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  Subjects -> MATHEMATICS (Total: 955 journals)
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    - MATHEMATICS (706 journals)
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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 Communications in Contemporary Mathematics
  [SJR: 1.329]   [H-I: 28]   [0 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0219-1997 - ISSN (Online) 1793-6683
   Published by World Scientific Homepage  [117 journals]
  • Regularity for a fractional [math]-Laplace equation
    • Authors: Armin Schikorra, Tien-Tsan Shieh, Daniel E. Spector
      Abstract: Communications in Contemporary Mathematics, Volume 20, Issue 01, February 2018.
      In this note, we consider regularity theory for a fractional [math]-Laplace operator which arises in the complex interpolation of the Sobolev spaces, the [math]-Laplacian. We obtain the natural analogue to the classical [math]-Laplacian situation, namely [math]-regularity for the homogeneous equation.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-23T08:03:42Z
      DOI: 10.1142/S0219199717500031
       
  • On the construction of suitable weak solutions to the 3D Navier–Stokes
           equations in a bounded domain by an artificial compressibility method
    • Authors: Luigi C. Berselli, Stefano Spirito
      Abstract: Communications in Contemporary Mathematics, Volume 20, Issue 01, February 2018.
      We prove that suitable weak solutions of 3D Navier–Stokes equations in bounded domains can be constructed by a particular type of artificial compressibility approximation.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-23T08:03:41Z
      DOI: 10.1142/S0219199716500644
       
  • Positive subharmonic solutions to nonlinear ODEs with indefinite weight
    • Authors: Alberto Boscaggin, Guglielmo Feltrin
      Abstract: Communications in Contemporary Mathematics, Volume 20, Issue 01, February 2018.
      We prove that the superlinear indefinite equation u″ + a(t)up = 0, where [math] and [math] is a [math]-periodic sign-changing function satisfying the (sharp) mean value condition [math], has positive subharmonic solutions of order [math] for any large integer [math], thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467–477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré–Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-23T08:03:39Z
      DOI: 10.1142/S0219199717500213
       
  • Exceptional collections and the bicanonical map of Keum’s fake
           projective planes
    • Authors: Gennaro Di Brino, Luca F. Di Cerbo
      Abstract: Communications in Contemporary Mathematics, Volume 20, Issue 01, February 2018.
      We apply the recent results of Galkin et al. [Derived categories of Keum’s fake projective planes, Adv. Math. 278 (2015) 238–253] to study some geometrical features of Keum’s fake projective planes. Among other things, we show that the bicanonical map of Keum’s fake projective planes is always an embedding. Moreover, we construct a nonstandard exceptional collection on the unique fake projective plane [math] with [math].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-23T08:03:38Z
      DOI: 10.1142/S0219199716500668
       
  • Expansion of the spectrum in the weak disorder regime for random operators
           in continuum space
    • Authors: Denis Borisov, Francisco Hoecker-Escuti, Ivan Veselić
      Abstract: Communications in Contemporary Mathematics, Volume 20, Issue 01, February 2018.
      We study the spectrum of random ergodic Schrödinger-type operators in the weak disorder regime. We give upper and lower bounds on how much the spectrum expands at its bottom for very general perturbations. The background operator is assumed to be a periodic elliptic differential operator on [math], not necessarily of second order.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-23T08:03:36Z
      DOI: 10.1142/S0219199717500080
       
  • Vanishing-concentration-compactness alternative for the
           Trudinger–Moser inequality in [math]
    • Authors: João Marcos Do Ó, Federica Sani, Cristina Tarsi
      Abstract: Communications in Contemporary Mathematics, Volume 20, Issue 01, February 2018.
      Let [math], [math] and [math]. Our aim is to clarify the influence of the constraint [math] on concentration phenomena of (spherically symmetric and non-increasing) maximizing sequences for the Trudinger–Moser supremum dN(a,b) :=supu∈Sa,b∫ℝNϕN(αN u N N−1)dx, where [math] is the sharp exponent of Moser, i.e. [math] and [math] is the surface measure of the [math]-dimensional unit sphere in [math]. We obtain a vanishing-concentration-compactness alternative showing that maximizing sequences for [math] cannot concentrate either when [math] or when [math] and [math] is sufficiently small. From this alternative, we deduce the attainability of [math] for special values of the parameters [math] and [math].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-23T08:03:34Z
      DOI: 10.1142/S021919971650036X
       
  • Finite-dimensional Leibniz algebras and combinatorial structures
    • Authors: M. Ceballos, J. Núñez, Á. F. Tenorio
      Abstract: Communications in Contemporary Mathematics, Volume 20, Issue 01, February 2018.
      Given a finite-dimensional Leibniz algebra with certain basis, we show how to associate such algebra with a combinatorial structure of dimension 2. In some particular cases, this structure can be reduced to a digraph or a pseudodigraph. In this paper, we study some theoretical properties about this association and we determine the type of Leibniz algebra associated to each of them.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-23T08:03:32Z
      DOI: 10.1142/S0219199717500043
       
  • On the Harnack inequality for degenerate and singular elliptic equations
           with unbounded lower order terms via sliding paraboloids
    • Authors: Nam Q. Le
      Abstract: Communications in Contemporary Mathematics, Volume 20, Issue 01, February 2018.
      We use the method of sliding paraboloids to establish a Harnack inequality for linear, degenerate and singular elliptic equation with unbounded lower order terms. The equations we consider include uniformly elliptic equations and linearized Monge–Ampère equations. Our argument allows us to prove the doubling estimate for functions which, at points of large gradient, are solutions of (degenerate and singular) elliptic equations with unbounded drift.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-23T08:03:31Z
      DOI: 10.1142/S0219199717500122
       
  • Norms supporting the Lebesgue differentiation theorem
    • Authors: Paola Cavaliere, Andrea Cianchi, Luboš Pick, Lenka Slavíková
      Abstract: Communications in Contemporary Mathematics, Volume 20, Issue 01, February 2018.
      A version of the Lebesgue differentiation theorem is offered, where the [math] norm is replaced with any rearrangement-invariant norm. Necessary and sufficient conditions for a norm of this kind to support the Lebesgue differentiation theorem are established. In particular, Lorentz, Orlicz and other customary norms for which Lebesgue’s theorem holds are characterized.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-23T08:03:29Z
      DOI: 10.1142/S0219199717500201
       
