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  • Generalized fractional integral operators on Orlicz–Hardy spaces
    Math. Nachr. (IF 0.91) Pub Date : 2020-11-20
    Ryutaro Arai; Eiichi Nakai; Yoshihiro Sawano

    The generalized fractional integral operators are shown to be bounded from an Orlicz–Hardy space H Φ ( R n ) to another Orlicz–Hardy space H Ψ ( R n ) , where Φ and Ψ are generalized Young functions. The result extends the boundedness of the usual fractional integral operator I α from H p ( R n ) to H q ( R n ) for α , p , q ∈ ( 0 , ∞ ) and − n / p + α = − n / q , which was proved by Stein and Weiss

    更新日期:2020-11-21
  • Dichotomy and μ‐pseudo almost automorphic solutions for delayed partial functional differential equations in admissible spaces
    Math. Nachr. (IF 0.91) Pub Date : 2020-11-12
    Chiraz Jendoubi

    We prove the existence and uniqueness of μ‐pseudo almost automorphic solution for a delayed non‐autonomous partial functional differential equation in the exponential dichotomic case, where the nonlinear operator F satisfies the φ‐Lipschitz condition and φ belongs to some admissible spaces. We further prove the existence of an invariant stable manifold around the μ‐pseudo almost automorphic solution

    更新日期:2020-11-13
  • Multiple peak solutions for polyharmonic equation with critical growth
    Math. Nachr. (IF 0.91) Pub Date : 2020-11-12
    Yuxia Guo; Ting Liu

    This paper is concerned with the following elliptic problem: ( − Δ ) m u = u + m ∗ − 1 + λ u − s 1 φ 1 , in B 1 , u ∈ D 0 m , 2 ( B 1 ) , ( P ) (P)where ( − Δ ) m is the polyharmonic operator, m ∗ = 2 N N − 2 m is the critical Sobolev embedding exponent. B1 is the unit ball in R N , s1 and λ > 0 are parameters, φ 1 > 0 is the eigenfunction of ( − Δ ) m , D 0 m , 2 ( B 1 ) corresponding to the first

    更新日期:2020-11-12
  • Nevanlinna and Carleson functions of analytic self‐maps on multiply‐connected domains
    Math. Nachr. (IF 0.91) Pub Date : 2020-11-10
    Michał Rzeczkowski

    In the paper we prove that the Nevanlinna counting function and the Carleson function of analytic self‐maps of finitely connected domains with smooth boundary are equivalent. Using this result we obtain the characterization of compact composition operators on Hardy–Orlicz spaces.

    更新日期:2020-11-12
  • A topological approach to nonlocal elliptic partial differential equations on an annulus
    Math. Nachr. (IF 0.91) Pub Date : 2020-11-05
    Christopher S. Goodrich

    For q ≥ 1 we consider the nonlocal ordinary differential equation − a ∫ 0 1 | y | q d s y ′ ′ ( t ) = λ f ( t , y ( t ) ) , 0 < t < 1 , subject to the Dirichlet boundary conditions y ( 0 ) = 0 = y ( 1 ) . Due to the term a ∫ 0 1 | y | q ds appearing in the equation, this is a class of nonlocal differential equations. By using a novel order cone we are able to establish existence of a positive solution

    更新日期:2020-11-06
  • On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation
    Math. Nachr. (IF 0.91) Pub Date : 2020-11-03
    Tomoyuki Nakatsuka

    We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution { u , p } of the Navier–Stokes equation such that | ∇ j u ( t , x ) | = O ( | x | 1 − n − j ) and | ∇ j p ( t , x ) | = O ( | x |

    更新日期:2020-11-03
  • Real hypersurfaces in the complex hyperbolic quadric with harmonic curvature
    Math. Nachr. (IF 0.91) Pub Date : 2020-11-01
    Young Jin Suh

    We give a classification of real hypersurfaces in the complex hyperbolic quadric Q m ∗ = S O 2 , m o / S O 2 S O m that have constant mean curvature and harmonic curvature.

