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Asymptotics for a parabolic problem of Kirchhoff type with singular critical exponential nonlinearity Math. Nachr. (IF 1.0) Pub Date : 2024-04-22 Tahir Boudjeriou
The main objective of this paper is to characterize stable sets based on the asymptotic behavior of solutions as goes to infinity for the following class of parabolic Kirchhoff equations: where is a bounded domain with a Lipschitz boundary, , , , , , and is the fractional ‐Laplacian operator, .
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Two‐weight extrapolation on function spaces and applications Math. Nachr. (IF 1.0) Pub Date : 2024-04-22 Mingming Cao, Andrea Olivo
This paper is devoted to studying the extrapolation theory of Rubio de Francia on general function spaces. We present endpoint extrapolation results including , , and extrapolation in the context of Banach function spaces, and also on modular spaces. We also include several applications that can be easily obtained using extrapolation: local decay estimates for various operators, Coifman–Fefferman inequalities
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On varieties whose general surface section has negative Kodaira dimension Math. Nachr. (IF 1.0) Pub Date : 2024-04-19 Ciro Ciliberto, Claudio Fontanari
In this paper, inspired by work of Fano, Morin, and Campana–Flenner, we give a projective classification of varieties of dimension 3 whose general hyperplane sections have negative Kodaira dimension, and we partly extend such a classification to varieties of dimension whose general surface sections have negative Kodaira dimension. In particular, we prove that a variety of dimension whose general surface
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Erratum to “A footnote to a theorem of Kawamata” Math. Nachr. (IF 1.0) Pub Date : 2024-04-19 Osamu Fujino, Margarida Mendes Lopes, Rita Pardini, Sofia Tirabassi
We give an alternative proof of Theorem A in the paper: Mendes Lopes, Pardini, Tirabassi, A footnote to a theorem of Kawamata. We also explain how to fill a gap in the original proof.
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Analytic Nullstellensätze and the model theory of valued fields Math. Nachr. (IF 1.0) Pub Date : 2024-04-15 Matthias Aschenbrenner, Ahmed Srhir
We present a uniform framework for establishing Nullstellensätze for power series rings using quantifier elimination results for valued fields. As an application, we obtain Nullstellensätze for ‐adic power series (both formal and convergent) analogous to Rückert's complex and Risler's real Nullstellensatz, as well as a ‐adic analytic version of Hilbert's 17th Problem. Analogous statements for restricted
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Groups having minimal covering number 2 of the diagonal type Math. Nachr. (IF 1.0) Pub Date : 2024-04-15 Marco Fusari, Andrea Previtali, Pablo Spiga
Garonzi and Lucchini explored finite groups possessing a normal 2‐covering, where no proper quotient of exhibits such a covering. Their investigation offered a comprehensive overview of these groups, delineating that such groups fall into distinct categories: almost simple, affine, product action, or diagonal.In this paper, we focus on the family falling under the diagonal type. Specifically, we present
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Nonsymmetric Lévy‐type operators Math. Nachr. (IF 1.0) Pub Date : 2024-04-11 Jakub Minecki, Karol Szczypkowski
We present a general approach to the parametrix construction. We apply it to prove the uniqueness and existence of a weak fundamental solution for the equation with nonsymmetric nonlocal operators under certain assumptions on , , and . The result allows more general coefficients even for .
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Geometric and analytic results for Einstein solitons Math. Nachr. (IF 1.0) Pub Date : 2024-04-10 Enrique F. L. Agila, José N. V. Gomes
We compute a lower bound for the scalar curvature of a gradient Einstein soliton under a certain assumption on its potential function. We establish an asymptotic behavior of the potential function on a noncompact gradient shrinking Einstein soliton. As a result, we obtain the finiteness of its fundamental group and its weighted volume. We also prove some geometric and analytic results for constructing
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On some properties of generalized squeezing functions and Fridman invariants Math. Nachr. (IF 1.0) Pub Date : 2024-04-08 Shichao Yang, Shuo Zhang
The purpose of this paper is twofold. The first aim is to study the comparison of generalized squeezing functions and Fridaman invariants of some special domains. Then, the second aim is to give estimates for these two invariants and discuss their boundary behavior near inessential boundary points.