  • Resonance tongues for the Hill equation with Duffing coefficients and
           instabilities in a nonlinear beam equation
    • Authors: Carlo Gasparetto, Filippo Gazzola
      Abstract: Communications in Contemporary Mathematics, Volume 20, Issue 01, February 2018.
      We consider a class of Hill equations where the periodic coefficient is the squared solution of some Duffing equation plus a constant. We study the stability of the trivial solution of this Hill equation and we show that a criterion due to Burdina [Boundedness of solutions of a system of differential equations, Dokl. Akad. Nauk. SSSR 92 (1953) 603–606] is very helpful for this analysis. In some cases, we are also able to determine exact solutions in terms of Jacobi elliptic functions. Overall, we obtain a fairly complete picture of the stability and instability regions. These results are then used to study the stability of nonlinear modes in some beam equations.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-23T08:03:27Z
      DOI: 10.1142/S0219199717500225
       
  • Unstable CMC spheres and outlying CMC spheres in AF 3-manifolds
    • Authors: Shiguang Ma
      Abstract: Communications in Contemporary Mathematics, Volume 20, Issue 01, February 2018.
      In this paper, we introduce a nonlinear ODE method to construct constant mean curvature (CMC) surfaces in Riemannian manifolds with symmetry. As an application, we construct unstable CMC spheres and outlying CMC spheres in asymptotically Schwarzschild manifolds with metrics like [math]. The existence of unstable CMC spheres tells us that the stability condition in Qing–Tian’s work [On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds, J. Amer. Math. Soc. 20(4) (2007) 1091–1110] cannot be removed generally.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-23T08:03:26Z
      DOI: 10.1142/S0219199716500656
       
  • Cordes–Nirenberg’s imbedding and restricting with application
           to an elliptic equation
    • Authors: S. Hou, J. Xiao
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      This paper not only presents a criterion for the Cordes–Nirenberg space [math] imbedding between the associate Morrey space [math] and the Morrey space [math], but also characterizes a Radon measure [math] such that the Cordes–Nirenberg potential space [math] is restricted to the [math]-based Campanato space [math] — thereby giving an application of the discovered characterization to the regularity for a class of the elliptic equations with symmetric [math]-coefficients.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:35Z
      DOI: 10.1142/S0219199717500808
       
  • Sharp measure contraction property for generalized H-type Carnot groups
    • Authors: Davide Barilari, Luca Rizzi
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We prove that H-type Carnot groups of rank [math] and dimension [math] satisfy the [math] if and only if [math] and [math]. The latter integer coincides with the geodesic dimension of the Carnot group. The same result holds true for the larger class of generalized H-type Carnot groups introduced in this paper, and for which we compute explicitly the optimal synthesis. This constitutes the largest class of Carnot groups for which the curvature exponent coincides with the geodesic dimension. We stress that generalized H-type Carnot groups have step 2, include all corank 1 groups and, in general, admit abnormal minimizing curves. As a corollary, we prove the absolute continuity of the Wasserstein geodesics for the quadratic cost on all generalized H-type Carnot groups.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:34Z
      DOI: 10.1142/S021919971750081X
       
  • Surfaces of general type with [math] are rigidified
    • Authors: Wenfei Liu
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      Let [math] be a minimal smooth projective surface of general type with irregularity [math]. We show that, if [math] has a nontrivial holomorphic automorphism acting trivially on the cohomology with rational coefficients, then it is a surface isogenous to a product. As a consequence of this geometric characterization, one infers that no nontrivial automorphism of surfaces of general type with [math] (which are not necessarily minimal) can be homotopic to the identity. In particular, such surfaces are rigidified in the sense of Fabrizio Catanese.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:34Z
      DOI: 10.1142/S0219199717500845
       
  • On the set of expansive measures
    • Authors: Keonhee Lee, C. A. Morales, Bomi Shin
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We prove that the set of expansive measures of a homeomorphism of a compact metric space is a [math] subset of the space of Borel probability measures equipped with the weak* topology. Next that every expansive measure of a homeomorphism of a compact metric space can be weak* approximated by expansive measures with invariant support. In addition, if the expansive measures of a homeomorphism of a compact metric space are dense in the space of Borel probability measures, then there is an expansive measure whose support is both invariant and close to the whole space with respect to the Hausdorff metric. Henceforth, if the expansive measures are dense in the space of Borel probability measures, the set of heteroclinic points has no interior and the space has no isolated points.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:34Z
      DOI: 10.1142/S0219199717500869
       
  • Existence of positive solutions to a linearly coupled Schrödinger
           system with critical exponent
    • Authors: Huiling Wu, Jianqing Chen, Yongqing Li
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We are concerned with the system of nonlinear Schrödinger equations −△u + μ(x)u = u p−2u + λ(x)v,x ∈ ℝN, −△v + ν(x)v = v 2∗−2v + λ(x)u,x ∈ ℝN,u,v ∈ H1(ℝN). The existence of a positive solution to the system is proved.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:33Z
      DOI: 10.1142/S0219199717500821
       
  • Periodic homogenization for quasi-filling fractal layers
    • Authors: Raffaela Capitanelli, Cristina Pocci
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we study the periodic homogenization of the stationary heat equation in a domain with two connected components, separated by an oscillating interface defined on prefractal Koch type curves. The problem depends both on the parameter [math], which is the index of the prefractal iteration, and [math], that defines the periodic structure of the composite material. First, we study the limit as [math] goes to infinity, giving rise to a limit problem defined on a domain with fractal interface. Then, we compute the limit as [math] vanishes, showing that the homogenized problem is strictly dependent on the amplitude of the oscillations and the parameter appearing in the transmission condition. Finally, we discuss about the commutative nature of the limits in [math] and [math].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:33Z
      DOI: 10.1142/S0219199717500882
       
  • A pointwise finite-dimensional reduction method for a fully coupled system
           of Einstein–Lichnerowicz type
    • Authors: Bruno Premoselli
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We construct non-compactness examples for the fully coupled Einstein–Lichnerowicz constraint system in the focusing case. The construction is obtained by combining pointwise a priori asymptotic analysis techniques, finite-dimensional reductions and a fixed-point argument. More precisely, we perform a fixed-point procedure on the remainders of the expected blow-up decomposition. The argument consists of an involved finite-dimensional reduction coupled with a ping-pong method. To overcome the non-variational structure of the system, we work with remainders which belong to strong function spaces and not merely to energy spaces. Performing both the ping-pong argument and the finite-dimensional reduction therefore heavily relies on the a priori pointwise asymptotic techniques of the [math] theory.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:33Z
      DOI: 10.1142/S0219199717500766
       