    更新日期:2020-11-02
  • Lp‐Estimates for the ∂¯b‐equation on a class of infinite type domains
    Math. Nachr. (IF 0.91) Pub Date : 2020-10-30
    Tran Vu Khanh; Andrew Raich

    We prove L p estimates, 1 ≤ p ≤ ∞ , for solutions to the tangential Cauchy–Riemann equations ∂ ¯ b u = ϕ on a class of infinite type domains Ω ⊂ C 2 . The domains under consideration are a class of convex ellipsoids, and we show that if ϕ is a ∂ ¯ b ‐closed (0,1)‐form with coefficients in L p , then there exists an explicit solution solution u satisfying ∥ u ∥ L p ( b Ω ) ≤ C ∥ ϕ ∥ L p ( b Ω ) . Moreover

    更新日期:2020-10-30
  • A probabilistic approach to a non‐local quadratic form and its connection to the Neumann boundary condition problem
    Math. Nachr. (IF 0.91) Pub Date : 2020-10-27
    Zoran Vondraček

    In this paper we look at a probabilistic approach to a non‐local quadratic form that has lately attracted some interest. This form is related to a recently introduced non‐local normal derivative. The goal is to construct two Markov processes: one corresponding to that form and the other which is related to a probabilistic interpretation of the Neumann problem. We also study the Dirichlet‐to‐Neumann

    更新日期:2020-10-30
  • Artificial boundary conditions for linearized stationary incompressible viscous flow around rotating and translating body
    Math. Nachr. (IF 0.91) Pub Date : 2020-10-22
    P. Deuring; S. Kračmar; Š. Nečasová

    We consider the linearized and nonlinear stationary incompressible flow around rotating and translating body in the exterior domain R 3 ∖ D ¯ , where D ⊂ R 3 is open and bounded, with Lipschitz boundary. We derive the pointwise estimates for the pressure in both cases. Moreover, we consider the linearized problem in a truncation domain D R : = B R ∖ D ¯ of the exterior domain R 3 ∖ D ¯ under certain

    更新日期:2020-10-23
  • Essentially finite generation of valuation rings in terms of classical invariants
    Math. Nachr. (IF 0.91) Pub Date : 2020-10-14
    Steven Dale Cutkosky; Josnei Novacoski

    The main goal of this paper is to study some properties of an extension of valuations from classical invariants. More specifically, we consider a valued field ( K , ν ) and an extension ω of ν to a finite extension L of K. Then we study when the valuation ring of ω is essentially finitely generated over the valuation ring of ν. We present a necessary condition in terms of classic invariants of the

    更新日期:2020-10-16
  • Degeneration of torsors over families of del Pezzo surfaces
    Math. Nachr. (IF 0.91) Pub Date : 2020-10-09
    Ulrich Derenthal; Norbert Hoffmann

    Let S be a split family of del Pezzo surfaces over a discrete valuation ring such that the general fiber is smooth and the special fiber has ADE ‐singularities. Let G be the reductive group given by the root system of these singularities. We construct a G‐torsor over S whose restriction to the generic fiber is the extension of structure group of the universal torsor. This extends a construction of

    更新日期:2020-10-11
  • The calculation of the sum of the spaces of the K‐method of real interpolation
    Math. Nachr. (IF 0.91) Pub Date : 2020-10-07
    Evgenii I. Berezhnoĭ

    It is shown that the calculation of the sum of the spaces of the K‐Peetre interpolation method can be reduced to the calculation of the sum of the cones of the concave functions included by the parameter in the definition of the spaces of the K‐Peetre interpolation method. As an example, a new extrapolation theorem for operators in Lipschitz spaces is obtained.

