Results 1 to 10 of about 1,721 (200)

Hyperplane Arrangements in the Grassmannian

Le Matematiche
The Euler characteristic of a very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the Grassmannian with $d$ hyperplane sections removed. We provide a combinatorial formula, and explain how to compute this Euler characteristic in practice, both symbolically and ...
E. Mazzucchelli, D. Pavlov, K. Wang
openaire   +3 more sources

A Converse to a Theorem of Oka and Sakamoto for Complex Line Arrangements

Mathematics, 2013
Let C1 and C2 be algebraic plane curves in ℂ 2 such that the curves intersect in d1 · d2 points where d1, d2 are the degrees of the curves respectively. Oka and Sakamoto proved that π1( ℂ 2 \ C1 U C2)) ≅ π1 ( ℂ 2 \ C1) × π1 ( ℂ 2 \
Kristopher Williams
doaj   +1 more source

Toral Arrangements and Hyperplane Arrangements

Rocky Mountain Journal of Mathematics, 1998
The author defines a toral arrangement to be a finite set \({\mathcal A}\) of characters of an algebraic torus \(T\). Such a set corresponds to an integral hyperplane arrangement \(d{\mathcal A}\) in the Lie algebra of the torus given by the kernels of the derivatives of the characters.
openaire   +2 more sources

A blowup algebra for hyperplane arrangements [PDF]

Algebra & Number Theory, 2018
22 ...
Garrousian, Mehdi, Simis, Aron, Tohăneanu, Ştefan O.   +2 more
openaire   +4 more sources

Artificial Intelligence‐Driven Insights into Electrospinning: Machine Learning Models to Predict Cotton‐Wool‐Like Structure of Electrospun Fibers

Advanced Intelligent Discovery, EarlyView.
Electrospinning allows the fabrication of fibrous 3D cotton‐wool‐like scaffolds for tissue engineering. Optimizing this process traditionally relies on trial‐and‐error approaches, and artificial intelligence (AI)‐based tools can support it, with the prediction of fiber properties. This work uses machine learning to classify and predict the structure of
Paolo D’Elia, Giovanna Pappalardo, Aldo R. Boccaccini, Liliana Liverani   +3 more
wiley   +1 more source

Lattice Sums of Hyperplane Arrangements

, 2023
39 pages, 4 ...
Yasushi, Komori, Kohji, Matsumoto, Hirofumi, Tsumura   +2 more
openaire   +2 more sources

Hyperplane arrangements with a lattice of regions [PDF]

Discrete & Computational Geometry, 1990
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anders Björner, Paul H. Edelman, Günter M. Ziegler   +2 more
openaire   +3 more sources

Machine Learning‐Based PAT Tool for Real‐Time Residual Moisture Monitoring in Lyophilized Biopharmaceuticals Using NIR Spectroscopy

Biotechnology and Bioengineering, EarlyView.
ABSTRACT There is a growing demand in the pharmaceutical industry to optimize analytical methodologies, reducing time and resource consumption while ensuring rapid process development and cost‐efficient manufacturing. Indeed, Food and Drug Administration (FDA) introduced the Process Analytical Technology (PAT) as an initiative enabling manufacturers to
Samuele Fiorenza, Mariapia D'Urso, Ambra Massei, Nunzia Falco, Davide Fissore, Enza Torino   +5 more
wiley   +1 more source

On contact loci of hyperplane arrangements

Advances in Applied Mathematics, 2022
We give an explicit expression for the contact loci of hyperplane arrangements and show that their cohomology rings are combinatorial invariants. We also give an expression for the restricted contact loci in terms of Milnor fibers of associated hyperplane arrangements.
Budur, Nero, Tran, Quang Tue
openaire   +4 more sources

A Geometric Characterization of Steady Laminar Flow

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non‐contractible streamlines which foliate the domain), then they must be either parallel or circular flows.
Theodore D. Drivas, Marc Nualart
wiley   +1 more source