  • Some Riemann Hypotheses from random walks over primes
    • Authors: Guilherme França, André LeClair
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      The aim of this paper is to investigate how various Riemann Hypotheses would follow only from properties of the prime numbers. To this end, we consider two classes of [math]-functions, namely, non-principal Dirichlet and those based on cusp forms. The simplest example of the latter is based on the Ramanujan tau arithmetic function. For both classes, we prove that if a particular trigonometric series involving sums of multiplicative characters over primes is [math], then the Euler product converges in the right half of the critical strip. When this result is combined with the functional equation, the non-trivial zeros are constrained to lie on the critical line. We argue that this [math] growth is a consequence of the series behaving like a one-dimensional random walk. Based on these results, we obtain an equation which relates every individual non-trivial zero of the [math]-function to a sum involving all the primes. Finally, we briefly mention important differences for principal Dirichlet [math]-functions due to the existence of the pole at [math], in which the Riemann [math]-function is a particular case.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:32Z
      DOI: 10.1142/S0219199717500857
       
  • Global weighted Orlicz estimates for irregular obstacle problems with
           general growth over bounded nonsmooth domains
    • Authors: Yumi Cho
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We study a generalized variational inequality with an irregular obstacle in the frame of Orlicz–Sobolev spaces. Over a bounded nonsmooth domain having a sufficiently flat boundary in the Reifenberg sense, a global weighted Orlicz estimate is established for the gradient of the solution to the obstacle problem assumed BMO smallness of a coefficient.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:32Z
      DOI: 10.1142/S0219199717500833
       
  • Generalized Littlewood–Paley characterizations of fractional Sobolev
           spaces
    • Authors: Shuichi Sato, Fan Wang, Dachun Yang, Wen Yuan
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, the authors characterize the Sobolev spaces [math] with [math] and [math] via a generalized Lusin area function and its corresponding Littlewood–Paley [math]-function. The range [math] is also proved to be nearly sharp in the sense that these new characterizations are not true when [math] and [math]. Moreover, in the endpoint case [math], the authors also obtain some weak type estimates. Since these generalized Littlewood–Paley functions are of wide generality, these results provide some new choices for introducing the notions of fractional Sobolev spaces on metric measure spaces.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:32Z
      DOI: 10.1142/S0219199717500778
       
  • Anisotropic regularity principle in sequence spaces and applications
    • Authors: Nacib Albuquerque, Lisiane Rezende
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We refine a recent technique introduced by Pellegrino, Santos, Serrano and Teixeira and prove a quite general anisotropic regularity principle in sequence spaces. As applications, we generalize previous results of several authors regarding Hardy–Littlewood inequalities for multilinear forms.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:31Z
      DOI: 10.1142/S0219199717500870
       
  • Some non-local logistic population model with non-zero boundary condition
    • Authors: Patricio Cerda, Marco Souto, Pedro Ubilla
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we study some type of equations which may model the behavior of species inhabiting in some habitat. For our purpose, using a priori bounded techniques, we obtain a positive solution to a family of non-local partial differential equations with non-homogeneous boundary conditions.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:31Z
      DOI: 10.1142/S0219199717500754
       
  • Irrationality of generic cubic threefold via Weil’s conjectures
    • Authors: Dimitri Markushevich, Xavier Roulleau
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      An arithmetic method of proving the irrationality of smooth projective 3-folds is described, using reduction modulo [math]. It is illustrated by an application to a cubic threefold, for which the hypothesis that its intermediate Jacobian is isomorphic to the Jacobian of a curve is contradicted by reducing modulo 3 and counting points over appropriate extensions of [math]. As a spin-off, it is shown that the 5-dimensional Prym varieties arising as intermediate Jacobians of certain cubic 3-folds have the maximal number of points over [math] which attains Perret’s and Weil’s upper bounds.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:31Z
      DOI: 10.1142/S021919971750078X
       
  • Global gradient estimates for asymptotically regular problems of
           [math]-Laplacian type
    • Authors: Sun-Sig Byun, Jehan Oh
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We study an asymptotically regular problem of [math]-Laplacian type with discontinuous nonlinearity in a nonsmooth bounded domain. A global Calderón–Zygmund estimate is established for such a nonlinear elliptic problem with nonstandard growth under the assumption that the associated nonlinearity has a more general kind of the asymptotic behavior near the infinity with respect to the gradient variable. We also address an optimal regularity requirement on the nonlinearity as well as a minimal geometric assumption on the boundary of the domain for the nonlinear Calderón–Zygmund theory in the setting of variable exponent Sobolev spaces.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-10-10T01:54:31Z
      DOI: 10.1142/S0219199717500791
       
  • Quasilinear parabolic problem with variable exponent: Qualitative analysis
           and stabilization
    • Authors: Jacques Giacomoni, Vicenţiu Rădulescu, Guillaume Warnault
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We discuss the existence and uniqueness of the weak solution of the following nonlinear parabolic problem: (PT) ut −∇⋅a(x,∇u) = f(x,u)in QT=def(0,T) × Ω,u = 0 on ΣT=def(0,T) × ∂Ω,u(0,x) = u0(x) in Ω, which involves a quasilinear elliptic operator of Leray–Lions type with variable exponents. Next, we discuss the global behavior of solutions and in particular the convergence to a stationary solution as [math].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:48Z
      DOI: 10.1142/S0219199717500651
       
  • An Ambrosetti–Prodi-type problem for the [math]-Laplacian operator
    • Authors: Taísa Junges Miotto, Márcio Luís Miotto
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      This work has objective to obtain results of existence and multiplicity of solutions for an Ambrosetti–Prodi-type problem for the [math] operator. Moreover, it was proved a continuity result for the parameter which limits the existence of solutions in relation of the parameter [math].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:48Z
      DOI: 10.1142/S0219199717500675
       
  • Higher order Adams' inequality with the exact growth condition
    • Authors: Nader Masmoudi, Federica Sani
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      Adams' inequality is the complete generalization of the Trudinger–Moser inequality to the case of Sobolev spaces involving higher order derivatives. The failure of the original form of the sharp inequality when the problem is considered on the whole space [math] served as a motivation to investigate in the direction of a refined sharp inequality, the so-called Adams' inequality with the exact growth condition. Due to the difficulties arising in the higher order case from the lack of direct symmetrization techniques, this refined result is known to hold on first- and second-order Sobolev spaces only. We extend the validity of Adams' inequality with the exact growth to higher order Sobolev spaces.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:47Z
      DOI: 10.1142/S0219199717500729
       
  • [math]-marked moduli spaces
    • Authors: Binru Li
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      The aim of this paper is to investigate the closed subschemes of moduli spaces corresponding to projective varieties which admit an effective action by a given finite group [math]. To achieve this, we introduce the moduli functor [math] of [math]-marked Gorenstein canonical models with Hilbert polynomial [math], and prove the existence of [math], the coarse moduli scheme for [math]. Then we show that [math] has a proper and finite morphism onto [math] so that its image [math] is a closed subscheme. In the end we obtain the canonical representation type decomposition [math] of [math] and use [math] to study the structure of [math].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:47Z
      DOI: 10.1142/S0219199717500614
       
