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For a matrix M∈Kn×n{\bf{M}}\in {{\mathbb{K}}}^{n\times n}, we establish a condition on the Galois group of the characteristic polynomial φM{\varphi }_{{\bf{M}}} that induces nonvanishing of the minors of the eigenvector matrix of M{\bf{M}}. For integer matrices, recent results by Eberhard show that, conditionally on the extended Riemann hypothesis, this condition is satisfied with high probability (We say “with high probability” for probability 1−o(1)1-o\left(1) as n→∞n\to \infty .) and hence, with high probability, the minors of eigenvector matrices of random integer matrices are nonzero. For random graphs, this yields a novel uncertainty principle, related to Chebotarëv’s theorem on the roots of unity and results from Tao and Meshulam. We also show the application in graph signal processing and the connection to the rank of the walk matrix.

The laudation for Jessica Wynne honors her photographs of chalkboards filled with mathematics, which are the subject of current research. The works were created in a project titled "Do Not Erase - Bitte nicht wegwischen" and include over 100 photographed chalkboards. A photo book was published in 2021 by Princeton University Press, combining the photographs with reflections from mathematicians. Jessica Wynne is a professor at the Fashion Institute of Technology in New York and is represented by the Edwynn Houk Gallery. In her work "Do Not Erase - Bitte nicht wegwischen," the photographer Jessica Wynne showcases blackboard images of mathematicians. The boards display both beautiful drawings and messy handwriting and scribbles. Wynne aims to capture the moment of inspiration and the beauty of expressing thoughts. The boards serve as a means of exchange and communication between the writer and the observer. Wynne's photographs also depict the surrounding space and correspond with the content on the board. Wynne's work showcases the working technique of mathematicians and challenges prejudices about mathematics. [Extracted from the article]

Copyright of Jahrbuch des Instituts für Deutsche Sprache is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article reports on the planned increase in membership fees of the DMV (German Mathematical Association) starting from January 1, 2023. The DMV's executive board has unanimously recommended a fee increase in order to ensure the long-term sustainability of the association's numerous activities and initiatives. The projected regular expenses for the coming years amount to a total of €410,000, resulting in an expected annual structural deficit of approximately €61,500. The executive board proposes to increase the membership fees from January 2023 in order to partially offset the deficit. [Extracted from the article]

The initial value problem for an evolution equation of type v ′ + A ⁢ v + B ⁢ K ⁢ v = f {v^{\prime}+Av+BKv=f} is studied, where A : V A → V A ′ {A:V_{A}\to V_{A}^{\prime}} is a monotone, coercive operator and where B : V B → V B ′ {B:V_{B}\to V_{B}^{\prime}} induces an inner product. The Banach space V A {V_{A}} is not required to be embedded in V B {V_{B}} or vice versa. The operator K incorporates a Volterra integral operator in time of convolution type with an exponentially decaying kernel. Existence of a global-in-time solution is shown by proving convergence of a suitable time discretisation. Moreover, uniqueness as well as stability results are proved. Appropriate integration-by-parts formulae are a key ingredient for the analysis. [ABSTRACT FROM AUTHOR]

We give an overview on existence results in nonlinear peridynamics, a nonlocal elasticity theory, and compare these results with those known for classical nonlinear elastodynamics. In peridynamics, it is possible to obtain stronger results under equal or even less restrictive assumptions on the stress. [ABSTRACT FROM AUTHOR]

Existence and uniqueness of generalized solutions to initial value problems for a class of abstract differential-algebraic equations (DAEs) is shown. The class of equations covers, in particular, the Stokes and Oseen problem describing the motion of an incompressible or nearly incompressible Newtonian fluid but also their spatial semi-discretization. The equations are governed by a block operator matrix with entries that fulfill suitable inf-sup conditions. The problem data are required to satisfy appropriate consistency conditions. The results in infinite dimensions are compared in detail with those known for the DAEs that arise after semi-discretization in space. Explicit solution formulas are derived in both cases. [ABSTRACT FROM AUTHOR]

Recent results on convergence of fully discrete approximations combining the Galerkin method with the explicit-implicit Euler scheme are extended to strong convergence under additional monotonicity assumptions. It is shown that these abstract results, formulated in the setting of evolution equations, apply, for example, to the partial differential equation for vibrating membrane with nonlinear damping and to another partial differential equation that is similar to one of the equations used to describe martensitic transformations in shape-memory alloys. Numerical experiments are performed for the vibrating membrane equation with nonlinear damping which support the convergence results. [ABSTRACT FROM AUTHOR]

The time discretisation of the initial-value problem for a first-order evolution equation by the two-step backward differentiation formula (BDF) on a uniform grid is analysed. The evolution equation is governed by a time-dependent monotone operator that might be perturbed by a time-dependent strongly continuous operator. Well-posedness of the numerical scheme, a priori estimates, convergence of a piecewise polynomial prolongation, stability as well as smooth-data error estimates are provided relying essentially on an algebraic relation that implies the G-stability of the two-step BDF with constant time steps. [ABSTRACT FROM AUTHOR]