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On noncompact warped product Ricci solitons Math. Nachr. (IF 1.0) Pub Date : 2024-04-06 V. Borges
The goal of this paper is to investigate complete noncompact warped product gradient Ricci solitons. Nonexistence results, estimates for the warping function and for its gradient are proven. When the soliton is steady or expanding these nonexistence results generalize to a broader context certain estimates and rigidity obtained when studying warped product Einstein manifolds. When the soliton is shrinking
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The boundedness of operators on weighted multi‐parameter mixed Hardy spaces Math. Nachr. (IF 1.0) Pub Date : 2024-04-03 Wei Ding, Min Gu, YuePing Zhu
In this paper, we discuss the boundedness of mixed Journé's class operators on weighted multi‐parameter mixed Hardy spaces via atoms decomposition. Moreover, we give a specific singular integral operator in mixed Journé's class which has better properties.
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Endpoint estimates for harmonic analysis operators associated with Laguerre polynomial expansions Math. Nachr. (IF 1.0) Pub Date : 2024-03-28 Jorge J. Betancor, Estefanía Dalmasso, Pablo Quijano, Roberto Scotto
In this paper, we give a criterion to prove boundedness results for several operators from the Hardy‐type space to and also from to the space of functions of bounded mean oscillation , with respect to the probability measure on when is a multi‐index in . We shall apply it to establish endpoint estimates for Riesz transforms, maximal operators, Littlewood–Paley functions, multipliers of the Laplace
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Kirchhoff-type critical fractional Laplacian system with convolution and magnetic field Math. Nachr. (IF 1.0) Pub Date : 2024-03-27 Sihua Liang, Binlin Zhang
In this paper, we consider a class of upper critical Kirchhoff-type fractional Laplacian system with Choquard nonlinearities and magnetic fields. With the help of the limit index theory and the concentration–compactness principles for fractional Sobolev spaces, we establish the existence of infinitely many nontrivial radial solutions for the above system. A distinguished feature of this paper is that
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On a class of doubly nonlinear evolution equations in Musielak–Orlicz spaces Math. Nachr. (IF 1.0) Pub Date : 2024-03-27 Goro Akagi, Giulio Schimperna
This paper is concerned with a parabolic evolution equation of the form , settled in a smooth bounded domain of , , and complemented with the initial conditions and with (for simplicity) homogeneous Dirichlet boundary conditions. Here, stands for a diffusion operator, possibly nonlinear, which may range in a very wide class, including the Laplacian, the ‐Laplacian for suitable , the “variable‐exponent”
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On rank 3 instanton bundles on P3$\mathbb {P}^3$ Math. Nachr. (IF 1.0) Pub Date : 2024-03-23 A. V. Andrade, D. R. Santiago, D. D. Silva, L. C. S. Sobral
We investigate rank 3 instanton vector bundles on of charge and its correspondence with rational curves of degree . For , we present a correspondence between stable rank 3 instanton bundles and stable rank 2 reflexive linear sheaves of Chern classes and we use this correspondence to compute the dimension of the family of stable rank 3 instanton bundles of charge 2. Finally, we use the results above
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The W(E6)$W(E_6)$‐invariant birational geometry of the moduli space of marked cubic surfaces Math. Nachr. (IF 1.0) Pub Date : 2024-03-23 Nolan Schock
The moduli space of marked cubic surfaces is one of the most classical moduli spaces in algebraic geometry, dating back to the nineteenth‐century work of Cayley and Salmon. Modern interest in was restored in the 1980s by Naruki's explicit construction of a ‐equivariant smooth projective compactification of , and in the 2000s by Hacking, Keel, and Tevelev's construction of the Kollár–Shepherd‐Barron–Alexeev
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Second‐order trace formulas Math. Nachr. (IF 1.0) Pub Date : 2024-03-23 Arup Chattopadhyay, Soma Das, Chandan Pradhan