  • Multiple positive solutions of elliptic systems in exterior domains
    • Authors: Haidong Liu, Zhaoli Liu
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, existence and multiplicity of positive solutions of the elliptic system − Δu + V1(x)u = μ1(x)u3 + β(x)uv2in Ω 𝜀, − Δv + V2(x)v = β(x)u2v + μ 2(x)v3 in Ω 𝜀,u = v = 0 on ∂Ω𝜀 is proved, where [math] is an exterior domain in [math] such that [math] is far away from the origin and contains a sufficiently large ball, [math], and the coefficients [math] are continuous functions on [math] which tend to positive constants at infinity. We do not assume [math] to be positive functions.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:47Z
      DOI: 10.1142/S0219199717500638
       
  • Diagonal-preserving graded isomorphisms of Steinberg algebras
    • Authors: Toke Meier Carlsen, James Rout
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We study Steinberg algebras constructed from ample Hausdorff groupoids over commutative integral domains with identity. We reconstruct (graded) groupoids from (graded) Steinberg algebras and use this to characterize when there is a diagonal-preserving (graded) isomorphism between two (graded) Steinberg algebras. We apply this characterization to groupoids of directed graphs in order to study diagonal-preserving (graded) isomorphisms of Leavitt path algebras and ∗-isomorphisms of graph [math]-algebras.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:47Z
      DOI: 10.1142/S021919971750064X
       
  • Adams inequality with exact growth in the hyperbolic space [math] and
           Lions lemma
    • Authors: Debabrata Karmakar
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we prove Adams inequality with exact growth condition in the four-dimensional hyperbolic space [math] ∫ℍ4 e32π2u2 − 1 (1 + u )2 dvg ≤ C∥u∥L2(ℍ4)2, (0.1) [math]. We will also establish an Adachi–Tanaka-type inequality in this setting. Another aspect of this paper is the Lions lemma in the hyperbolic space. We prove Lions lemma for the Moser functional and for a few cases of the Adams functional on the whole hyperbolic space.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:46Z
      DOI: 10.1142/S0219199717500663
       
  • Concentration between Lévy’s inequality and the Poincaré inequality
           for log-concave densities
    • Authors: Erez Buchweitz
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      Given a suitably normalized random vector [math], we observe that the function [math], defined for [math], admits surprisingly strong concentration far surpassing what is expected on account of Lévy’s isoperimetric inequality. Among the measures to which the above holds are all log-concave measures, for which a solution of the similar problem concerning the third marginal moments [math] would imply the hyperplane conjecture.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:46Z
      DOI: 10.1142/S0219199717500687
       
  • The Noether–Lefschetz locus of surfaces in toric threefolds
    • Authors: Ugo Bruzzo, Antonella Grassi
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      The Noether–Lefschetz theorem asserts that any curve in a very general surface [math] in [math] of degree [math] is a restriction of a surface in the ambient space, that is, the Picard number of [math] is [math]. We proved previously that under some conditions, which replace the condition [math], a very general surface in a simplicial toric threefold [math] (with orbifold singularities) has the same Picard number as [math]. Here we define the Noether–Lefschetz loci of quasi-smooth surfaces in [math] in a linear system of a Cartier ample divisor with respect to a [math]-regular, respectively 0-regular, ample Cartier divisor, and give bounds on their codimensions. We also study the components of the Noether–Lefschetz loci which contain a line, defined as a rational curve which is minimal in a suitable sense.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:46Z
      DOI: 10.1142/S0219199717500705
       
  • Minimization problems for inhomogeneous Rayleigh quotients
    • Authors: Marian Bocea, Mihai Mihăilescu
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, the minimization problem Λ1(p) :=infu∈X0∖{0}∫Ωsinh( ∇u p)dx ∫Ωsinh( u p)dx , where [math] is studied when [math] ([math]) is an open, bounded, convex domain with smooth boundary and [math]. We show that [math] is either zero, when the maximum of the distance function to the boundary of [math] is greater than [math], or it is a positive real number, when the maximum of the distance function to the boundary of [math] belongs to the interval [math]. In the latter case, we provide estimates for [math] and show that for [math] sufficiently large [math] coincides with the principal frequency of the [math]-Laplacian in [math]. Some particular cases and related problems are also discussed.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:46Z
      DOI: 10.1142/S0219199717500742
       
  • Global blowup controllability of heat equation with feedback control
    • Authors: Ping Lin
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      This paper concerns a global controllability problem for heat equations. In the absence of control, the solution to the linear heat system globally exists. While for each initial data, we can find a feedback control acting on an internal subset of the space domain such that the corresponding solution to the system blows up at given time.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:45Z
      DOI: 10.1142/S0219199717500626
       
  • The polynomial growth solutions to some sub-elliptic equations on the
           Heisenberg group
    • Authors: Hairong Liu, Tian Long, Xiaoping Yang
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We give an explicit description of polynomial growth solutions to some sub-elliptic operators of divergence form with [math]-periodic coefficients on the Heisenberg group, where the periodicity has to be meant with respect to the Heisenberg geometry. We show that the polynomial growth solutions are necessarily polynomials with [math]-periodic coefficients. We also prove the Liouville-type theorem for the Dirichlet problem to these sub-elliptic equations on an unbounded domain on the Heisenberg group, show that any bounded solution to the Dirichlet problem must be constant.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:45Z
      DOI: 10.1142/S0219199717500699
       
  • On Auslander’s formula and cohereditary torsion pairs
    • Authors: Abhishek Banerjee
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      For a small abelian category [math], Auslander’s formula allows us to express [math] as a quotient of the category [math] of coherent functors on [math]. We consider an abelian category with the added structure of a cohereditary torsion pair [math]. We prove versions of Auslander’s formula for the torsion-free class [math] of [math], for the derived torsion-free class [math] of the triangulated category [math] as well as the induced torsion-free class in the ind-category [math] of [math]. Further, for a given regular cardinal [math], we also consider the category [math] of [math]-presentable objects in the functor category [math]. Then, under certain conditions, we show that the torsion-free class [math] can be recovered as a subquotient of [math].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:45Z
      DOI: 10.1142/S0219199717500717
       