    更新日期:2020-10-07
  • Well‐posedness of degenerate fractional integro‐differential equations in vector‐valued functional spaces
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-30
    Shangquan Bu; Gang Cai

    We study the well‐posedness of the fractional degenerate integro‐differential equations ( P α ) : D α ( M u ) ( t ) = A u ( t ) + ∫ − ∞ t a ( t − s ) A u ( s ) d s + ∫ − ∞ t b ( t − s ) B u ( s ) d s + f ( t ) , ( t ∈ T : = [ 0 , 2 π ] ) , in Lebesgue–Bochner spaces L p ( T ; X ) and Besov spaces B p , q s ( T ; X ) , where A, B and M are closed linear operators on a Banach space X satisfying D ( A

    更新日期:2020-10-07
  • Multiplicity of solutions for fractional equation involving the Bessel operator in RN
    Math. Nachr. (IF 0.91) Pub Date : 2020-08-05
    Nguyen Van Thin

    The aim of this paper is to study the existence of solution to an equation involving the Bessel operator in R N ( I − Δ ) α u + λ V ( x ) u = γ f ( x , u ) , where λ , γ are real positive parameters, V : R N → R + is a continuous function, 0 < α < 1 with 2 α < N , f is a continuous function on R N × R which does not satisfy the Ambrosetti–Rabinowitz condition. By using the Fountain theorem and Morse

    更新日期:2020-10-07
  • Geometric regularity estimates for fully nonlinear elliptic equations with free boundaries
    Math. Nachr. (IF 0.91) Pub Date : 2020-10-05
    João Vitor da Silva; Raimundo Alves Leitão Júnior; Gleydson Chaves Ricarte

    In this manuscript we study geometric regularity estimates for problems driven by fully nonlinear elliptic operators (which can be either degenerate or singular when “the gradient is small”) under strong absorption conditions of the general form: G ( x , D u , D 2 u ) = f ( u ) χ { u > 0 } in Ω , where the mapping u ↦ f ( u ) fails to decrease fast enough at the origin, so allowing that nonnegative

    更新日期:2020-10-05
  • Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I
    Math. Nachr. (IF 0.91) Pub Date : 2020-10-05
    Adrian Vasiu

    We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic (0, p). As a first application we provide a smooth solution (answer) to a conjecture (question) of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic (0, p) of integral canonical

    更新日期:2020-10-05
  • Direct limits of regular Lie groups
    Math. Nachr. (IF 0.91) Pub Date : 2020-10-03
    Helge Glöckner

    Let G be a regular Lie group which is a directed union of regular Lie groups G i (all modelled on possibly infinite‐dimensional, locally convex spaces). We show that G = lim ⟶ G i as a regular Lie group if G admits a so‐called direct limit chart. Notably, this allows the regular Lie group Diff c ( M ) of compactly supported diffeomorphisms to be interpreted as a direct limit of the regular Lie groups

    更新日期:2020-10-04
  • Noncompact quasi‐Einstein manifolds conformal to a Euclidean space
    Math. Nachr. (IF 0.91) Pub Date : 2020-09-28
    Ernani Ribeiro Jr; Keti Tenenblat

    The goal of this article is to investigate nontrivial m‐quasi‐Einstein manifolds globally conformal to an n‐dimensional Euclidean space. By considering such manifolds, whose conformal factors and potential functions are invariant under the action of an ( n − 1 ) ‐dimensional translation group, we provide a complete classification when λ = 0 and m ≥ 1 or m = 2 − n .

    更新日期:2020-09-29
  • Heat kernels and regularity for rough metrics on smooth manifolds
    Math. Nachr. (IF 0.91) Pub Date : 2020-09-28
    Lashi Bandara; Paul Bryan

    We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Hölder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.

    更新日期:2020-09-29
  • Ricci η‐recurrent real hypersurfaces in 2‐dimensional nonflat complex space forms
    Math. Nachr. (IF 0.91) Pub Date : 2020-09-28
    Yaning Wang

    Let M be a Hopf hypersurface in a nonflat complex space form M 2 ( c ) , c ≠ 0 , of complex dimension two. In this paper, we prove that M has η‐recurrent Ricci operator if and only if it is locally congruent to a homogeneous real hypersurface of type (A) or (B) or a non‐homogeneous real hypersurface with vanishing Hopf principal curvature. This is an extension of main results in [17, 21] for real hypersurfaces

