω 1 .

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.021
      Issue No: Vol. 325 (2017)
       
  • Building blocks of polarized endomorphisms of normal projective varieties
    • Authors: Sheng Meng; De-Qi Zhang
      Pages: 243 - 273
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Sheng Meng, De-Qi Zhang
      An endomorphism f of a projective variety X is polarized (resp. quasi-polarized) if f ⁎ H ∼ q H (linear equivalence) for some ample (resp. nef and big) Cartier divisor H and integer q > 1 . First, we use cone analysis to show that a quasi-polarized endomorphism is always polarized, and the polarized property descends via any equivariant dominant rational map. Next, we show that a suitable maximal rationally connected fibration (MRC) can be made f-equivariant using a construction of N. Nakayama, that f descends to a polarized endomorphism of the base Y of this MRC and that this Y is a Q-abelian variety (quasi-étale quotient of an abelian variety). Finally, we show that we can run the minimal model program (MMP) f-equivariantly for mildly singular X and reach either a Q-abelian variety or a Fano variety of Picard number one. As a consequence, the building blocks of polarized endomorphisms are those of Q-abelian varieties and those of Fano varieties of Picard number one. Along the way, we show that f always descends to a polarized endomorphism of the Albanese variety Alb ( X ) of X, and that the pullback of a power of f acts as a scalar multiplication on the Néron–Severi group of X (modulo torsion) when X is smooth and rationally connected. Partial answers about X being of Calabi–Yau type, or Fano type are also given with an extra primitivity assumption on f which seems necessary by an example.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.026
      Issue No: Vol. 325 (2017)
       
  • A vanishing theorem for Dirac cohomology of standard modules
    • Authors: Kei Yuen Chan
      Pages: 274 - 311
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Kei Yuen Chan
      This paper studies the Dirac cohomology of standard modules in the setting of graded Hecke algebras with geometric parameters. We prove that the Dirac cohomology of a standard module vanishes if and only if the module is not twisted-elliptic tempered. The proof makes use of two deep results. One is some structural information from the generalized Springer correspondence obtained by S. Kato and Lusztig. Another one is a computation of the Dirac cohomology of tempered modules by Barbasch–Ciubotaru–Trapa and Ciubotaru. We apply our result to compute the Dirac cohomology of ladder representations for type A n . For each of such representations with non-zero Dirac cohomology, we associate to a canonical Weyl group representation. We use the Dirac cohomology to conclude that such representations appear with multiplicity one.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.023
      Issue No: Vol. 325 (2017)
       
  • Quantales and Fell bundles
    • Authors: Pedro Resende
      Pages: 312 - 374
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Pedro Resende
      We study Fell bundles on groupoids from the viewpoint of quantale theory. Given any saturated upper semicontinuous Fell bundle π : E → G on an étale groupoid G with G 0 locally compact Hausdorff, equipped with a suitable completion C*-algebra A of its convolution algebra, we obtain a map of involutive quantales p : Max A → Ω ( G ) , where Max A consists of the closed linear subspaces of A and Ω ( G ) is the topology of G. We study various properties of p which mimick, to various degrees, those of open maps of topological spaces. These are closely related to properties of G, π, and A, such as G being Hausdorff, principal, or topological principal, or π being a line bundle. Under suitable conditions, which include G being Hausdorff, but without requiring saturation of the Fell bundle, A is an algebra of sections of the bundle if and only if it is the reduced C*-algebra C r ⁎ ( G , E ) . We also prove that Max A is stably Gelfand. This implies the existence of a pseudogroup I B and of an étale groupoid B associated canonically to any sub-C*-algebra B ⊂ A . We study a correspondence between Fell bundles and sub-C*-algebras based on these constructions, and compare it to the construction of Weyl groupoids from Cartan subalgebras.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.12.001
      Issue No: Vol. 325 (2017)
       
