Spectral ACMS: A robust localized Approximated Component Mode Synthesis
Method
September 12, 2017
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Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
We consider finite element methods of multiscale type to approximate
solutions for two-dimensional symmetric elliptic partial differential equations
with heterogeneous L∞ coefficients. The methods are of Galerkin type
and follow the...
Is completeness necessary? Estimation in nonidentified linear models
September 11, 2017
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Mathematics
Economics
Statistics
Statistics Theory
Econometrics
Machine Learning
Statistics Theory
Statistics Theory
Econometrics
Machine Learning
Statistics Theory
Modern data analysis depends increasingly on estimating models via flexible
high-dimensional or nonparametric machine learning methods, where the
identification of structural parameters is often challenging and untestable. In
linear setting...
Quantum Drinfeld Modules and Ray Class Fields of Real Quadratic Global
Function Fields
September 11, 2017
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Mathematics
Number Theory
This is the second in a series of two papers presenting a solution to
Hilbert's 12th problem for real quadratic function fields in positive
characteristic, in the sense of proving an analog of the Theorem of
Weber-Fueter. We also offer a co...
The Asymptotic Binary Goldbach and Lemoine Conjectures
September 11, 2017
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Mathematics
Number Theory
In this paper we use the former of the authors developed theory of
\textbf{circles of partition} to investigate possibilities to prove the binary
Goldbach as well as the Lemoine conjecture. We state the \textit{squeeze
principle} and its co...
Learning to Detect Entanglement
September 11, 2017
Physics
Quantum Physics
Classifying states as entangled or separable is a fundamental, but expensive
task. This paper presents a method, the forest algorithm, to improve the amount
of resources needed to detect entanglement. Starting from 'optimized' methods
for u...
The Shape of a Benedictine Monastery: The SaintGall Ontology (Extended
Version)
September 8, 2017
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Computer Science
Logic in Computer Science
Artificial Intelligence
We present an OWL 2 ontology representing the Saint Gall plan, one of the
most ancient documents arrived intact to us, which describes the ideal model of
a Benedictine monastic complex that inspired the design of many European
monasteries....
Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues
September 6, 2017
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Mathematics
Spectral Theory
Analysis of PDEs
Spectral Theory
Analysis of PDEs
In the present paper we develop an approach to obtain sharp spectral
asymptotics for Steklov type problems on planar domains with corners. Our main
focus is on the two-dimensional sloshing problem, which is a mixed
Steklov-Neumann boundary ...
Convergence estimates for the Magnus expansion I. Banach algebras
September 6, 2017
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Mathematics
Functional Analysis
Rings and Algebras
Functional Analysis
Rings and Algebras
We review and provide simplified proofs related to the Magnus expansion, and
improve convergence estimates. Observations and improvements concerning the
Baker--Campbell--Hausdorff expansion are also made. In this Part I, we consider
the gen...
A power structure over the Grothendieck ring of geometric dg categories
September 6, 2017
Mathematics
Algebraic Geometry
We prove the existence of a power structure over the Grothendieck ring of
geometric dg categories. We show that a conjecture by Galkin and Shinder
(proved recently by Bergh, Gorchinskiy, Larsen, and Lunts) relating the motivic
and categoric...
The Recursive Stopping Time Structure of the 3x+1 Function
September 5, 2017
Mathematics
General Mathematics
The 3x+1 problem concerns iteration of the map
T:Z→Z given by \begin{align*}
T(x)=\left\{\begin{array}{lcr}\;\;\;\;\displaystyle{\frac{x}{2}} & \mbox{if
x≡0(mod2)},\\ \\\displaystyle{\fra...