    更新日期:2020-09-29
  • Focusing nonlinear Hartree equation with inverse‐square potential
    Math. Nachr. (IF 0.91) Pub Date : 2020-09-21
    Yu Chen; Jing Lu; Fanfei Meng

    In this paper, we consider the scattering theory of the radial solution to focusing energy‐subcritical Hartree equation with inverse‐square potential in the energy space H 1 ( R d ) using the method from [4]. The main difficulties are the equation is not space‐translation invariant and the nonlinearity is non‐local. Using the radial Sobolev embedding and a virial‐Morawetz type estimate we can exclude

    更新日期:2020-09-21
  • Critical point equation and closed conformal vector fields
    Math. Nachr. (IF 0.91) Pub Date : 2020-09-21
    J. F. da Silva Filho

    In this article, we study the critical points of the total scalar curvature functional restricted to the space of metrics with constant scalar curvature of unitary volume, for simplicity, CPE metrics. Here, we prove that a CPE metric admitting a non‐trivial closed conformal vector field must be isometric to a round sphere metric, which provides a partial answer to the CPE conjecture.

    更新日期:2020-09-21
  • Remarks on solitons for inverse mean curvature flow
    Math. Nachr. (IF 0.91) Pub Date : 2020-09-21
    Daehwan Kim; Juncheol Pyo

    Homothetic and translating solitons for the inverse mean curvature flow (IMCF) in R n + 1 are self‐similar solutions deformed by only homothety and translation under IMCF, respectively. In this paper, we address some geometric properties of these solitons. To be specific, the incompleteness for the homothetic soliton of velocity C with 0 < C < 1 n and for any translating soliton are proved. In addition

    更新日期:2020-09-21
  • Finsler Hardy inequalities
    Math. Nachr. (IF 0.91) Pub Date : 2020-09-17
    Anna Mercaldo; Megumi Sano; Futoshi Takahashi

    In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the non‐attainability of the constants in the inequalities are also proved.

    更新日期:2020-09-18
  • Stability of the radially symmetric stationary wave of the Burgers equation with multi‐dimensional initial perturbations in exterior domain
    Math. Nachr. (IF 0.91) Pub Date : 2020-09-15
    Itsuko Hashimoto

    The present paper is concerned with stability of the stationary solution of the Burgers equation in exterior domains in R n . In the previous papers [5, 6, 7] the asymptotic behavior of radially symmetric solutions for the multi‐dimensional Burgers equation in exterior domains in R n , n ≥ 3 , has been considered. The results [5, 6, 7] are restricted to stability of radially solutions within the class

    更新日期:2020-09-15
  • Littlewood–Paley–Stein operators on Damek–Ricci spaces
    Math. Nachr. (IF 0.91) Pub Date : 2020-09-11
    Anestis Fotiadis; Effie Papageorgiou

    We obtain pointwise upper bounds on the derivatives of the heat kernel on Damek–Ricci spaces and we study the L p ‐boundedness of Littlewood–Paley–Stein operators.

    更新日期:2020-09-11
  • Pullbacks of universal Brill–Noether classes via Abel–Jacobi morphisms
    Math. Nachr. (IF 0.91) Pub Date : 2020-09-09
    Nicola Pagani; Andrea T. Ricolfi; Jason van Zelm

    Following Mumford and Chiodo, we compute the Chern character of the derived pushforward ch ( R • π * O ( D ) ) , for D an arbitrary element of the Picard group of the universal curve over the moduli stack of stable marked curves. This allows us to express the pullback of universal Brill–Noether classes via Abel–Jacobi sections to the compactified universal Jacobians, for all compactifications such

    更新日期:2020-09-10
  • Higher differentiability for solutions of stationary p‐Stokes systems
    Math. Nachr. (IF 0.91) Pub Date : 2020-08-31
    Flavia Giannetti; Antonia Passarelli di Napoli; Christoph Scheven

