Mathematische Annalen最新文献

This paper is dedicated to studying the long-term dynamics of a beam model known as the Shear beam model (without rotary inertia). Unlike the classical Timoshenko beam model, which combines bending moment and shear force, the Shear beam model has only one wave speed without blow-up at lower frequencies. This distinction has a significant impact on the analysis of long-term dynamic properties. We prove that the Euler–Bernoulli beam equation can be obtained as a singular limit of the Shear beam model when the shear elasticity modulus (kappa ) tends to infinity. By introducing a dissipative mechanism in the vertical displacement equation, we prove the existence of a smooth global attractor with finite fractal dimension. Finally, we demonstrate that the global attractor for the Shear beam model converges upper-semicontinuously to the global attractor for the Euler–Bernoulli equation as (kappa rightarrow infty ).

In this paper, we study the stability and minimizing properties of higher codimensional surfaces in Euclidean space associated with the f-weighted area-functional

with the density function (f(x)=g(|x|)) and g(t) is non-negative, which develop the recent works by U. Dierkes and G. Huisken (Math Ann, 20 October 2023) on hypersurfaces with the density function (|x|^alpha ). Under suitable assumptions on g(t), we prove that minimal cones with globally flat normal bundles are f-stable, and we also prove that the minimal cones satisfy the Lawlor curvature criterion, the determinantal varieties and the Pfaffian varieties without some exceptional cases are f-minimizing. As an application, we show that k-dimensional cones over product of spheres are (|x|^alpha )-stable for (alpha ge -k+2sqrt{2(k-1)}), the oriented stable minimal hypercones are (|x|^alpha )-stable for (alpha ge 0), and we also show that the cones over product of spheres (mathcal {C}=C left( S^{k_1} times cdots times S^{k_{m}}right) ) are (|x|^alpha )-minimizing for (dim mathcal {C} ge 7), (k_i>1) and (alpha ge 0), the Simons cones (C(S^{p} times S^{p})) are (|x|^alpha )-minimizing for (alpha ge 1), which relaxes the assumption (1le alpha le 2p) in Dierkes and Huisken ( Math Ann, https://doi.org/10.1007/s00208-023-02726-3, 2023). Recently, Dierkes (Rend Sem Mat Univ Padova, 2024) prove that (C(S^{p} times S^{p})) are (|x|^alpha )-minimizing for (alpha ge 3-p), which has improved our assumption (alpha ge 1) for (pge 3).

We investigate the relative assembly map from the family of finite subgroups to the family of virtually cyclic subgroups for the algebraic K-theory of twisted group rings of a group G with coefficients in a regular ring R or, more generally, with coefficients in a regular additive category. They are known to be isomorphisms rationally. We show that it suffices to invert only those primes p for which G contains a non-trivial finite p-group and p is not invertible in R. The key ingredient is the detection of Nil-terms of a twisted group ring of a finite group F after localizing at p in terms of the p-subgroups of F using Verschiebungs and Frobenius operators. We construct and exploit the structure of a module over the ring of big Witt vectors on the Nil-terms. We analyze the algebraic K-theory of the Hecke algebras of subgroups of reductive p-adic groups in prime characteristic.

We propose an iterative scheme generating method to address common fixed point problems. Our approach yields diverse iterative schemes for finding common fixed points. The derivative results include the Ishikawa iterative method and its variations. An application to the variational inequality problem is provided to illustrate the usefulness of our method. The class of mappings we target is general. This category includes nonexpansive mappings and various other types, even those that lack continuity.

We describe the subgroup of the mapping class group of a hypersurface in (mathbb{C}mathbb{P}^4) consisting of those diffeomorphisms which can be realised by monodromy.

Let G be a linear semisimple algebraic group and B its Borel subgroup. Let ({mathbb {T}}subset B) be the maximal torus. We study the inductive construction of Bott–Samelson varieties to obtain recursive formulas for the twisted motivic Chern classes of Schubert cells in G/B. To this end we introduce two families of operators acting on the equivariant K-theory ({text {K}}_{mathbb {T}}(G/B)[y]), the right and left Demazure–Lusztig operators depending on a parameter. The twisted motivic Chern classes coincide (up to normalization) with the K-theoretic stable envelopes. Our results imply wall-crossing formulas for a change of the weight chamber and slope parameters. The right and left operators generate a twisted double Hecke algebra. We show that in the type A this algebra acts on the Laurent polynomials. This action is a natural lift of the action on ({text {K}}_{mathbb {T}}(G/B)[y]) with respect to the Kirwan map. We show that the left and right twisted Demazure–Lusztig operators provide a recursion for twisted motivic Chern classes of matrix Schubert varieties.

We prove the local connectivity of the boundaries of invariant simply connected attracting basins for a class of transcendental meromorphic maps. The maps within this class need not be geometrically finite or in class ({mathcal {B}}), and the boundaries of the basins (possibly unbounded) are allowed to contain an infinite number of post-singular values, as well as the essential singularity at infinity. A basic assumption is that the unbounded parts of the basins are contained in regions which we call ‘repelling petals at infinity’, where the map exhibits a kind of ‘parabolic’ behaviour. In particular, our results apply to a wide class of Newton’s methods for transcendental entire maps. As an application, we prove the local connectivity of the Julia set of Newton’s method for (sin z), providing the first non-trivial example of a locally connected Julia set of a transcendental map outside class ({mathcal {B}}), with an infinite number of unbounded Fatou components.

We define family versions of the invariant of 4-manifolds with contact boundary due to Kronheimer and Mrowka and use these to detect exotic diffeomorphisms of 4-manifolds with boundary. Further, we show the existence of the first example of exotic 3-spheres in a smooth closed 4-manifold with diffeomorphic complements.

If two conducting or insulating inclusions are closely located, the gradient of the solution may become arbitrarily large as the distance between inclusions tends to zero, resulting in high concentration of stress in between two inclusions. This happens if the bonding of the inclusions and the matrix is perfect, meaning that the potential and flux are continuous across the interface. In this paper, we consider the case when the bonding is imperfect. We consider the case when there are two circular inclusions of the same radii with the imperfect bonding interfaces and prove that the gradient of the solution is bounded regardless of the distance between inclusions if the bonding parameter is finite. This result is of particular importance since the imperfect bonding interface condition is an approximation of the membrane structure of biological inclusions such as biological cells.

Let (f:Xrightarrow Y) be a surjective morphism of Fano manifolds of Picard number 1 whose VMRTs at a general point are not dual defective. Suppose that the tangent bundle (T_X) is big. We show that (f) is an isomorphism unless (Y) is a projective space. As applications, we explore the bigness of the tangent bundles of complete intersections, del Pezzo manifolds, and Mukai manifolds, as well as their dynamical rigidity.