  • Cyclotomic root systems and bad primes
    • Authors: Michel Broué; Ruth Corran; Jean Michel
      Pages: 375 - 458
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Michel Broué, Ruth Corran, Jean Michel
      We generalize the definition and properties of root systems to complex reflection groups — roots become rank one projective modules over the ring of integers of a number field k. In the irreducible case, we provide a classification of root systems over the field of definition k of the reflection representation. In the case of spetsial reflection groups, we generalize as well the definition and properties of bad primes.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.020
      Issue No: Vol. 325 (2017)
       
  • On polytopes with congruent projections or sections
    • Authors: Sergii Myroshnychenko; Dmitry Ryabogin
      Pages: 482 - 504
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Sergii Myroshnychenko, Dmitry Ryabogin
      Let 2 ≤ k ≤ d − 1 and let P and Q be two convex polytopes in E d . Assume that their projections, P H , Q H , onto every k-dimensional subspace H, are congruent. In this paper we show that P and Q or P and −Q are translates of each other. We also prove an analogous result for sections by showing that P = Q or P = − Q , provided the polytopes contain the origin in their interior and their sections, P ∩ H , Q ∩ H , by every k-dimensional subspace H, are congruent.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.12.003
      Issue No: Vol. 325 (2017)
       
  • On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a
           variation of Ramanujan's ω(q)
    • Authors: Kathrin Bringmann; Chris Jennings-Shaffer; Karl Mahlburg
      Pages: 505 - 532
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Kathrin Bringmann, Chris Jennings-Shaffer, Karl Mahlburg
      We analyze the mock modular behavior of P ¯ ω ( q ) , a partition function introduced by Andrews, Dixit, Schultz, and Yee. This function arose in a study of smallest parts functions related to classical third order mock theta functions, one of which is ω ( q ) . We find that the modular completion of P ¯ ω ( q ) is not simply a harmonic Maass form, but is instead the derivative of a linear combination of products of various harmonic Maass forms and theta functions. We precisely describe its behavior under modular transformations and find that the image under the Maass lowering operator lies in a relatively simpler space.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.12.002
      Issue No: Vol. 325 (2017)
       
  • On the dynamics of finite temperature trapped Bose gases
    • Authors: Avy Soffer; Minh-Binh Tran
      Pages: 533 - 607
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Avy Soffer, Minh-Binh Tran
      The system that describes the dynamics of a Bose–Einstein Condensate (BEC) and the thermal cloud at finite temperature consists of a nonlinear Schrodinger (NLS) and a quantum Boltzmann (QB) equations. In such a system of trapped Bose gases at finite temperature, the QB equation corresponds to the evolution of the density distribution function of the thermal cloud and the NLS is the equation of the condensate. The quantum Boltzmann collision operator in this temperature regime is the sum of two operators C 12 and C 22 , which describe collisions of the condensate and the non-condensate atoms and collisions between non-condensate atoms. Above the BEC critical temperature, the system is reduced to an equation containing only a collision operator similar to C 22 , which possesses a blow-up positive radial solution with respect to the L ∞ norm (cf. [29]). On the other hand, at the very low temperature regime (only a portion of the transition temperature T B E C ), the system can be simplified into an equation of C 12 , with a different (much higher order) transition probability, which has a unique global classical positive radial solution with weighted L 1 norm (cf. [3]). In our model, we first decouple the QB, which contains C 12 + C 22 , and the NLS equations, then show a global existence and uniqueness result for classical positive radial solutions to the spatially homogeneous kinetic system. Different from the case considered in [29], due to the presence of the BEC, the collision integrals are associated to sophisticated energy manifolds rather than spheres, since the particle energy is approximated by the Bogoliubov dispersion law. Moreover, the mass of the full system is not conserved while it is conserved for the case considered in [29]. A new theory is then supplied.

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.12.007
      Issue No: Vol. 325 (2017)
       
  • The necessity of nowhere equivalence
    • Authors: Wei He; Yeneng Sun
      Pages: 608 - 639
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Wei He, Yeneng Sun
      We prove some regularity properties (convexity, closedness, compactness and preservation of upper hemicontinuity) for distribution and regular conditional distribution of correspondences under the nowhere equivalence condition. We show the necessity of such a condition for any of these properties to hold. As an application, we demonstrate that the nowhere equivalence condition is satisfied on the underlying agent space if and only if pure-strategy Nash equilibria exist in general large games with any fixed uncountable compact action space.