    We consider weak solutions ( u , π ) : Ω → R n × R to stationary p‐Stokes systems of the type − div a ( x , E u ) + ∇ π + [ D u ] u = f , div u = 0 in Ω ⊂ R n , where the function a ( x , ξ ) satisfies p‐growth conditions in ξ and depends Hölder continuously on x. By E u we denote the symmetric part of the gradient D u and we write [ D u ] u for the convective term. In this setting, we establish results

    更新日期:2020-09-01
  • On a transmission problem for equation and dynamic boundary condition of Cahn–Hilliard type with nonsmooth potentials
    Math. Nachr. (IF 0.91) Pub Date : 2020-08-31
    Pierluigi Colli; Takeshi Fukao; Hao Wu

    This paper is concerned with well‐posedness of the Cahn–Hilliard equation subject to a class of new dynamic boundary conditions. The system was recently derived in Liu–Wu (Arch. Ration. Mech. Anal. 233 (2019), 167–247) via an energetic variational approach and it naturally fulfils three physical constraints such as mass conservation, energy dissipation and force balance. The target problem examined

    更新日期:2020-08-31
  • Dual characterization of fractional capacity via solution of fractional p‐Laplace equation
    Math. Nachr. (IF 0.91) Pub Date : 2020-08-31
    Shaoguang Shi; Lei Zhang

    In terms of weak solutions of the fractional p‐Laplace equation with measure data, this paper offers a dual characterization for the fractional Sobolev capacity on bounded domain. In addition, two further results are given: one is an equivalent estimate for the fractional Sobolev capacity; the other is the removability of sets of zero capacity and its relation to solutions of the fractional p‐Laplace

    更新日期:2020-08-31
  • Sectorial extensions for ultraholomorphic classes defined by weight functions
    Math. Nachr. (IF 0.91) Pub Date : 2020-08-26
    J. Jiménez‐Garrido; J. Sanz; Gerhard Schindl

    We prove an extension theorem for ultraholomorphic classes defined by so‐called Braun–Meise–Taylor weight functions ω and transfer the proofs from the single weight sequence case from V. Thilliez to the weight function setting. We are following a different approach than the results obtained in a recent paper by the authors, more precisely we are working with real methods by applying the ultradifferentiable

    更新日期:2020-08-27
  • Holomorphic symmetric differentials and a birational characterization of abelian varieties
    Math. Nachr. (IF 0.91) Pub Date : 2020-08-20
    Ernesto C. Mistretta

    A generically generated vector bundle on a smooth projective variety yields a rational map to a Grassmannian, called Kodaira map. We answer a previous question, raised by the asymptotic behaviour of such maps, giving rise to a birational characterization of abelian varieties. In particular we prove that, under the conjectures of the Minimal Model Program, a smooth projective variety is birational to

    更新日期:2020-08-21
  • Compactness and dichotomy in nonlocal shape optimization
    Math. Nachr. (IF 0.91) Pub Date : 2020-08-17
    E. Parini; A. Salort

    We prove a general result about the behaviour of minimizing sequences for nonlocal shape functionals satisfying suitable structural assumptions. Typical examples include functions of the eigenvalues of the fractional Laplacian under homogeneous Dirichlet boundary conditions. Exploiting a nonlocal version of Lions' concentration‐compactness principle, we prove that either an optimal shape exists or

    更新日期:2020-08-18
  • Hardy spaces for the Dunkl harmonic oscillator
    Math. Nachr. (IF 0.91) Pub Date : 2020-08-09
    Agnieszka Hejna

    Let Δ and L = Δ − ∥ x ∥ 2 be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space H 1 associated with the Dunkl harmonic oscillator by means of the nontangential maximal function with respect to the semigroup e t L . We prove that the space H 1 admits characterizations by relevant Riesz transforms and atomic decompositions. The atoms which occur in the atomic

    更新日期:2020-08-10
  • Aluthge transforms of unbounded weighted composition operators in L2‐spaces
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-26
    Chafiq Benhida; Piotr Budzyński; Jacek Trepkowski

    We describe the Aluthge transform of an unbounded weighted composition operator acting in an L2‐space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize p‐hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation

