Results 31 to 40 of about 988,365 (280)
The Strong Maximal Rank conjecture and higher rank Brill–Noether theory [PDF]
Journal of the London Mathematical Society, 2021 38 pages, significantly reorganized final version to appear in J.
Cotterill, Ethan +2 more
openaire +2 more sources
Maximal Generalized Rank in Graphical Matrix Spaces [PDF]
, 2022 In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a ...
Spiridonov, Igor +2 more
core +1 more source
Optimization Problems of Hermitian Quadratic Matrix-Valued Functions and Applications
AxiomsIn this paper, we investigate optimization problems for a Hermitian quadratic matrix-valued function involving two variable matrices. We derive algebraic formulas for the maximal and minimal ranks and partial inertias of this function based on a ...
Sihem Guerarra
doaj +1 more source
On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction
Abstract and Applied Analysis, 2014 We discuss the feasible interval of the parameter k and a general expression of matrix X which satisfies the rank equation r(A-BXC)=k. With these results, we study two problems under the rank constraint r(A-BXC)=k.
Hongxing Wang, Yeguo Sun
doaj +1 more source
Upper Bounds for the Isolation Number of a Matrix over Semirings
Mathematics, 2019 Let S be an antinegative semiring. The rank of an m × n matrix B over S is the minimal integer r such that B is a product of an m × r matrix and an r × n matrix.
LeRoy B. Beasley, Seok-Zun Song
doaj +1 more source
A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane
Journal of Function Spaces and Applications, 2012 We determine, via classroom proofs, the maximal ideal space, the Bass stable rank as well as the topological and dense stable rank of the uniform closure of all complex-valued functions continuously differentiable on neighborhoods of a compact planar set
Raymond Mortini, Rudolf Rupp
doaj +1 more source
Terracini Loci: Dimension and Description of Its Components
Mathematics, 2023 We study the Terracini loci of an irreducible variety X embedded in a projective space: non-emptiness, dimensions and the geometry of their maximal dimension’s irreducible components.
Edoardo Ballico
doaj +1 more source
Estimating α-Rank by Maximizing Information Gain
Proceedings of the AAAI Conference on Artificial Intelligence, 2021 Game theory has been increasingly applied in settings where the game is not known outright, but has to be estimated by sampling. For example, meta-games that arise in multi-agent evaluation can only be accessed by running a succession of expensive experiments that may involve simultaneous deployment of several agents. In this paper, we focus on α-rank,
Tabish Rashid +2 more
openaire +2 more sources
Canonical heights for abelian group actions of maximal dynamical rank
Forum of Mathematics, SigmaLet X be a smooth projective variety of dimension $n\geq 2$ and $G\cong \mathbf {Z}^{n-1}$ a free abelian group of automorphisms of X over $\overline {\mathbf {Q}}$ . Suppose that G is of positive entropy.
Fei Hu, Guolei Zhong
doaj +1 more source
The Maximal Rank Conjecture and Rank Two Brill-Noether Theory [PDF]
Pure and Applied Mathematics Quarterly, 2011 We describe applications of Koszul cohomology to the Brill-Noether theory of rank 2 vector bundles. Among other things, we show that in every genus g>10, there exist curves invalidating Mercat's Conjecture for rank 2 bundles. On the other hand, we prove that Mercat's Conjecture holds for general curves of bounded genus, and its failure locus is a ...
Farkas, Gavril, Ortega, Angela
openaire +2 more sources