Journal of the London Mathematical Society-Second Series最新文献

Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over $��F_q��\left(�t�\right)��$, provided $��char�\left(�F_q�\right)�>�3�$. Under the same hypotheses, we also verify weak approximation.

Let $�A$ be a Noetherian domain and $�R$ be a finitely generated $�A$-algebra. We study several features regarding the generic freeness over $�A$ of an $�R$-module. For an ideal $��I�\subset �R�$, we show that the local cohomology modules $��H_I^i��\left(�R�\right)��$ are generically free over $�A$ under certain settings where $�R$ is a smooth $�A$-algebra. By utilizing the theory of Gröbner bases over arbitrary Noetherian rings, we provide an effective method to b make explicit the generic freeness over $�A$ of a finitely generated $�R$-module.

In this work, we prove the existence of time-periodic solutions to a model describing a ferrofluid flow heated from below. Navier–Stokes equations satisfied by the fluid velocity are coupled to the temperature equation and the magnetostatic equation satisfied by the magnetic potential. The magnetization is assumed to be parallel to the magnetic field and is given by a nonlinear magnetization law generalizing the Langevin law. The proof is based on a semi-Galerkin approximation and regularization methods together with the fixed point method.

The $�q$-Araki-Woods factor associated to a group of orthogonal transformations on a real separable Hilbert space $�H_R$ is full as soon as $��dim�H_R�⩾�2�$.

We show that the cone multiplier satisfies local $�L^p$-$�L^q$ bounds only in the trivial range $��1�⩽�q�⩽�2�⩽�p�⩽�\infty �$. To do so, we suitably adapt to this setting the proof of Fefferman for the ball multiplier. As a consequence we answer negatively a question by Békollé and Bonami, regarding the continuity from $��L^p�\to �L^q�$ of the Cauchy–Szegö projections associated with a class of bounded symmetric domains in $�C^n$ with rank $��r�⩾�2�$.

A general modulus of continuity is quantified for locally bounded, local, weak solutions to nonlocal parabolic equations, under a minimal tail condition. Hölder modulus of continuity is then deduced under a slightly stronger tail condition. These regularity estimates are demonstrated under the framework of nonlocal $�p$-Laplacian with measurable kernels.

The core object of this paper is a pair $��(�L�,�e�)�$, where $�L$ is a Nijenhuis operator and $�e$ is a vector field satisfying a specific Lie derivative condition, that is, $��L_e�L�=�Id�$. Our research unfolds in two parts. In the first part, we establish a splitting theorem for Nijenhuis operators with a unity, offering an effective reduction of their study to cases where $�L$ has either one real or two complex conjugate eigenvalues at a given point. We further provide the normal forms for $�\mathrm{gl}$-regular Nijenhuis operators with a unity around algebraically generic points, along with seminormal forms for dimensions 2 and 3. In the second part, we establish the relationship between Nijenhuis operators with a unity and $�F$-manifolds. Specifically, we prove that the class of regular $�F$-manifolds coincides with the class of Nijenhuis manifolds with a cyclic unity. Extending our results from dimension 3, we reveal seminormal forms for corresponding $�F$-manifolds around singularities.