    更新日期:2020-07-26
  • Improvements on Sawyer type estimates for generalized maximal functions
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-23
    Fabio Berra; Marilina Carena; Gladis Pradolini

    In this paper we prove mixed inequalities for the maximal operator M Φ , for general Young functions Φ with certain additional properties, improving and generalizing some previous estimates for the Hardy–Littlewood maximal operator proved by E. Sawyer. We show that given r ≥ 1 , if u , v r are weights belonging to the A1‐Muckenhoupt class and Φ is a Young function as above, then the inequality u v

    更新日期:2020-07-23
  • Entropy for semigroup actions on general topological spaces
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-23
    Josiney A. Souza; Alexandre J. Santana

    This paper introduces both notions of topological entropy and invariance entropy for semigroup actions on general topological spaces. We use the concept of admissible family of open coverings to extending and studying the notions of Adler–Konheim–McAndrew topological entropy, Bowen topological entropy, and invariance entropy to the general theory of topological dynamics.

    更新日期:2020-07-23
  • A note on the polynomial decay of a weakly dissipative viscoelastic system
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-16
    Jamilu Hashim Hassan; Salim A. Messaoudi

    In this note we study an abstract class of weakly dissipative second‐order systems with finite memory. We establish the polynomial decay of Rivera, Naso and Vegni for the solution of the system under a very weak condition on the relaxation function.

    更新日期:2020-07-16
  • Littlewood–Paley characterization of BMO and Triebel–Lizorkin spaces
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-15
    Anton Tselishchev; Ioann Vasilyev

    We prove a generalization of the Littlewood–Paley characterisation of the BMO space where the shifts of a Schwartz function are replaced by a family of functions with suitable conditions imposed on them. We also prove that a certain family of Triebel–Lizorkin spaces can be characterized in a similar way.

    更新日期:2020-07-15
  • Triangular representations of functions of operators with Schatten–von Neumann Hermitian components
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-13
    Michael Gil'

    Let H be a separable Hilbert space with the unit operator I, let A be a bounded linear operator in H with a Schatten–von Neumann Hermitian component ( A − A ∗ ) / 2 i ( A ∗ means the operator adjoint to A) and let f ( z ) be a function analytic on the spectra of A and A ∗ . For f ( A ) we obtain the representation in the form of the sum of a normal operator and a quasi‐nilpotent Schatten–von Neumann

    更新日期:2020-07-13
  • Fractional Cauchy problem with memory effects
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-13
    Luciano Abadias; Edgardo Alvarez

    We give an original representation integral formula for the resolvent families associated to the fractional Cauchy equation with memory effects C D t α u ( t ) − A u ( t ) + ∫ 0 t β ( t − s ) A u ( s ) d s = f ( t , u ( t ) ) , t ∈ [ 0 , T ] , T > 0 , where u ( 0 ) = u 0 ∈ X and A is a sectorial operator on a Banach space X. Moreover, we get spatial bounds for the resolvent families in order to study

    更新日期:2020-07-13
  • g‐natural symmetries on tangent bundles
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-08
    Mohamed Tahar Kadaoui Abbassi; Noura Amri; Giovanni Calvaruso

    The study of symmetries is a well known research topic in differential geometry with relevant physical interpretations. Given a Riemannian manifold ( M , g ) , we consider pseudo‐Riemannian g‐natural metrics G on its tangent bundle T M and characterize conformal, homothetic and Killing vector fields of ( T M , G ) obtained from natural lifts of vector fields of M.

