Mathematische Nachrichten最新文献

In this paper, we study geometric and analytical features of complete noncompact $�\rho$-Einstein solitons, which are self-similar solutions of the Ricci–Bourguignon flow. We study the spectrum of the drifted Laplacian operator for complete gradient shrinking $�\rho$-Einstein solitons. Moreover, similar to classical results due to Calabi–Yau and Bishop for complete Riemannian manifolds with nonnegative Ricci curvature, we prove new volume growth estimates for geodesic balls of complete noncompact $�\rho$-Einstein solitons. In particular, the rigidity case is discussed. In addition, we establish weighted volume growth estimates for geodesic balls of such manifolds.

In this paper, we introduce the notion of algebraic $�*$-Ricci solitons of three-dimensional almost contact Lorentzian Lie groups, which represents a fundamentally novel class of solitons. We give the classification of algebraic $�*$-Ricci solitons of three-dimensional Lorentzian contact unimodular and non-unimodular Lie groups. At last we give an example of expanding algebraic $�*$-Ricci soliton.

In this paper, we study stronger forms of Goldbach's conjecture enriched with the linear representations of prime numbers given by the classical Dirichlet theorem and its extensions. We call such a representation a Goldbach–Dirichlet representation (GD-representation). Among other results, we show that Dirichlet's theorem on arithmetic progressions is, in general, not true in the ring of formal power series over the integers. Additionally, we use a polynomial version of the Schinzel hypothesis due to A. Bodin, P. Dèbes, and S. Najib to prove the existence of GD-representations for a wide collection of polynomial rings over special families of fields of characteristic zero, among others. Moreover, we study the (non)validity of Dirichlet's theorem over several families of commutative rings with unity like polynomial and formal series rings. Finally, we obtain a generalization for polyomial rings of the celebrated Green–Tao theorem.

This paper investigates a Sellers-type energy balance model coupled to the primitive equations by a dynamic boundary condition with and without noise on the boundary. It is shown that this system is globally strongly well-posed both in the deterministic setting for arbitrary large data in $�W^{�2�(�1�-���1���/���p���)�,�p�}$ for $��p�\in �[�2�,�\infty �)�$ and in the stochastic setting for arbitrary large data in $�H^1$.

We consider an even-order ordinary differential operator with a spectral parameter and integral conditions. An a priori estimate of the solutions to the problem is obtained for sufficiently large values of the spectral parameter. The discreteness and the sectoral structure of the spectrum of the corresponding operators are proved.

In order to well understand the behavior of the Riemann zeta function inside the critical strip, we show, among other things, the Fourier expansion of the $��{\zeta }^k��\left(�s�\right)��$ ($��k�\in �N�$) in the half-plane $��\Re �s�>�1�/�2�$ and we deduce a necessary and sufficient condition for the truth of the Lindelöf hypothesis. Moreover, if $�{\Delta }_k$ denotes the error term in the Piltz divisor problem then for almost all $��x�\ge �1�$ and any given $��k�\in �N�$ we have

The paper deals with a family of evolution problems arising in the physical modeling of small amplitude acoustic phenomena occurring in a fluid, bounded by a surface of extended reaction. They are all derived in a Lagrangian framework. We study well-posedness of these problems, their mutual relations, and their relations with other evolution problems modeling the same physical phenomena. They are those introduced in an Eulerian framework and those which deal with the (standard in Theoretical Acoustics) velocity potential. The latter reduce to the well-known wave equation with acoustic boundary conditions. Finally, we prove that all problems are asymptotically stable provided the system is linearly damped.

We consider a class of physically relevant one-dimensional isentropic compressible Navier–Stokes equations with viscoelastic constitutive law of Oldroyd type. By establishing uniform a priori estimates (with respect to relaxation time), we show global existence of smooth solutions with small initial data. Moreover, we get global-in-time convergence of the system toward the classical isentropic compressible Navier–Stokes equations.