Koplienko [Sib. Mat. Zh. 25 (1984), 62–71; English transl. in Siberian Math. J. 25 (1984), 735–743] found a trace formula for perturbations of self‐adjoint operators by operators of Hilbert–Schmidt class . Later, Neidhardt introduced a similar formula in the case of pairs of unitaries via multiplicative path in [Math. Nachr. 138 (1988), 7–25]. In 2012, Potapov and Sukochev [Comm. Math. Phys. 309 (2012)
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Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts Math. Nachr. (IF 1.0) Pub Date : 2024-03-23 Yuri Latushkin, Alin Pogan
We study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the resolvent operators of the generators along vertical segments to estimate the growth/decay rate of the
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Equivariant K$K$‐theory of flag Bott manifolds of general Lie type Math. Nachr. (IF 1.0) Pub Date : 2024-03-23 Bidhan Paul, Vikraman Uma
The aim of this paper is to describe the equivariant and ordinary Grothendieck ring and the equivariant and ordinary topological ‐ring of flag Bott manifolds of the general Lie type. This will generalize the results on the equivariant and ordinary cohomology of flag Bott manifolds of the general Lie type due to Kaji, Kuroki, Lee, and Suh.
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Normalized solutions to nonlinear Schrödinger equations with competing Hartree‐type nonlinearities Math. Nachr. (IF 1.0) Pub Date : 2024-03-13 Divyang Bhimani, Tianxiang Gou, Hichem Hajaiej
In this paper, we consider solutions to the following nonlinear Schrödinger equation with competing Hartree‐type nonlinearities, under the ‐norm constraint where , , and appearing as Lagrange multiplier is unknown. First, we establish the existence of ground states in the mass subcritical, critical, and supercritical cases. Then, we consider the well‐posedness and dynamical behaviors of solutions to
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Effects of indirect signal absorption in the chemotaxis system involving singularly signal‐dependent motilities Math. Nachr. (IF 1.0) Pub Date : 2024-03-13 Yan Li, Jiaqi Wang, Fei Pan
We consider the initial‐boundary problem of the chemotaxis system with indirect consumption in a smoothly bounded domain with . It is shown that for all suitably regular initial data, global solvability in classical sense can be established even with singularly signal‐dependent motilities involved. To be specific, the global classical solution is constructed for arbitrary .
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Convexity properties of Yoshikawa–Sparr interpolation spaces Math. Nachr. (IF 1.0) Pub Date : 2024-03-13 Karol Aleksandrowicz, Stanisław Prus
We study stability of the three geometric properties: uniform convexity, nearly uniform convexity, and property under the Yoshikawa–Sparr interpolation method when the resulting interpolation space is considered with various equivalent norms. We give an example which shows that interpolation spaces obtained by the discrete and continuous versions of the method need not be isometric and present a method
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Complete real Kähler submanifolds Math. Nachr. (IF 1.0) Pub Date : 2024-03-12 A. de Carvalho
Let denote an isometric immersion of a Kähler manifold with complex dimension into Euclidean space with codimension . We show that generic rank conditions on the second fundamental form of a non‐minimal complete real Kähler submanifold imply that is a cylinder over a real Kähler submanifold .
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Ergodic properties of multiplication and weighted composition operators on spaces of holomorphic functions Math. Nachr. (IF 1.0) Pub Date : 2024-03-12 Daniel Santacreu
We obtain different results about the mean ergodicity of weighted composition operators when acting on the spaces , , and , where is the open unit ball of a Banach space, as well as about the compactness and the mean ergodicity of the multiplication operator. This study relates these properties of the operators with properties of the symbol and the weight defining such operators.