    更新日期:2020-07-08
  • Graphs encoding the generating properties of a finite group
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-08
    Cristina Acciarri, Andrea Lucchini

    Assume that G is a finite group. For every a , b ∈ N , we define a graph Γ a , b ( G ) whose vertices correspond to the elements of G a ∪ G b and in which two tuples ( x 1 , ⋯ , x a ) and ( y 1 , ⋯ , y b ) are adjacent if and only if ⟨ x 1 , ⋯ , x a , y 1 , ⋯ , y b ⟩ = G . We study several properties of these graphs (isolated vertices, loops, connectivity, diameter of the connected components) and

    更新日期:2020-07-08
  • The asymptotic behavior for anisotropic parabolic p‐Laplacian equations
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-07
    Chenyin Qian; Daorui Yuan

    The global existence and asymptotic behavior for anisotropic parabolic equation in R n are considered. By using the classical Galerkin approximation and suitable conditions on the weighted function, it is obtained the global estimate and the uniformly estimates for the global weak solution. Besides, the L 2 ( R n ) ∩ L r ( R n ) global attractor for anisotropic parabolic p‐Laplacian equation is also

    更新日期:2020-07-07
  • Depth and extremal Betti number of binomial edge ideals
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-07
    Arvind Kumar, Rajib Sarkar

    Let G be a simple graph on the vertex set [n] and let J G be the corresponding binomial edge ideal. Let G = v ∗ H be the cone of v on H. In this article, we compute all the Betti numbers of J G in terms of the Betti numbers of J H and as a consequence, we get the Betti diagram of wheel graph. Also, we study Cohen–Macaulay defect of S / J G in terms of Cohen–Macaulay defect of S H / J H and using this

    更新日期:2020-07-07
  • A simpler description of the κ‐topologies on the spaces DLp,Lp,M1
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-06
    Christian Bargetz, Eduard A. Nigsch, Norbert Ortner

    For the spaces D L p , L p and M 1 , we consider the topology of uniform convergence on absolutely convex compact subsets of their (pre‐)dual space. Following the notation of J. Horváth's book we call these topologies κ‐topologies. They are given by a neighbourhood basis consisting of polars of absolutely convex and compact subsets of their (pre‐)dual spaces. In many cases it is more convenient to

    更新日期:2020-07-06
  • Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-06
    Wencai Liu

    For perturbed Stark operators H u = − u ′ ′ − x u + q u , the author has proved that lim sup x → ∞ x 1 2 | q ( x ) | must be larger than 1 2 N 1 2 in order to create N linearly independent eigensolutions in L 2 ( R + ) [29]. In this paper, we apply generalized Wigner–von Neumann type functions to construct embedded eigenvalues for a class of Schrödinger operators, including a proof that the bound 1

    更新日期:2020-07-06
  • Multiple solutions for superlinear Klein–Gordon–Maxwell equations†
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-02
    Dong‐Lun Wu, Hongxia Lin

    In this paper, we consider the following Klein–Gordon–Maxwell equations − Δ u + V ( x ) u − ( 2 ω + ϕ ) ϕ u = f ( x , u ) + h ( x ) in R 3 , − Δ ϕ + ϕ u 2 = − ω u 2 in R 3 , where ω > 0 is a constant, u, ϕ : R 3 → R , V : R 3 → R is a potential function. By assuming the coercive condition on V and some new superlinear conditions on f, we obtain two nontrivial solutions when h is nonzero and infinitely

    更新日期:2020-07-02
  • Weighted operator least squares problems and the J‐trace in Krein spaces
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-29
    Maximiliano Contino, Alejandra Maestripieri, Stefania Marcantognini

    Given B , C and W operators in the algebra L ( H ) of bounded linear operators on the Krein space H , the minimization problem min ( B X − C ) # W ( B X − C ) , for X ∈ L ( H ) , is studied when the weight W is selfadjoint. The analogous maximization and min‐max problems are also considered. Complete answers to these problems and to those naturally associated to trace clase operators on Krein spaces

    更新日期:2020-06-29
  • Revisiting the Gross–Zagier discriminant formula
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-24
    Dongxi Ye

    We derive a formula for the discriminant of the ring class polynomial of conductor N associated to the j‐invariant and an imaginary quadratic field of odd discriminant − d using the theory of Borcherds lifts. When d is a prime and N = 1 , the formula recovers the Gross–Zagier discriminant formula.