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.11.032
      Issue No: Vol. 325 (2017)
       
  • Projections of planar Mandelbrot random measures
    • Authors: Julien Barral; De-Jun Feng
      Pages: 640 - 718
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Julien Barral, De-Jun Feng
      Let μ be a planar Mandelbrot measure and π ⁎ μ its orthogonal projection on one of the principal axes. We study the thermodynamic and geometric properties of π ⁎ μ . We first show that π ⁎ μ is exact dimensional, with dim ⁡ ( π ⁎ μ ) = min ⁡ ( dim ⁡ ( μ ) , dim ⁡ ( ν ) ) , where ν is the Bernoulli product measure obtained as the expectation of π ⁎ μ . We also prove that π ⁎ μ is absolutely continuous with respect to ν if and only if dim ⁡ ( μ ) > dim ⁡ ( ν ) . Our results provides a new proof of Dekking–Grimmett–Falconer formula for the Hausdorff and box dimension of the topological support of π ⁎ μ , as well as a new variational interpretation. We obtain the free energy function τ π ⁎ μ of π ⁎ μ on a wide subinterval [ 0 , q c ) of R + . For q ∈ [ 0 , 1 ] , it is given by a variational formula which sometimes yields phase transitions of order larger than 1. For q > 1 , it is given by min ⁡ ( τ ν , τ μ ) , which can exhibit first order phase transitions. This is in contrast with the analyticity of τ μ over [ 0 , q c ) . Also, we prove the validity of the multifractal formalism for π ⁎ μ at each α ∈ ( τ π ⁎ μ ′ ( q c − ) , τ π ⁎ μ ′ ( 0 + ) ] .

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.12.008
      Issue No: Vol. 325 (2017)
       
  • Long term regularity of the one-fluid Euler–Maxwell system in 3D
           with vorticity
    • Authors: Alexandru D. Ionescu; Victor Lie
      Pages: 719 - 769
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Alexandru D. Ionescu, Victor Lie
      A basic model for describing plasma dynamics is given by the “one-fluid” Euler–Maxwell system, in which a compressible electron fluid interacts with its own self-consistent electromagnetic field. In this paper we prove long-term regularity of solutions of this system in 3 spatial dimensions, in the case of small initial data with nontrivial vorticity. Our main conclusion is that the time of existence of solutions depends only on the size of the vorticity of the initial data, as long as the initial data is sufficiently close to a constant stationary solution.

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.11.027
      Issue No: Vol. 325 (2017)
       
  • Heisenberg uniqueness pairs corresponding to a finite number of parallel
           lines
    • Authors: Sayan Bagchi
      Pages: 814 - 823
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Sayan Bagchi
      In this paper, we study the Heisenberg uniqueness pairs corresponding to a finite number of parallel lines Γ. We give a necessary condition and a sufficient condition for a subset Λ of R 2 so that ( Γ , Λ ) becomes a HUP.

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.12.012
      Issue No: Vol. 325 (2017)
       
  • Brunn–Minkowski inequalities in product metric measure spaces
    • Authors: Manuel Ritoré; Jesús Yepes Nicolás
      Pages: 824 - 863
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Manuel Ritoré, Jesús Yepes Nicolás
      Given one metric measure space X satisfying a linear Brunn–Minkowski inequality, and a second one Y satisfying a Brunn–Minkowski inequality with exponent p ≥ − 1 , we prove that the product X × Y with the standard product distance and measure satisfies a Brunn–Minkowski inequality of order 1 / ( 1 + p − 1 ) under mild conditions on the measures and the assumption that the distances are strictly intrinsic. The same result holds when we consider restricted classes of sets. We also prove that a linear Brunn–Minkowski inequality is obtained in X × Y when Y satisfies a Prékopa–Leindler inequality. In particular, we show that the classical Brunn–Minkowski inequality holds for any pair of weakly unconditional sets in R n (i.e., those containing the projection of every point in the set onto every coordinate subspace) when we consider the standard distance and the product measure of n one-dimensional real measures with positively decreasing densities. This yields an improvement of the class of sets satisfying the Gaussian Brunn–Minkowski inequality. Furthermore, associated isoperimetric inequalities as well as recently obtained Brunn–Minkowski's inequalities are derived from our results.