  • Quasi-particles in the principal picture of [math] and
           Rogers–Ramanujan-type identities
    • Authors: Slaven Kožić, Mirko Primc
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In their seminal work Lepowsky and Wilson gave a vertex-operator theoretic interpretation of Gordon–Andrews–Bressoud’s generalization of Rogers–Ramanujan combinatorial identities, by constructing bases of vacuum spaces for the principal Heisenberg subalgebra of standard [math]-modules, parametrized with partitions satisfying certain difference 2 conditions. In this paper, we define quasi-particles in the principal picture of [math] and construct quasi-particle monomial bases of standard [math]-modules for which principally specialized characters are given as products of sum sides of the corresponding analytic Rogers–Ramanujan-type identities with the character of the Fock space for the principal Heisenberg subalgebra.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-08-17T06:24:44Z
      DOI: 10.1142/S0219199717500730
       
  • Codimension one Fano distributions on Fano manifolds
    • Authors: Carolina Araujo, Mauricio Corrêa, Alex Massarenti
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we investigate codimension one Fano distributions on Fano manifolds with Picard number one. We classify Fano distributions of maximal index on complete intersections in weighted projective spaces, Fano contact manifolds, Grassmannians of lines and their linear sections, and describe their moduli spaces. As a consequence, we obtain a classification of codimension one del Pezzo distributions on Fano manifolds with Picard number one.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-06-21T09:19:21Z
      DOI: 10.1142/S0219199717500584
       
  • Conformal scalar curvature equation on [math]: Functions with two close
           critical points (Twin Pseudo-Peaks)
    • Authors: Man Chun Leung, Feng Zhou
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      By using the Lyapunov–Schmidt reduction method without perturbation, we consider existence results for the conformal scalar curvature on [math] ([math]) when the prescribed function (after being projected to [math]) has two close critical points, which have the same value (positive), equal “flatness” (“twin”; flatness [math]), and exhibit maximal behavior in certain directions (“pseudo-peaks”). The proof relies on a balance between the two main contributions to the reduced functional — one from the critical points and the other from the interaction of the two bubbles.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-06-13T09:36:17Z
      DOI: 10.1142/S0219199717500511
       
  • On Lipschitz vector fields and the Cauchy problem in homogeneous groups
    • Authors: Valentino Magnani, Dario Trevisan
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We introduce a class of “Lipschitz horizontal” vector fields in homogeneous groups, for which we show equivalent descriptions, e.g., in terms of suitable derivations. We then investigate the associated Cauchy problem, providing a uniqueness result both at equilibrium points and for vector fields of an involutive submodule of Lipschitz horizontal vector fields. We finally exhibit a counterexample to the general well-posedness theory for Lipschitz horizontal vector fields, in contrast with the Euclidean theory.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-06-13T09:36:17Z
      DOI: 10.1142/S0219199717500572
       
  • Trapped submanifolds contained into a null hypersurface of de Sitter
           spacetime
    • Authors: Luis J. Alías, Verónica L. Cánovas, Marco Rigoli
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We study codimension two trapped submanifolds contained into one of the two following null hypersurfaces of de Sitter spacetime: (i) the future component of the light cone, and (ii) the past infinite of the steady state space. For codimension two compact spacelike submanifolds in the light cone we show that they are conformally diffeomorphic to the round sphere. This fact enables us to deduce that the problem of characterizing compact marginally trapped submanifolds into the light cone is equivalent to solving the Yamabe problem on the round sphere, allowing us to obtain our main classification result for such submanifolds. We also fully describe the codimension two compact marginally trapped submanifolds contained into the past infinite of the steady state space and characterize those having parallel mean curvature field. Finally, we consider the more general case of codimension two complete, non-compact, weakly trapped spacelike submanifolds contained into the light cone.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-06-13T09:36:17Z
      DOI: 10.1142/S0219199717500596
       
  • Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs
    • Authors: Alvaro Martínez-Pérez, José M. Rodríguez
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we study the relationship of hyperbolicity and (Cheeger) isoperimetric inequality in the context of Riemannian manifolds and graphs. We characterize the hyperbolic manifolds and graphs (with bounded local geometry) verifying this isoperimetric inequality, in terms of their Gromov boundary. Furthermore, we characterize the trees with isoperimetric inequality (without any hypothesis). As an application of our results, we obtain the solvability of the Dirichlet problem at infinity for these Riemannian manifolds and graphs, and that the Martin boundary is homeomorphic to the Gromov boundary.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-06-13T09:36:16Z
      DOI: 10.1142/S021919971750050X
       
  • Hamiltonian elliptic systems in dimension two with potentials which can
           vanish at infinity
    • Authors: Sérgio H. Monari Soares, Yony R. Santaria Leuyacc
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system − Δu + V (x)u = g(v),x ∈ ℝ2, − Δv + V (x)v = f(u), x ∈ ℝ2, where [math] is a positive function which can vanish at infinity and be unbounded from above and [math] and [math] have exponential growth range. The proof involves a truncation argument combined with the linking theorem and a finite-dimensional approximation.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-06-13T09:36:16Z
      DOI: 10.1142/S0219199717500535
       
  • Concentration of cylindrical Wigner measures
    • Authors: Marco Falconi
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we aim to characterize the cylindrical Wigner measures associated to regular quantum states in the Weyl C*-algebra of canonical commutation relations. In particular, we provide conditions at the quantum level sufficient to prove the concentration of all the corresponding cylindrical Wigner measures as Radon measures on suitable topological vector spaces. The analysis is motivated by variational and dynamical problems in the semiclassical study of bosonic quantum field theories.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-06-13T09:36:16Z
      DOI: 10.1142/S0219199717500559
       
  • Translation surfaces of some new types in 3-dimensional Minkowski space
           [math] satisfying [math]
    • Authors: Bendehiba Senoussi, Mohammed Bekkar
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we study translation surfaces of some new types with non-lightlike axis in 3-dimensional Minkowski space [math] satisfying the condition [math], where [math] and [math] denotes the Laplace operator and we obtain the complete classification for those ones.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-06-13T09:36:15Z
      DOI: 10.1142/S0219199717500523
       
  • Some open problems on locally finite or locally nilpotent derivations and
           [math]-derivations
    • Authors: Wenhua Zhao
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      Let [math] be a commutative ring and [math] an [math]-algebra. An [math]-[math]-derivation of [math] is an [math]-linear map of the form [math] for some [math]-algebra endomorphism [math] of [math], where [math] denotes the identity map of [math]. In this paper, we discuss some open problems on whether or not the image of a locally finite (LF) [math]-derivation or [math]-[math]-derivation of [math] is a Mathieu subspace [W. Zhao, Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl. Algebra 214 (2010) 1200–1216; Mathieu subspaces of associative algebras, J. Algebra 350(2) (2012) 245–272] of [math], and whether or not a locally nilpotent (LN) [math]-derivation or [math]-[math]-derivation of [math] maps every ideal of [math] to a Mathieu subspace of [math]. We propose and discuss two conjectures which state that both questions above have positive answers if the base ring [math] is a field of characteristic zero. We give some examples to show the necessity of the conditions of the two conjectures, and discuss some positive cases known in the literature. We also show some cases of the two conjectures. In particular, both the conjectures are proved for LF or LN algebraic derivations and [math]-[math]-derivations of integral domains of characteristic zero.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-06-13T09:36:15Z
      DOI: 10.1142/S0219199717500560
       
