Auflistung nach Erscheinungsdatum
Anzeige der Dokumente 1521-1540 von 1987
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Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary
[OWP-2018-06] (Mathematisches Forschungsinstitut Oberwolfach, 2018-04-16)We consider a domain $\Omega_\varepsilon\subset\mathbb{R}^N$, $N\geq2$, with a very rough boundary depending on~$\varepsilon$. For instance, if $N=3$ the domain $\Omega_\varepsilon$ has the form of a brush with an ... -
On the Gauss Algebra of Toric Algebras
[OWP-2018-07] (Mathematisches Forschungsinstitut Oberwolfach, 2018-04-25)Let $A$ be a $K$-subalgebra of the polynomial ring $S=K[x_1,\ldots,x_d]$ of dimension $d$, generated by finitely many monomials of degree $r$. Then the Gauss algebra $\mathbb{G}(A)$ of $A$ is generated by monomials of ... -
Categorical Linearly Ordered Structures
[OWP-2018-08] (Mathematisches Forschungsinstitut Oberwolfach, 2018-04-26)We prove that for every computable limit ordinal $\alpha$ there exists a computable linear ordering $\mathcal{A}$ which is $\Delta^0_\alpha$-categorical and $\alpha$ is smallest such, but nonetheless for every isomorphic ... -
Max-Linear Models on Infinite Graphs Generated by Bernoulli Bond Percolation
[OWP-2018-09] (Mathematisches Forschungsinstitut Oberwolfach, 2018-05-17)We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs, and investigate their relations to classical percolation theory. We formulate results for the oriented square lattice graph ... -
A Well-Posedness Result for Viscous Compressible Fluids with Only Bounded Density
[OWP-2018-10] (Mathematisches Forschungsinstitut Oberwolfach, 2018-05-28)We are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible Navier-Stokes equations. Assuming that the initial velocity has slightly sub-critical regularity and ... -
The mathematics of aquatic locomotion
[SNAP-2018-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-19)Aquatic locomotion is a self-propelled motion through a liquid medium. It can be of biological nature (fish, microorganisms,. . .) or performed by robotic swimmers. This snapshot aims to introduce the reader to some ... -
The codimension
[SNAP-2018-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-19)In this snapshot we discuss the notion of codimension, which is, in a sense, “dual” to the notion of dimension and is useful when studying the relative position of one object insider another one. -
Geometry behind one of the Painlevé III differential equations
[SNAP-2018-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-20)The Painlevé equations are second order differential equations, which were first studied more than 100 years ago. Nowadays they arise in many areas in mathematics and mathematical physics. This snapshot discusses the ... -
A Deformed Quon Algebra
[OWP-2018-11] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-25)The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and ... -
MOSES: A Streaming Algorithm for Linear Dimensionality Reduction
[OWP-2018-12] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-26)This paper introduces Memory-limited Online Subspace Estimation Scheme (MOSES) for both estimating the principal components of data and reducing its dimension. More specifically, consider a scenario where the data vectors ... -
Fast Solvers for Highly Oscillatory Problems
[SNAP-2018-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-26)Waves of diverse types surround us. Sound, light and other waves, such as microwaves, are crucial for speech, mobile phones, and other communication technologies. Elastic waves propagating through the Earth bounce ... -
The Magic Square of Reflections and Rotations
[OWP-2018-13] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-01)We show how Coxeter’s work implies a bijection between complex reflection groups of rank two and real reflection groups in 0(3). We also consider this magic square of reflections and rotations in the framework of Clifford ... -
A McKay Correspondence for Reflection Groups
[OWP-2018-14] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-02)We construct a noncommutative desingularization of the discriminant of a finite reflection group $G$ as a quotient of the skew group ring $A=S*G$. If $G$ is generated by order two reflections, then this quotient identifies ... -
An Optimal Bound for the Ratio Between Ordinary and Uniform Exponents of Diophantine Approximation
[OWP-2018-15] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-09)We provide a lower bound for the ratio between the ordinary and uniform exponents of both simultaneous Diophantine approximation to n real numbers and Diophantine approximation for one linear form in n variables. This ... -
Data assimilation: mathematics for merging models and data
[SNAP-2018-011-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-10)When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a self-driving car, you typically have two sources of information. The first is a mathematical model, and the ... -
Metric Connections with Parallel Skew-Symmetric Torsion
[OWP-2018-16] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-16)A geometry with parallel skew-symmetric torsion is a Riemannian manifold carrying a metric connection with parallel skew-symmetric torsion. Besides the trivial case of the Levi-Civita connection, geometries with non-vanishing ... -
Generalized Vector Cross Products and Killing Forms on Negatively Curved Manifolds
[OWP-2018-17] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-17)Motivated by the study of Killing forms on compact Riemannian manifolds of negative sectional curvature, we introduce the notion of generalized vector cross products on $\mathbb{R}^n$ and give their classification. Using ... -
Tropical geometry
[SNAP-2018-007-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-19)What kind of strange spaces hide behind the enigmatic name of tropical geometry? In the tropics, just as in other geometries, one of the simplest objects is a line. Therefore, we begin our exploration by considering tropical ... -
Number theory in quantum computing
[SNAP-2018-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-07)Algorithms are mathematical procedures developed to solve a problem. When encoded on a computer, algorithms must be "translated" to a series of simple steps, each of which the computer knows how to do. This task is ... -
A short story on optimal transport and its many applications
[SNAP-2018-013-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-08)We present some examples of optimal transport problems and of applications to different sciences (logistics, economics, image processing, and a little bit of evolution equations) through the crazy story of an industrial ...