    更新日期:2020-06-24
  • Ergodicity for neutral type SDEs with infinite length of memory
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-24
    Jianhai Bao, Feng‐Yu Wang, Chenggui Yuan

    In this paper, the weak Harris theorem developed in [18] is illustrated by using a straightforward Wasserstein coupling, which implies the exponential ergodicity of the functional solutions to a range of neutral type SDEs with infinite length of memory. A concrete example is presented to illustrate the main result.

    更新日期:2020-06-24
  • Nef‐partitions arising from unimodular configurations
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-22
    Hidefumi Ohsugi, Akiyoshi Tsuchiya

    Reflexive polytopes have been studied from viewpoints of combinatorics, commutative algebra and algebraic geometry. A nef‐partition of a reflexive polytope P is a decomposition P = P 1 + ⋯ + P r such that each P i is a lattice polytope containing the origin. Batyrev and van Straten gave a combinatorial method for explicit constructions of mirror pairs of Calabi–Yau complete intersections obtained from

    更新日期:2020-06-22
  • Erratum to the paper “Quadratic descent of hermitian forms”
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-22
    A.‐H. Nokhodkar

    There exists a mistake in the proof of Theorem 4.2. We present a new proof of this theorem, which shows that the main results of the paper are still true.

    更新日期:2020-06-22
  • Parallel and totally geodesic hypersurfaces of non‐reductive homogeneous four‐manifolds
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-21
    Giovanni Calvaruso, Reinier Storm, Joeri Van der Veken

    We classify totally geodesic and parallel hypersurfaces of four‐dimensional non‐reductive homogeneous pseudo‐Riemannian manifolds.

    更新日期:2020-06-21
  • On Bohr's theorem for general Dirichlet series
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-17
    I. Schoolmann

    We present quantitative versions of Bohr's theorem on general Dirichlet series D = ∑ a n e − λ n s assuming different assumptions on the frequency λ = ( λ n ) , including the conditions introduced by Bohr and Landau. Therefore, using the summation method by typical (first) means invented by M. Riesz, without any condition on λ, we give upper bounds for the norm of the partial sum operator S N ( D )

    更新日期:2020-06-17
  • A classification of surfaces with isotropic Para‐Blaschke tensor
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-15
    Fengjiang Li, Jianbo Fang, Jianxiang Li

    Let M 2 → S 3 be an umbilic‐free surface. Four basic invariants of M2 under the Möbius transformation group of S 3 are the Möbius metric g, the Blaschke tensor A, the Möbius second fundamental form B and the Möbius form Φ. A symmetric (0,2) tensor D = A + μ B called Para‐Blaschke tensor, where μ is constant, is also Möbius invariant. In this paper, we classify the surfaces with isotropic Para‐Blaschke

    更新日期:2020-06-15
  • Advection‐diffusion dynamics with nonlinear boundary flux as a model for crystal growth
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-15
    Antoine Pauthier, Arnd Scheel

    We analyze the effect of nonlinear boundary conditions on an advection‐diffusion equation on the half‐line. Our model is inspired by models for crystal growth where diffusion models diffusive relaxation of a displacement field, advection is induced by apical growth, and boundary conditions incorporate non‐adiabatic effects on displacement at the boundary. The equation, in particular the boundary fluxes

    更新日期:2020-06-15
  • Coarse homotopy groups
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-14
    Paul D. Mitchener, Behnam Norouzizadeh, Thomas Schick

    In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse homotopy groups. The main result is that the coarse homotopy groups of a cone over a compact simplicial complex coincide with the usual homotopy groups of the underlying

    更新日期:2020-06-14
  • A p‐adic analogue of Siegel's theorem on sums of squares
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-08
    Sylvy Anscombe, Philip Dittmann, Arno Fehm

    Siegel proved that every totally positive element of a number field K is the sum of four squares, so in particular the Pythagoras number is uniformly bounded across number fields. The p‐adic Kochen operator provides a p‐adic analogue of squaring, and a certain localisation of the ring generated by this operator consists of precisely the totally p‐integral elements of K. We use this to formulate and

    更新日期:2020-06-08
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