Mathematische Nachrichten最新文献

Given a Hermitian holomorphic vector bundle over a complex manifold, consider its flag bundles with the associated universal vector bundles endowed with the induced metrics. We prove that the universal formula for the push-forward of a polynomial in the Chern classes of all the possible universal vector bundles also holds pointwise at the level of Chern forms. A key step in our proof is the explicit computation, at a point of any flag bundle, of the Chern curvature of the universal vector bundles with the induced metrics. As an application, we provide an alternative version of the Jacobi–Trudi identity at the level of differential forms. We also show the positivity of a family of polynomials in the Chern forms of Griffiths semipositive vector bundles. This latter result partially confirms the Griffiths' conjecture on positive characteristic forms, which has raised considerable interest in recent years.

Systems of the first-order partial differential equations with singular solutions appear in many multiphysics problems and the weak formulation of the solution involves, in many cases, the product of distributions. In this paper, we study such a system derived from Eulerian droplet model for air particle flow. This is a $��2�\times ��2�$ non-strictly hyperbolic system of conservation laws with linear damping. We first study a regularized viscous system with variable viscosity term, obtain a weak asymptotic solution with general initial data and also get the solution in Colombeau algebra. We study the vanishing viscosity limit and show that this limit is a distributional solution. Further, we study the large-time asymptotic behavior of the viscous system. This important system is not very well studied due to complexities in the analysis. As far as we know, the only work done on this system is for Riemann type of initial data. The significance of this paper is that we work on the system having general initial data and not just initial data of the Riemann type.

In this paper, we discuss the boundedness of generalized fractional integral operators $�I_{�\rho �,�\tau �}$ on Musielak–Orlicz–Morrey spaces of an integral form $��L^{�\Phi �,�\omega �,�{\theta }_1�}��\left(�X�\right)��$ over bounded non-doubling metric measure spaces $�X$, where both $�\rho$ and $�\omega$ depend on $��x�\in �X�$. As an application, we give Sobolev-type inequalities for multiphase functions

We study the Dirichlet problem for the pseudoparabolic equation perturbed with the $��p�\left[�u�\right]�$-Laplacian diffusion term,

We study the smoothness of the topological equivalence between a linear equation and its unbounded nonlinear perturbation. To the best of our knowledge, without using spectral bound conditions, such a study has not been previously considered in the literature. The main result of this work fills in this gap. It shows on the positive half line that this kind of topological equivalence is of class $��C^r��(�r�\ge �1�)��$ when the linear part is a uniform contraction and the nonlinearities considered are unbounded with respect to the space variable.

The expression for the Weyl–Titchmarsh function is presented for skew-self-adjoint Dirac systems with rectangular potentials. As a specific application of this expression, we provide a new proof of the celebrated local Borg–Marchenko uniqueness theorem. Furthermore, we establish the high-energy asymptotic expansion of the Weyl function and the local uniqueness theorem for locally smooth potentials at the right endpoint.

In this paper, we establish the sharp criteria for the existence and the nonexistence of negative solutions of the following $�k$-Hessian inequality with a nonlocal term:

A new operator for certain types of ultrametric Cantor sets is constructed using the measure coming from the spectral triple associated with the Cantor set, as well as its zeta function. Under certain mild conditions on that measure, it is shown that it is an integral operator similar to the Vladimirov–Taibleson operator on the $�p$-adic integers. Its spectral properties are studied, and the Markov property and kernel representation of the heat kernel generated by this so-called Vladimirov–Pearson operator is shown, viewed as acting on a certain Sobolev space. A large class of these operators have a heat kernel and a Green function explicitly given by the ultrametric wavelets on the Cantor set, which are eigenfunctions of the operator.

This paper studies stability of solutions for the 3D generalized incompressible Hall-MHD Megnetohydrodynamics equations in the periodic domain $�T^3$ with the magnetic field near a nontrivial equilibrium. Some new observations and estimates are implemented to exploit the enhanced dissipation produced by the nontrivial background magnetic field, which satisfies the Diophantine condition. Global stability and explicit time decay rates of solutions are shown.