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K3 surfaces with a symplectic automorphism of order 4 Math. Nachr. (IF 1.0) Pub Date : 2024-03-12 Benedetta Piroddi
Given , a K3 surface admitting a symplectic automorphism of order 4, we describe the isometry on . Having called and , respectively, the minimal resolutions of the quotient surfaces and , we also describe the maps induced in cohomology by the rational quotient maps and : With this knowledge, we are able to give a lattice‐theoretic characterization of , and find the relation between the Néron–Severi
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On the completeness of root function system of the Dirac operator with two‐point boundary conditions Math. Nachr. (IF 1.0) Pub Date : 2024-03-06 Alexander Makin
The paper is concerned with the completeness property of root functions of the Dirac operator with summable complex‐valued potential and nonregular boundary conditions. We also obtain an explicit form for the fundamental solution system of the considered operator.
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On the structure of Nevanlinna measures Math. Nachr. (IF 1.0) Pub Date : 2024-03-04 Mitja Nedic, Eero Saksman
In this paper, we study the structural properties of Nevanlinna measures, that is, Borel measures that arise in the integral representation of Herglotz–Nevanlinna functions. In particular, we give a characterization of these measures in terms of their Fourier transform, characterize measures supported on hyperplanes including extremal measures, describe the structure of the singular part of the measures
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Global existence for nonlocal quasilinear diffusion systems in nonisotropic nondivergence form Math. Nachr. (IF 1.0) Pub Date : 2024-03-04 Catharine W. K. Lo, José Francisco Rodrigues
We consider the quasilinear diffusion problem of for an open set , , for , and any . Here, denotes an operator which may involve the distributional Riesz fractional gradient of order , with , the classical gradient or/and nonlocal derivatives , with . We show global existence results for various quasilinear diffusion systems in nondivergence form for linear elliptic operators , including classical
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Totally geodesic Lagrangian submanifolds of the pseudo‐nearly Kähler SL(2,R)×SL(2,R)$\mathrm{SL}(2,\mathbb {R})\times \mathrm{SL}(2,\mathbb {R})$ Math. Nachr. (IF 1.0) Pub Date : 2024-03-04 Mateo Anarella, J. Van der Veken
In this paper, we study Lagrangian submanifolds of the pseudo‐nearly Kähler . First, we show that they split into four different classes depending on their behavior with respect to a certain almost product structure on the ambient space. Then, we give a complete classification of totally geodesic Lagrangian submanifolds of this space.
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Extrapolation to mixed Herz spaces and its applications Math. Nachr. (IF 1.0) Pub Date : 2024-03-04 Mingquan Wei
In this paper, we extend the extrapolation theory to mixed Herz spaces and . To prove the main result, we first study the dual spaces of mixed Herz spaces, and then give the boundedness of the Hardy–Littlewood maximal operator on mixed Herz spaces. By using the extrapolation theorems, we obtain the boundedness of many integral operators on mixed Herz spaces. We also give a new characterization of via
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The Metivier inequality and ultradifferentiable hypoellipticity Math. Nachr. (IF 1.0) Pub Date : 2024-02-28 Paulo D. Cordaro, Stefan Fürdös
In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of ‐solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when the solutions can be taken as hyperfunctions and present some
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On the zero set of the holomorphic sectional curvature Math. Nachr. (IF 1.0) Pub Date : 2024-02-28 Yongchang Chen, Gordon Heier
A notable example due to Heier, Lu, Wong, and Zheng shows that there exist compact complex Kähler manifolds with ample canonical line bundle such that the holomorphic sectional curvature is negative semi‐definite and vanishes along high‐dimensional linear subspaces in every tangent space. The main result of this note is an upper bound for the dimensions of these subspaces. Due to the holomorphic sectional
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Energy behavior for Sobolev solutions to viscoelastic damped wave models with time‐dependent oscillating coefficient Math. Nachr. (IF 1.0) Pub Date : 2024-02-28 Xiaojun Lu
In this work, we study the asymptotic behavior of the structurally damped wave equations arising from the viscoelastic mechanics. We are particularly interested in the complicated interaction of the time‐dependent oscillating coefficients on the Dirichlet Laplacian operator and the structurally damped terms. On the one hand, by the application of WKB analysis, we explore the asymptotic energy estimates
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Extension and embedding theorems for Campanato spaces on C0,γ$C^{0,\gamma }$ domains Math. Nachr. (IF 1.0) Pub Date : 2024-02-28 Damiano Greco, Pier Domenico Lamberti
We consider Campanato spaces with exponents on domains of class in the N‐dimensional Euclidean space endowed with a natural anisotropic metric depending on . We discuss several results including the appropriate Campanato's embedding theorem and we prove that functions of those spaces can be extended to the whole of the Euclidean space without deterioration of the exponents .
