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Horrocks theorem for odd orthogonal groups
Ambily A A, Sugilesh H
https://arxiv.org/abs/2506.10360 https://arxiv.org/pdf/2506.10360…

Horrocks theorem for odd orthogonal groups
We prove Horrocks' theorem for the odd elementary orthogonal group, which gives a decomposition of an orthogonal matrix with entries from a polynomial ring $R[X]$, over a commutative ring $R$ in which 2 is invertible, as a product of an orthogonal matrix with entries in $R$ and an elementary orthogonal matrix with entries from $R[X]$.

Improved Learning via k-DTW: A Novel Dissimilarity Measure for Curves
Amer Krivo\v{s}ija, Alexander Munteanu, Andr\'e Nusser, Chris Schwiegelshohn
https://arxiv.org/abs/2505.23431

Improved Learning via k-DTW: A Novel Dissimilarity Measure for Curves
This paper introduces $k$-Dynamic Time Warping ($k$-DTW), a novel dissimilarity measure for polygonal curves. $k$-DTW has stronger metric properties than Dynamic Time Warping (DTW) and is more robust to outliers than the Fréchet distance, which are the two gold standards of dissimilarity measures for polygonal curves. We show interesting properties of $k$-DTW and give an exact algorithm as well as a $(1+\varepsilon)$-approximation algorithm for $k$-DTW by a parametric search for the $k$-th lar…