  • A multiplicity result for a fractional Kirchhoff equation in [math] with a
           general nonlinearity
    • Authors: Vincenzo Ambrosio, Teresa Isernia
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we deal with the following fractional Kirchhoff equation p + q(1 − s)∬ℝ2N u(x) − u(y) 2 x − y N+2s dxdy (−Δ)su = g(u)inℝN, where [math], [math], [math], [math] is a small positive parameter and [math] is an odd function satisfying Berestycki–Lions type assumptions. By using minimax arguments, we establish a multiplicity result for the above equation, provided that [math] is sufficiently small.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-06-13T09:36:14Z
      DOI: 10.1142/S0219199717500547
       
  • Local estimate on convexity radius and decay of injectivity radius in a
           Riemannian manifold
    • Authors: Shicheng Xu
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we prove the following pointwise and curvature-free estimates on convexity radius, injectivity radius and local behavior of geodesics in a complete Riemannian manifold [math]: (1)the convexity radius of [math], [math], where [math] is the injectivity radius of [math] and [math] is the focal radius of open ball centered at [math] with radius [math]; (2)for any two points [math] in [math], [math] where [math] is the conjugate radius of [math]; (3)for any [math], any (not necessarily minimizing) geodesic in [math] has length [math]. We also clarify two different concepts on convexity radius and give examples to illustrate that the one more frequently used in literature is not continuous.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-06-13T09:36:14Z
      DOI: 10.1142/S0219199717500602
       
  • Solitary waves for nonlinear Schrödinger equation with derivative
    • Authors: Changxing Miao, Xingdong Tang, Guixiang Xu
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we characterize a family of solitary waves for nonlinear Schrödinger equation (NLS) with derivative (DNLS) by the structure analysis and the variational argument. Since DNLS does not enjoy the Galilean invariance any more, the structure analysis here is closely related with the nontrivial momentum and shows the equivalence of nontrivial solutions between the quasilinear and the semilinear equations. Firstly, for the subcritical parameters [math] and the critical parameters [math], we show the existence and uniqueness of the solitary waves for DNLS, up to the phase rotation and spatial translation symmetries. Secondly, for the critical parameters [math], [math] and the supercritical parameters [math], there is no nontrivial solitary wave for DNLS. At last, we make use of the invariant sets, which is related to the variational characterization of the solitary wave, to obtain the global existence of solution for DNLS with initial data in the invariant set [math], with [math], [math] or [math]. On the one hand, different with the scattering result for the [math]-critical NLS in [B. Dodson, Global well-posedness and scattering for the mass critical nonlinear Schrödinger equation with mass below the mass of the ground state, Adv. Math. 285(5) (2015) 1589–1618], the scattering result of DNLS does not hold for initial data in [math] because of the existence of infinity many small solitary/traveling waves in [math] with [math], [math] or [math]. On the other hand, our global result improves the global result in [Y. Wu, Global well-posedness of the derivative nonlinear Schrödinger equations in energy space, Anal. Partial Differential Equations 6(8) (2013) 1989–2002; Global well-posedness on the derivative nonlinear Schrödinger equation, Anal. Partial Differential Equations 8(5) (2015) 1101–1112] (see Corollary 1.6).
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-25T10:15:14Z
      DOI: 10.1142/S0219199717500493
       
  • On the integrability of Hamiltonian systems with [math] degrees of freedom
           and homogenous polynomial potential of degree [math]
    • Authors: Jaume Llibre, Clàudia Valls
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We consider Hamiltonian systems with [math] degrees of freedom and a Hamiltonian of the form H = 1 2∑i=1dp 12 + V (q 1,…,qd), where [math] is a homogenous polynomial of degree [math]. We prove that such Hamiltonian systems with [math] odd or [math], have a Darboux first integral if and only if they have a polynomial first integral.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-25T10:15:11Z
      DOI: 10.1142/S0219199717500456
       
  • A uniqueness lemma with applications to regularization and incompressible
           fluid mechanics
    • Authors: Guillaume Lévy
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we extend our previous result from [On uniqueness for a rough transport-diffusion equation, C. R. Acad. Sci. Sér. I[math] Math. 354(8) (2016) 804–807]. We prove that transport equations with rough coefficients do possess a uniqueness property, even in the presence of viscosity. Our method relies strongly on duality and bears a strong resemblance with the well-known DiPerna–Lions theory first developed in [Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989) 511–547]. As an application, we show that the zero solution is the unique solution at the Leray regularity scale of the Euler and Navier–Stokes equations for zero initial datum. This uniqueness result allows us to reprove the celebrated theorem of Serrin [On the interior regularity of weak solutions of the Navier–Stokes equations, Arch. Ration. Mech. Anal. 9(1) (1962) 187–195] in a novel way.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-25T10:15:07Z
      DOI: 10.1142/S0219199717500481
       
  • On the autonomous norm on the group of Hamiltonian diffeomorphisms of the
           torus
    • Authors: Michael Brandenbursky, Jarek Kędra, Egor Shelukhin
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We prove that the autonomous norm on the group of Hamiltonian diffeomorphisms of the two-dimensional torus is unbounded. We provide examples of Hamiltonian diffeomorphisms with arbitrarily large autonomous norm. For the proofs we construct explicit quasimorphisms on [math], some of them are [math]-continuous and vanish on all autonomous diffeomorphisms, and some of them are Calabi.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-25T10:15:06Z
      DOI: 10.1142/S0219199717500420
       
  • Some remarks on moduli spaces of lattice polarized holomorphic symplectic
           manifolds
    • Authors: Chiara Camere
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We construct quasi-projective moduli spaces of [math]-general lattice polarized irreducible holomorphic symplectic manifolds. Moreover, we study their Baily–Borel compactification and investigate a relation between one-dimensional boundary components and equivalence classes of rational Lagrangian fibrations defined on mirror manifolds.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-25T10:15:04Z
      DOI: 10.1142/S0219199717500444
       