      PubDate: 2017-12-27T05:35:23Z
      DOI: 10.1016/j.aim.2017.12.010
      Issue No: Vol. 325 (2017)
       
  • Floer homology and fractional Dehn twists
    • Authors: Matthew Hedden; Thomas E. Mark
      Pages: 1 - 39
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Matthew Hedden, Thomas E. Mark
      We establish a relationship between Heegaard Floer homology and the fractional Dehn twist coefficient of surface automorphisms. Specifically, we show that the rank of the Heegaard Floer homology of a 3-manifold bounds the absolute value of the fractional Dehn twist coefficient of the monodromy of any of its open book decompositions with connected binding. We prove this by showing that the rank of Floer homology gives bounds for the number of boundary parallel right or left Dehn twists necessary to add to a surface automorphism to guarantee that the associated contact manifold is tight or overtwisted, respectively. By examining branched double covers, we also show that the rank of the Khovanov homology of a link bounds the fractional Dehn twist coefficient of its odd-stranded braid representatives.

      PubDate: 2017-11-18T16:22:33Z
      DOI: 10.1016/j.aim.2017.11.008
      Issue No: Vol. 324 (2017)
       
  • Norms of random matrices: Local and global problems
    • Authors: Elizaveta Rebrova; Roman Vershynin
      Pages: 40 - 83
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Elizaveta Rebrova, Roman Vershynin
      Can the behavior of a random matrix be improved by modifying a small fraction of its entries' Consider a random matrix A with i.i.d. entries. We show that the operator norm of A can be reduced to the optimal order O ( n ) by zeroing out a small submatrix of A if and only if the entries have zero mean and finite variance. Moreover, we obtain an almost optimal dependence between the size of the removed submatrix and the resulting operator norm. Our approach utilizes the cut norm and Grothendieck–Pietsch factorization for matrices, and it combines the methods developed recently by C. Le and R. Vershynin and by E. Rebrova and K. Tikhomirov.

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.001
      Issue No: Vol. 324 (2017)
       
  • Ramsey properties of nonlinear Diophantine equations
    • Authors: Mauro Di Nasso; Lorenzo Luperi Baglini
      Pages: 84 - 117
      Abstract: Publication date: 14 January 2018
      Source:Advances in Mathematics, Volume 324
      Author(s): Mauro Di Nasso, Lorenzo Luperi Baglini
      We present general sufficient and necessary conditions for the partition regularity of Diophantine equations, which extend the classic Rado's Theorem by covering large classes of nonlinear equations. The goal is to contribute to an overall theory of Ramsey properties of (nonlinear) Diophantine equations that encompasses the known results in this area under a unified framework. Sufficient conditions are obtained by exploiting algebraic properties in the space of ultrafilters β N , grounding on combinatorial properties of positive density sets and IP sets. Necessary conditions are proved by a new technique in nonstandard analysis, based on the use of the relation of u-equivalence for the hypernatural numbers N ⁎ .

      PubDate: 2017-12-13T02:41:29Z
      DOI: 10.1016/j.aim.2017.11.003
      Issue No: Vol. 324 (2017)
       
  • Bressoud's conjecture
    • Authors: Sun Kim
      Abstract: Publication date: 5 February 2018
      Source:Advances in Mathematics, Volume 325
      Author(s): Sun Kim
      In 1980, D. M. Bressoud obtained an analytic generalization of the Rogers–Ramanujan–Gordon identities. He then tried to establish a combinatorial interpretation of his identity, which specializes to many well-known Rogers–Ramanujan type identities. He proved that a certain partition identity follows from his identity in a very restrictive case and conjectured that the partition identity holds true in general. In this paper, we prove Bressoud's conjecture for the general case by providing bijective proofs.

      PubDate: 2017-12-27T05:35:23Z
       
 
 
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