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Anzeige der Dokumente 1641-1660 von 1987
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A Cheeger Type Inequality in Finite Cayley Sum Graphs
[OWP-2019-21] (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-31) - (5 May - 27 July 2019)Let $G$ be a finite group and $S$ be a symmetric generating set of $G$ with $|S| = d$. We show that if the undirected Cayley sum graph $C_{\Sigma}(G,S)$ is an expander graph and is non-bipartite, then the spectrum of its ... -
Group-Graded Rings Satisfying the Strong Rank Condition
[OWP-2019-22] (Mathematisches Forschungsinstitut Oberwolfach, 2019-08-16)A ring $R$ satisfies the $\textit{strong rank condition}$ (SRC) if, for every natural number $n$, the free $R$-submodules of $R^n$ all have rank $\leq n$. Let $G$ be a group and $R$ a ring strongly graded by $G$ such that ... -
On Logic, Choices and Games
[SNAP-2019-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-04)Can we always mathematically formalise our taste and preferences? We discuss how this has been done historically in the field of game theory, and how recent ideas from logic and computer science have brought an interesting ... -
Limits of graph sequences
[SNAP-2019-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-04)Graphs are simple mathematical structures used to model a wide variety of real-life objects. With the rise of computers, the size of the graphs used for these models has grown enormously. The need to efficiently represent ... -
Nonlinear Acoustics
[SNAP-2019-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-04)Nonlinear acoustics has been a topic of research for more than 250 years. Driven by a wide range and a large number of highly relevant industrial and medical applications, this area has expanded enormously in the last ... -
Groups with Spanier-Whitehead Duality
[OWP-2019-23] (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-17)We introduce the notion of Spanier-Whitehead $K$-duality for a discrete group $G$, defined as duality in the KK-category between two $C*$-algebras which are naturally attached to the group, namely the reduced group ... -
Configuration spaces and braid groups
[SNAP-2019-011-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-10-08)In this snapshot we introduce configuration spaces and explain how a mathematician studies their ‘shape’. This will lead us to consider paths of configurations and braid groups, and to explore how algebraic properties of ... -
Reflective Prolate-Spheroidal Operators and the KP/KdV Equations
[OWP-2019-24] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-05)Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and ... -
Matchings and Squarefree Powers of Edge Ideals
[OWP-2019-25] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-11)Squarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper we give bounds for the regularity of squarefree powers of edge ideals, and we consider the question of when such ... -
Global Solutions to Stochastic Wave Equations with Superlinear Coefficients
[OWP-2019-26] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-13)We prove existence and uniqueness of a random field solution $(u(t,x);(t,x)\in [0,T]\times \mathbb{R}^d)$ to a stochastic wave equation in dimensions $d=1,2,3$ with diffusion and drift coefficients of the form $|x| ... -
Touching the transcendentals: tractional motion from the bir th of calculus to future perspectives
[SNAP-2019-013-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)When the rigorous foundation of calculus was developed, it marked an epochal change in the approach of mathematicians to geometry. Tools from geometry had been one of the foundations of mathematics until the 17th century ... -
Analogue mathematical instruments: Examples from the “theoretical dynamics” group (France, 1948–1964)
[SNAP-2019-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)Throughout the history of dynamical systems, instruments have been used to calculate and visualize (approximate) solutions of differential equations. Here we describe the approach of a group of physicists and engineers ... -
Deep Learning and Inverse Problems
[SNAP-2019-015-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)Big data and deep learning are modern buzz words which presently infiltrate all fields of science and technology. These new concepts are impressive in terms of the stunning results they achieve for a large variety of ... -
Mixed-dimensional models for real-world applications
[SNAP-2019-014-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)We explore mathematical models for physical problems in which it is necessary to simultaneously consider equations in different dimensions; these are called mixed-dimensional models. We first give several examples, and ... -
Expander graphs and where to find them
[SNAP-2019-016-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-22)Graphs are mathematical objects composed of a collection of “dots” called vertices, some of which are joined by lines called edges. Graphs are ideal for visually representing relations between things, and mathematical ... -
A surprising connection between quantum mechanics and shallow water waves
[SNAP-2019-018-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-11)We describe a connection between quantum mechanics and nonlinear wave equations and highlight a few problems at the forefront of modern research in the intersection of these areas. -
Formation Control and Rigidity Theory
[SNAP-2019-017-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-11)Formation control is one of the fundamental coordination tasks for teams of autonomous vehicles. Autonomous formations are used in applications ranging from search-and-rescue operations to deep space exploration, with ... -
Is it possible to predict the far future before the near future is known accurately?
[SNAP-2019-021-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-18)It has always been the dream of mankind to predict the future. If the future is governed by laws of physics, like in the case of the weather, one can try to make a model, solve the associated equations, and thus predict ... -
The Mathematics of Fluids and Solids
[SNAP-2019-019-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-18)Fluid-structure interaction is a rich and active field of mathematics that studies the interaction between fluids and solid objects. In this short article, we give a glimpse into this exciting field, as well as a ... -
The Interaction of Curvature and Topology
[SNAP-2019-020-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-18)In this snapshot we will outline the mathematical notion of curvature by means of comparison geometry. We will then try to address questions as the ways in which curvature might influence the topology of a space, and ...