Mathematische Nachrichten最新文献

Working with function spaces in various branches of mathematical analysis introduces optimality problems, where the question of choosing a function space both accessible and expressive becomes a nontrivial exercise. A good middle ground is provided by Orlicz spaces, parameterized by a single Young function and thus accessible, yet expansive. In this work, we study optimality problems on Sobolev embeddings in the so-called Maz'ya classes of Euclidean domains which are defined through their isoperimetric behavior. In particular, we prove the non-existence of optimal Orlicz spaces in certain Orlicz–Sobolev embeddings in a limiting (critical) state, whose pivotal special case is the celebrated embedding of Brezis and Wainger for John domains.

The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here, we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions.

We investigate the topology of the double cover of the complex affine plane branching along a nodal real line arrangement. We define certain topological 2-cycles in the double plane using the real structure of the arrangement, and calculate their intersection numbers.

In this paper, we focus on the pair correlation of fractions whose denominators are products of primes. We show that the limiting pair correlation function of such fractions on any short interval $��I�\subset �[�0�,�1�]�$ exists and is independent of $�I$. Furthermore, we use this result to compute the pair correlation function of the angles of elements in specific types of regions.

Given a smooth projective complex curve inside a smooth projective surface, one can ask how its Hodge structure varies when the curve moves inside the surface. In this paper, we develop a general theory to study the infinitesimal version of this question in the case of ample curves. We can then apply the machinery to show that the infinitesimal variation of the Hodge structure of a general deformation of an ample curve in $��P^1�\times �P^1�$ is an isomorphism.

First, we solve a crucial problem under which conditions increasing uniform $�K$-monotonicity is equivalent to lower local uniform $�K$-monotonicity. Next, we investigate properties of substochastic operators on $��L^1�+�L^{\infty }�$ with applications. Namely, we show that a countable infinite combination of substochastic operators is also substochastic. Using $�K$-monotonicity properties, we prove several theorems devoted to the convergence of the sequence of substochastic operators in the norm of a symmetric space $�E$ under addition assumption on $�E$. In our final discussion, we focus on compactness of admissible operators for Banach couples under additional assumption.

We develop criteria to guarantee uniqueness of the $�C^{\ast }$-norm on a $�\ast$-algebra $�B$. Nontrivial examples are provided by the noncommutative algebras of $�C$-valued functions $��S_J^C��\left(�R^n�\right)��$ and $��B_J^C��\left(�R^n�\right)��$ defined by M.A. Rieffel via a deformation quantization procedure, where $�C$ is a $�C^{\ast }$-algebra and $�J$ is a skew-symmetric linear transformation on $�R^n$ with respect to which the usual pointwise product is de

We study reiteration theorems for quasi-subadditive functions on Banach spaces. We prove various reiteration theorems that are generalizations of classical reiteration theorems.

The aim of this paper is to study some new results on the convergence of solutions for controlled systems driven by generalized multiobjective games, optimal control problems where the systems are governed by generalized multiobjective games and controlled systems of traffic networks. First, we recall the controlled systems of generalized multiobjective games proposed by Hung and Keller (Math. Nachr. 296 (2023), 3676–3698). Second, we introduce gap functions and a key Assumption 3.6 using nonlinear scalarization functions for these games. Results on the lower convergence and convergence of the solutions for such problems using the key Assumption 3.6 are established. Third, we revisit optimal control problems governed by generalized multiobjective games. We investigate necessary and sufficient conditions for the convergence of solutions to optimal control problems. Finally, as a real-world application, we consider the special case of controlled systems of traffic networks. The necessary and sufficient conditions for the convergence of solutions for these problems are also obtained. Many examples are given for the illustration of our results.

We show that K3 surfaces in characteristic 2 can admit sets of $�n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $��n�=�8�,�12�,�16�,�20�$. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only $��n�=�8�$ is possible.