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I‐surfaces from surfaces with one exceptional unimodal point Math. Nachr. (IF 1.0) Pub Date : 2024-02-24 Sönke Rollenske, Diana Torres
We complement recent work of Gallardo, Pearlstein, Schaffler, and Zhang, showing that the stable surfaces with and they construct are indeed the only ones arising from imposing an exceptional unimodal double point.In addition, we explicitly describe the birational type of the surfaces constructed from singularities of type , , .
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The Mullins–Sekerka problem via the method of potentials Math. Nachr. (IF 1.0) Pub Date : 2024-02-24 Joachim Escher, Anca‐Voichita Matioc, Bogdan‐Vasile Matioc
It is shown that the two‐dimensional Mullins–Sekerka problem is well‐posed in all subcritical Sobolev spaces with . This is the first result, where this issue is established in an unbounded geometry. The novelty of our approach is the use of the potential theory to formulate the model as an evolution problem with nonlinearities expressed by singular integral operators.
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Density of smooth functions in Musielak–Orlicz–Sobolev spaces Wk,Φ(Ω)$W^{k,\Phi }(\Omega)$ Math. Nachr. (IF 1.0) Pub Date : 2024-02-24 Anna Kamińska, Mariusz Żyluk
We consider here Musielak–Orlicz–Sobolev (MOS) spaces , where is an open subset of , and is a Musielak–Orlicz function. The main outcomes consist of the results on density of the space of compactly supported smooth functions in . One section is devoted to compare the various conditions on appearing in the literature in the context of maximal operator and density theorems in MOS spaces. The assumptions
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A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities Math. Nachr. (IF 1.0) Pub Date : 2024-02-24 Yulan Wang, Michael Winkler
A no‐flux initial‐boundary value problem for is considered in a ball , where and .Under the assumption that , it is shown that for each , there exist and a positive with the property that whenever is nonnegative with , the global solutions to () emanating from the initial data have the property that
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The strongest Banach–Stone theorem for C0(K,ℓ22)$C_{0}(K, \ell _2^2)$ spaces Math. Nachr. (IF 1.0) Pub Date : 2024-02-22 Elói Medina Galego
As usual denote by the real two‐dimensional Hilbert space. We prove that if K and S are locally compact Hausdorff spaces and T is a linear isomorphism from onto satisfying then K and S are homeomorphic.This theorem is the strongest of all the other vector‐valued Banach–Stone theorems known so far in the sense that in none of them the distortion of the isomorphism T, denoted by , is as large as .Some
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Generalized noncooperative Schrödinger–Kirchhoff–type systems in RN$\mathbb {R}^N$ Math. Nachr. (IF 1.0) Pub Date : 2024-02-22 Nabil Chems Eddine, Dušan D. Repovš
We consider a class of noncooperative Schrödinger–Kirchhof–type system, which involves a general variable exponent elliptic operator with critical growth. Under certain suitable conditions on the nonlinearities, we establish the existence of infinitely many solutions for the problem by using the limit index theory, a version of concentration–compactness principle for weighted‐variable exponent Sobolev
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Littlewood–Paley and wavelet characterization for mixed Morrey spaces Math. Nachr. (IF 1.0) Pub Date : 2024-02-21 Toru Nogayama
In this paper, we consider the Littlewood–Paley characterization for mixed Morrey spaces and its predual spaces. The topology to converge the Littlewood–Paley decomposition for the element of mixed Morrey spaces is the weak‐* topology. If we consider the topology of mixed Morrey spaces, we must give other characterization by using the heat semigroup. As an application, we show the wavelet characterization