  • Least energy solutions for indefinite biharmonic problems via modified
           Nehari–Pankov manifold
    • Authors: Miaomiao Niu, Zhongwei Tang, Lushun Wang
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, by using a modified Nehari–Pankov manifold, we prove the existence and the asymptotic behavior of least energy solutions for the following indefinite biharmonic equation: Δ2u + (λV (x) − δ(x))u = u p−2uinℝN, (P λ) where [math], [math], [math] is a parameter, [math] is a nonnegative potential function with nonempty zero set [math], [math] is a positive function such that the operator [math] is indefinite and non-degenerate for [math] large. We show that both in subcritical and critical cases, equation [math] admits a least energy solution which for [math] large localized near the zero set [math].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-25T10:15:01Z
      DOI: 10.1142/S021919971750047X
       
  • Time decay for solutions to the Stokes equations with drift
    • Authors: M. Schonbek, G. Seregin
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this note, we study the behavior of Lebesgue norms [math] of solutions [math] to the Cauchy problem for the Stokes system with drift [math], which is supposed to be a divergence free smooth vector valued function satisfying a scale invariant condition.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-25T10:14:58Z
      DOI: 10.1142/S0219199717500468
       
  • Calculating Galois groups of third-order linear differential equations
           with parameters
    • Authors: Andrei Minchenko, Alexey Ovchinnikov
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      Motivated by developing algorithms that decide hypertranscendence of solutions of extensions of the Bessel differential equation, algorithms computing the unipotent radical of a parameterized differential Galois group have been recently developed. Extensions of Bessel’s equation, such as the Lommel equation, can be viewed as homogeneous parameterized linear differential equations of the third order. In this paper, we give the first known algorithm that calculates the differential Galois group of a third-order parameterized linear differential equation.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-21T03:46:53Z
      DOI: 10.1142/S0219199717500389
       
  • A strongly indefinite Choquard equation with critical exponent due to the
           Hardy–Littlewood–Sobolev inequality
    • Authors: Fashun Gao, Minbo Yang
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we are concerned with the following nonlinear Choquard equation −Δu + V (x)u = ∫ℝN G(y,u) x − y μdyg(x,u)in ℝN, where [math], [math] and [math]. If [math] lies in a gap of the spectrum of [math] and [math] is of critical growth due to the Hardy–Littlewood–Sobolev inequality, we obtain the existence of nontrivial solutions by variational methods. The main result here extends and complements the earlier theorems obtained in [N. Ackermann, On a periodic Schrödinger equation with nonlocal superlinear part, Math. Z. 248 (2004) 423–443; B. Buffoni, L. Jeanjean and C. A. Stuart, Existence of a nontrivial solution to a strongly indefinite semilinear equation, Proc. Amer. Math. Soc. 119 (1993) 179–186; V. Moroz and J. Van Schaftingen, Existence of groundstates for a class of nonlinear Choquard equations, Trans. Amer. Math. Soc. 367 (2015) 6557–6579].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-21T03:46:53Z
      DOI: 10.1142/S0219199717500377
       
  • Isolated singularities of positive solutions for Choquard equations in
           sublinear case
    • Authors: Huyuan Chen, Feng Zhou
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case [math] −Δu + u = Iα[up]uqinℝN ∖{0},lim x →+∞u(x) = 0, where [math] and [math] is the Riesz potential, which appears as a nonlocal term in the equation. We investigate the nonexistence and existence of isolated singular solutions of Choquard equation under different range of the pair of exponent [math]. Furthermore, we obtain qualitative properties for the minimal singular solutions of the equation.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-21T03:46:52Z
      DOI: 10.1142/S0219199717500407
       
  • [math]-Symmetric rings
    • Authors: Fanyun Meng, Junchao Wei
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      Let [math] be a ring and [math] an idempotent of [math], [math] is called an [math]-symmetric ring if [math] implies [math] for all [math]. Obviously, [math] is a symmetric ring if and only if [math] is a [math]-symmetric ring. In this paper, we show that a ring [math] is [math]-symmetric if and only if [math] is left semicentral and [math] is symmetric. As an application, we show that a ring [math] is left min-abel if and only if [math] is [math]-symmetric for each left minimal idempotent [math] of [math]. We also introduce the definition of strongly [math]-symmetric ring and prove that [math] is a strongly [math]-symmetric ring if and only if [math] and [math] is a symmetric ring. Finally, we introduce [math]-reduced ring and study some properties of it.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-21T03:46:52Z
      DOI: 10.1142/S0219199717500390
       
  • Small data scattering for energy critical NLKG on product spaces [math]
    • Authors: Lysianne Hari, Nicola Visciglia
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We study small data scattering in the energy space of solutions to the [math]-critical NLKG posed on product spaces [math] with [math] and [math] is a compact Riemannian manifold.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-04-19T09:35:33Z
      DOI: 10.1142/S0219199717500365
       
  • Transformations preserving the Lyapunov exponents
    • Authors: Luis Barreira, Claudia Valls
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We give a complete characterization of the existence of Lyapunov coordinate changes bringing an invertible sequence of matrices to one in block form. In other words, we give a criterion for the block-trivialization of a nonautonomous dynamics with discrete time while preserving the asymptotic properties of the dynamics. We provide two nontrivial applications of this criterion: we show that any Lyapunov regular sequence of invertible matrices can be transformed by a Lyapunov coordinate change into a constant diagonal sequence; and we show that the family of all coordinate changes preserving simultaneously the Lyapunov exponents of all sequences of invertible matrices (with finite exponent) coincides with the family of Lyapunov coordinate changes.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-02-17T08:12:57Z
      DOI: 10.1142/S0219199717500274
       
  • Towards sharp Bohnenblust–Hille constants
    • Authors: Daniel Pellegrino, Eduardo V. Teixeira
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We investigate the optimality problem associated with the best constants in a class of Bohnenblust–Hille-type inequalities for [math]-linear forms. While germinal estimates indicated an exponential growth, in this work we provide strong evidences to the conjecture that the sharp constants in the classical Bohnenblust–Hille inequality are universally bounded, irrespectively of the value of [math]; hereafter referred as the Universality Conjecture. In our approach, we introduce the notions of entropy and complexity, designed to measure, to some extent, the complexity of such optimization problems. We show that the notion of entropy is critically connected to the Universality Conjecture; for instance, that if the entropy grows at most exponentially with respect to [math], then the optimal constants of the [math]-linear Bohnenblust–Hille inequality for real scalars are indeed bounded universally with respect to [math]. It is likely that indeed the entropy grows as [math], and in this scenario, we show that the optimal constants are precisely [math]. In the bilinear case, [math], we show that any extremum of the Littlewood’s [math] inequality has entropy [math] and complexity [math], and thus we are able to classify all extrema of the problem. We also prove that, for any mixed [math]-Littlewood inequality, the entropy do grow exponentially and the sharp constants for such a class of inequalities are precisely [math]. In addition to the notions of entropy and complexity, the approach we develop in this work makes decisive use of a family of strongly non-symmetric [math]-linear forms, which has further consequences to the theory, as we explain herein.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-02-17T08:12:56Z
      DOI: 10.1142/S0219199717500298
       
