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In this diploma thesis, the calibration of the vector polarimeter POLIS will be described. The instrument is built by the Kiepenheuer-Institut fuer Sonnenphysik (Freiburg/Germany) in cooperation with the High Altitude Observatory (Boulder/USA) and wi...
Here we examine some Erdos-Falconer-type problems in vector spaces over finite fields involving right angles. Our main goals are to show that a) a subset A of F_q^d of size >> q^[(d+2)/3] contains three points which generate a right angle, and b) a s...
Tags: ros, camera-calibration, euler-angles, rotational-matrices, aruco | Score: 1
Graded vector bundles over a given $\mathbb{Z}$-graded manifold can be defined in three different ways: certain sheaves of graded modules over the structure sheaf of the base graded manifold, finitely generated projective graded modules over the alge...
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In this monograph, we lay some foundations of a theory of infinite dimensional Euclidean lattices - and more generally, of infinite dimensional Hermitian vector bundles over some "arithmetic curve" ${\rm Spec}\,\mathcal{O}_K$ attached to the ring of...
Given a submanifold $M\subset \mathbf{R}^ν$, a curve $γ:I\to M$ and tangent vectors $v$ along $γ$, we roll the tangent space along $γ$. In doing so, we get an imprint of $γ$ on the tangent space, as well as an imprint of tangent vectors. We show...
Methods are presented for finding Killing-Yano tensors, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector. These methods are similar to a method developed by the authors for find...
Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely ge...
This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\toδ$) drawn from a Gaussian mixture...
During the last two decades, locally stationary processes have been widely studied in the time series literature. In this paper we consider the locally-stationary vector-auto-regression model of order one, or LS-VAR(1), and estimate its parameters by...
A Kochen-Specker contradiction is produced with 36 vectors in a real 8-dimensional Hilbert space. These vectors can be combined into 30 distinct projection operators (14 of rank 2, and 16 of rank 1). A state-specific variant of this contradiction r...
Our study on nondegenerate dark-bright-bright solitons in a three-component Manakov model with repulsive interactions reveals the existence of diverse branches of nondegenerate vector solitons. For fixed bright component particle numbers and a given...
We define two algebra automorphisms $T_0$ and $T_1$ of the $q$-Onsager algebra $B_c$, which provide an analog of G. Lusztig's braid group action for quantum groups. These automorphisms are used to define root vectors which give rise to a PBW basis fo...
We extend results of Bénéteau, Condori, Liaw, Seco, and the author concerning cyclic vectors in Dirichlet-type spaces to the setting of the unit ball, identifying some classes of cyclic and non-cyclic functions, and noting the necessity of certain...
A search for singly produced vector-like $T/Y$ quark is performed in proton-proton collision data at a centre-of-mass energy of $13$ TeV corresponding to an integrated luminosity of $139.1 fb^{-1}$, recorded with the ATLAS detector at the LHC from 20...
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A set $S\subseteq\{0,1\}^E$ of binary vectors, with positions indexed by $E$, is said to be a \textit{powerful code} if, for all $X\subseteq E$, the number of vectors in $S$ that are zero in the positions indexed by $X$ is a power of 2. By treating b...
Approximate nearest neighbor (ANN) search is a performance-critical component of many machine learning pipelines. Rigorous benchmarking is essential for evaluating the performance of vector indexes for ANN search. However, the datasets of the existin...