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Infinite time blow-up with arbitrary initial energy for a damped plate equation Math. Nachr. (IF 1.0) Pub Date : 2024-02-20 Xiatong Li, Zhong Bo Fang
This paper deals with the infinite blow-up phenomena for a class of damped plate equations with logarithmic nonlinearity under the Navier boundary condition. Combining potential well method and modified differential inequality technique, we establish the infinite blow-up result of solutions with arbitrary initial energy. In particular, it is not necessary to suppose that the initial velocity and the
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On the commuting probability of π-elements in finite groups Math. Nachr. (IF 1.0) Pub Date : 2024-02-15 Juan Martínez
Let G be a finite group, π be a set of primes, and p be the smallest prime in π. In this work, we prove that G possesses a normal and abelian Hall π-subgroup if and only if the probability that two random π-elements of G commute is larger than p2+p−1p3$\frac{p^2+p-1}{p^3}$. We also prove that if x is a π-element not lying in Oπ(G)$O_{\pi }(G)$, then the proportion of π-elements commuting with x is
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Bilinear Θ-type Calderón–Zygmund operators and their commutators on product generalized fractional mixed Morrey spaces Math. Nachr. (IF 1.0) Pub Date : 2024-02-12 Guanghui Lu, Shuangping Tao, Miaomiao Wang
The aim of this paper is to investigate the boundedness of the bilinear θ-type Calderón–Zygmund operator and its commutator on the product of generalized fractional mixed Morrey spaces. Under assumption that the positive and increasing functions φ(·)$\varphi (\cdot)$ defined on [0, ∞) satisfy doubling conditions, we prove that the bilinear θ-type Calderón–Zygmund operator T∼θ$\widetilde{T}_{\theta
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Parallel and totally umbilical hypersurfaces of the four-dimensional Thurston geometry Sol04 Math. Nachr. (IF 1.0) Pub Date : 2024-02-01 Marie D'haene, Jun-ichi Inoguchi, Joeri Van der Veken
We study hypersurfaces of the four-dimensional Thurston geometry Sol 0 4 $\mathrm{Sol}^4_0$ , which is a Riemannian homogeneous space and a solvable Lie group. In particular, we give a full classification of hypersurfaces whose second fundamental form is a Codazzi tensor—including totally geodesic hypersurfaces and hypersurfaces with parallel second fundamental form—and of totally umbilical hypersurfaces
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On Fourier–Mukai type autoequivalences of Kuznetsov components of cubic threefolds Math. Nachr. (IF 1.0) Pub Date : 2024-01-23 Ziqi Liu
We determine the group of all Fourier–Mukai type autoequivalences of Kuznetsov components of smooth complex cubic threefolds, and provide yet another proof for the Fourier–Mukai version of the categorical Torelli theorem for smooth complex cubic threefolds.
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Arithmeticity of the Kontsevich–Zorich monodromies of certain families of square-tiled surfaces II Math. Nachr. (IF 1.0) Pub Date : 2024-01-23 Manuel Kany, Carlos Matheus
In this note, we extend the scope of our previous work joint with Bonnafoux, Kattler, Niño, Sedano-Mendoza, Valdez, and Weitze-Schmithüsen by showing the arithmeticity of the Kontsevich–Zorich monodromies of infinite families of square-tiled surfaces of genera four, five, and six.
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Correction to “Integral Ricci curvature and the mass gap of Di-richlet Laplacians on domains” Math. Nachr. (IF 1.0) Pub Date : 2024-01-12
Xavier Ramos Olivé, Christian Rose, Lili Wang, Guofang Wei. Integral Ricci curvature and the mass gap of Di-richlet Laplacians on domains. Math. Nachr. 296 (2023), no. 8, 3559–3578. The “funding information” on the first page of the article is incomplete: Lili Wang has been also supported by NSFC grant number 12111025.