  • Hölder regularity for the gradient of the inhomogeneous parabolic
           normalized [math]-Laplacian
    • Authors: Amal Attouchi, Mikko Parviainen
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we study an evolution equation involving the normalized [math]-Laplacian and a bounded continuous source term. The normalized [math]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [math] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-02-17T08:12:56Z
      DOI: 10.1142/S0219199717500353
       
  • Real hypersurfaces in the complex hyperbolic quadrics with isometric Reeb
           flow
    • Authors: Young Jin Suh
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We classify real hypersurfaces with isometric Reeb flow in the complex hyperbolic quadrics [math], [math]. We show that [math] is even, say [math], and any such hypersurface becomes an open part of a tube around a [math]-dimensional complex hyperbolic space [math] which is embedded canonically in [math] as a totally geodesic complex submanifold or a horosphere whose center at infinity is [math]-isotropic singular. As a consequence of the result, we get the nonexistence of real hypersurfaces with isometric Reeb flow in odd-dimensional complex quadrics [math], [math].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-02-17T08:12:54Z
      DOI: 10.1142/S0219199717500316
       
  • An improved Leray–Trudinger inequality
    • Authors: Arka Mallick, Cyril Tintarev
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we derive the following Leray–Trudinger type inequality on a bounded domain [math] in [math] containing the origin. supu∈W01,n(Ω),In[u,Ω,R]≤1∫Ωecn u(x) E2β x R n n−1dx < +∞,  for some cn > 0 depending only on n. Here, [math], [math], [math] and [math], [math] for [math] This improves an earlier result by Psaradakis and Spector. Also, we prove that for any [math] in the place of [math], the above inequality is false if we take [math].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-02-17T08:12:52Z
      DOI: 10.1142/S0219199717500341
       
  • Large blow-up sets for the prescribed [math]-curvature equation in the
           Euclidean space
    • Authors: Ali Hyder, Stefano Iula, Luca Martinazzi
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      Let [math] be an integer. For any open domain [math], non-positive function [math] such that [math], and bounded sequence [math] we prove the existence of a sequence of functions [math] solving the Liouville equation of order [math] (−Δ)mu k = Vke2mukin Ω,limsupk→∞∫Ωe2mukdx < ∞, and blowing up exactly on the set [math], i.e. limk→∞uk(x) = +∞ for x ∈ Sφandlimk→∞uk(x) = −∞ for x ∈ Ω ∖ Sφ, thus showing that a result of Adimurthi, Robert and Struwe is sharp. We extend this result to the boundary of [math] and to the case [math]. Several related problems remain open.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-02-17T08:12:52Z
      DOI: 10.1142/S0219199717500262
       
  • A sharp estimate à la Calderón–Zygmund for the
           [math]-Laplacian
    • Authors: Lorenzo Brasco, Filippo Santambrogio
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We consider local weak solutions of the Poisson equation for the [math]-Laplace operator. We prove a higher differentiability result, under an essentially sharp condition on the right-hand side. The result comes with a local scaling invariant a priori estimate.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-02-17T08:12:49Z
      DOI: 10.1142/S0219199717500304
       
  • Jordan property and automorphism groups of normal compact Kähler
           varieties
    • Authors: Jin Hong Kim
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      It has been recently shown by Meng and Zhang that the full automorphism group [math] is a Jordan group for all projective varieties in arbitrary dimensions. The aim of this paper is to show that the full automorphism group [math] is, in fact, a Jordan group even for all normal compact Kähler varieties in arbitrary dimensions. The meromorphic structure of the identity component of the automorphism group and its Rosenlicht-type decomposition play crucial roles in the proof.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-02-17T08:12:48Z
      DOI: 10.1142/S0219199717500249
       
  • Quadratic systems with an invariant conic having Darboux invariants
    • Authors: Jaume Llibre, Regilene Oliveira
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      The complete characterization of the phase portraits of real planar quadratic vector fields is very far from being accomplished. As it is almost impossible to work directly with the whole class of quadratic vector fields because it depends on twelve parameters, we reduce the number of parameters to five by using the action of the group of real affine transformations and time rescaling on the class of real quadratic differential systems. Using this group action, we obtain normal forms for the class of quadratic systems that we want to study with at most five parameters. Then working with these normal forms, we complete the characterization of the phase portraits in the Poincaré disc of all planar quadratic polynomial differential systems having an invariant conic [math]: [math], and a Darboux invariant of the form [math] with [math].
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-02-17T08:12:47Z
      DOI: 10.1142/S021919971750033X
       
  • Existence results of positive solutions for nonlinear cooperative elliptic
           systems involving fractional Laplacian
    • Authors: Alexander Quaas, Aliang Xia
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      In this paper, we prove existence results of positive solutions for the following nonlinear elliptic problem with gradient terms: (−Δ)αu = f(x,u,v,∇u,∇v)in Ω,(−Δ)αv = g(x,u,v,∇u,∇v)in Ω,u = v = 0 in ℝN∖Ω, where [math] denotes the fractional Laplacian and [math] is a smooth bounded domain in [math]. It shown that under some assumptions on [math] and [math], the problem has at least one positive solution [math]. Our proof is based on the classical scaling method of Gidas and Spruck and topological degree theory.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-02-17T08:12:45Z
      DOI: 10.1142/S0219199717500328
       
  • Bilinear decompositions of products of local Hardy and Lipschitz or BMO
           spaces through wavelets
    • Authors: Jun Cao, Luong Dang Ky, Dachun Yang
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      Let [math] and [math] be the local Hardy space in the sense of D. Goldberg. In this paper, the authors establish two bilinear decompositions of the product spaces of [math] and their dual spaces. More precisely, the authors prove that [math] and, for any [math], [math], where [math] denotes the local BMO space, [math], for any [math] and [math], the inhomogeneous Lipschitz space and [math] a variant of the local Orlicz–Hardy space related to the Orlicz function [math] for any [math] which was introduced by Bonami and Feuto. As an application, the authors establish a div-curl lemma at the endpoint case.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-02-17T08:12:44Z
      DOI: 10.1142/S0219199717500250
       
  • Existence results for double-phase problems via Morse theory
    • Authors: Kanishka Perera, Marco Squassina
      Abstract: Communications in Contemporary Mathematics, Ahead of Print.
      We obtain nontrivial solutions for a class of double-phase problems using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get an estimate of the critical groups at zero.
      Citation: Communications in Contemporary Mathematics
      PubDate: 2017-01-17T11:17:52Z
      DOI: 10.1142/S0219199717500237
       
 
 
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