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Darcy's law and groundwater flow modelling
[SNAP2015007EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)Formulations of natural phenomena are derived, sometimes, from experimentation and observation. Mathematical methods can be applied to expand on these formulations, and develop them into better models. In the year 1856, ... 
Data assimilation: mathematics for merging models and data
[SNAP2018011EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180710)When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a selfdriving car, you typically have two sources of information. The first is a mathematical model, and the ... 
Definable orthogonality classes in accessible categories are small
[OWP201114] (Mathematisches Forschungsinstitut Oberwolfach, 20110515)We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary ... 
Deformation Classification of Real NonSingular Cubic Threefolds with a Marked Line
[OWP201802] (Mathematisches Forschungsinstitut Oberwolfach, 20180221)We prove that the space of pairs $(X,l)$ formed by a real nonsingular cubic hypersurface $X\subset P^4$ with a real line $l\subset X$ has 18 connected components and give for them several quite explicit interpretations. ... 
A Deformed Quon Algebra
[OWP201811] (Mathematisches Forschungsinstitut Oberwolfach, 20180625)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 ... 
Demailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Maps
[OWP201820] (Mathematisches Forschungsinstitut Oberwolfach, 20181008)Demailly's conjecture, which is a consequence of the GreenGriffithsLang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to ... 
Detecting Ineffective Features for Pattern Recognition
[OWP201726] (Mathematisches Forschungsinstitut Oberwolfach, 20171017)For a binary classification problem, the hypothesis testing is studied, that a component of the observation vector is not effective, i.e., that component carries no information for the classification. We introduce nearest ... 
Diophantine equations and why they are hard
[SNAP2019003EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190424)Diophantine equations are polynomial equations whose solutions are required to be integer numbers. They have captured the attention of mathematicians during millennia and are at the center of much of contemporary research. ... 
Dirichlet Approximation and Universal Dirichlet
[OWP201612] (Mathematisches Forschungsinstitut Oberwolfach, 20160816)We characterize the uniform limits of Dirichlet polynomials on a right half plane. We extend the approximation theorems of Runge, Mergelyan and Vitushkin to the Dirichlet setting with respect to the Euclidean distance and ... 
Dirichlet Series
[SNAP2014001EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)Mathematicians are very interested in prime numbers. In this snapshot, we will discuss some problems concerning the distribution of primes and introduce some special infinite series in order to study them. 
Discrete Differential Geometry
[OWS38] (Birkhäuser Basel, 2008)Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential ... 
Discrete noncommutative integrability: the proof of a conjecture by M. Kontsevich
[OWP200924] (Mathematisches Forschungsinstitut Oberwolfach, 20090317)We prove a conjecture of Kontsevich regarding the solutions of rank two recursion relations for noncommutative variables which, in the commutative case, reduce to rank two cluster algebras of affine type. The conjecture ... 
Discrete Translates in Lp (R)
[OWP201509] (Mathematisches Forschungsinstitut Oberwolfach, 20150618)A set $\Lambda$ is called $p$spectral if there is a function $g \in L^p (\mathbb{R})$ such that all $\Lambda$translates $\{g(t\lambda),\lambda \in \Lambda\}$ span $L^p(\mathbb{R})$. We prove that exponentially small ... 
Dispersive Equations and Nonlinear Waves
[OWS45] (Birkhäuser Basel, 2014)The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized ... 
Dominance and Transmissions in Supertropical Valuation Theory
[OWP201107] (Mathematisches Forschungsinstitut Oberwolfach, 2011)This paper is a sequel of [IKR1], where we defined supervaluations on a commutative ring $R$ and studied a dominance relation $\Phi >= v$ between supervaluations $\varphi$ and $\upsilon$ on $R$, aiming at an enrichment of ... 
Domino tilings of the Aztec diamond
[SNAP2015016EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can cover exactly two squares of the squared paper. How many different ways are there to cover the entire paper cutout with ... 
Drawing large pictures at random : Oberwolfach Lecture 2007
[OWP200708] (Mathematisches Forschungsinstitut Oberwolfach, 2007)This lecture is of very introductory nature. The goal will be to describe specific concrete questions, and to use them as a tool to convey some general ideas. Let me therefore skip the general introduction and immediately ... 
Drugs, herbicides, and numerical simulation
[SNAP2014010EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)[also available in German] The Colombian government sprays coca fields with herbicides in an effort to reduce drug production. Spray drifts at the EcuadorColombia border became an international issue. We developed a ... 
Enhanced Spatial SkinEffect for Free Vibrations of a Thick Cascade Junction with "Super Heavy" Concentrated Masses
[OWP201326] (Mathematisches Forschungsinstitut Oberwolfach, 20131213)The asymptotic behavior (as $\varepsilon \to 0$) of eigenvalues and eigenfunctions of a boundaryvalue problem for the Laplace operator in a thick cascade junction with concentrated masses is studied. This cascade junction ... 
Epsilonhypercyclic operators
[OWP200819] (Mathematisches Forschungsinstitut Oberwolfach, 20080319)For each fixed number $\varepsilon$ in $(0, 1)$ we construct a bounded linear operator on the Banach space $\ell_1$ having a certain orbit which intersects every cone of aperture $\varepsilon$, but with every orbit avoiding ...