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Global integrability for solutions to quasilinear elliptic systems with degenerate coercivity Math. Nachr. (IF 1.0) Pub Date : 2024-01-11 Ya Li, Gaoyang Liu, Hongya Gao
This paper deals with global integrability for solutions to quasilinear elliptic systems involving N equations of the form
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Cohomological connectivity of perturbations of map-germs Math. Nachr. (IF 1.0) Pub Date : 2024-01-03 Yongqiang Liu, Guillermo Peñafort Sanchis, Matthias Zach
Let f : ( C n , S ) → ( C p , 0 ) $f: (\mathbb {C}^n,S)\rightarrow (\mathbb {C}^p,0)$ be a finite map-germ with n < p $n
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Kadec–Klee property with respect to the local convergence in measure of Orlicz–Lorentz spaces Math. Nachr. (IF 1.0) Pub Date : 2024-01-02 Paweł Foralewski, Joanna Kończak
In this paper, we find criteria for the Kadec–Klee property with respect to the local convergence in measure in both Orlicz–Lorentz spaces as well as their subspaces of order continuous elements. In the case of Orlicz norm, the presented results are new, whereas in the case of Luxemburg norm, we rely heavily on known results, which we show for the first time as a whole. Finally, we apply the obtained
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Properties of local orthonormal systems Part I: Unconditionality in Lp, 1 Math. Nachr. (IF 1.0) Pub Date : 2024-01-02 Jacek Gulgowski, Anna Kamont, Markus Passenbrunner
Assume that we are given a filtration (Fn)$(\mathcal F_n)$ on a probability space (Ω,F,P)$(\Omega,\mathcal F,\mathbb {P})$ of the form that each Fn$\mathcal F_n$ is generated by the partition of one atom of Fn−1$\mathcal F_{n-1}$ into two atoms of Fn$\mathcal F_n$ having positive measure. Additionally, assume that we are given a finite-dimensional linear space S of F$\mathcal F$-measurable, bounded
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Pointwise eigenvector estimates by landscape functions: Some variations on the Filoche–Mayboroda–van den Berg bound Math. Nachr. (IF 1.0) Pub Date : 2023-12-28 Delio Mugnolo
Landscape functions are a popular tool used to provide upper bounds for eigenvectors of Schrödinger operators on domains. We review some known results obtained in the last 10 years, unify several approaches used to achieve such bounds, and extend their scope to a large class of linear and nonlinear operators. We also use landscape functions to derive lower estimates on the principal eigenvalue—much
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Degrees of closed points on hypersurfaces Math. Nachr. (IF 1.0) Pub Date : 2023-12-28 Francesca Balestrieri
Let k be any field. Let X⊂PkN$X \subset \mathbb {P}_k^N$ be a degree d≥2$d \ge 2$ hypersurface. Under some conditions, we prove that if X(K)≠∅$X(K) \ne \emptyset$ for some extension K/k$K/k$ with n:=[K:k]≥2$n:=[K:k] \ge 2$ and gcd(n,d)=1$\gcd (n,d)=1$, then X(L)≠∅$X(L) \ne \emptyset$ for some extension L/k$L/k$ with gcd([L:k],d)=1$\gcd ([L:k], d)=1$, n∤[L:k]$n \nmid [L:k]$, and [L:k]≤nd−n−d$[L:k]
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Probabilistic limit theorems induced by the zeros of polynomials Math. Nachr. (IF 1.0) Pub Date : 2023-12-26 Nils Heerten, Holger Sambale, Christoph Thäle
Sequences of discrete random variables are studied whose probability generating functions are zero-free in a sector of the complex plane around the positive real axis. Sharp bounds on the cumulants of all orders are stated, leading to Berry–Esseen bounds, moderate deviation results, concentration inequalities, and mod-Gaussian convergence. In addition, an alternate proof of the cumulant bound with