Results 11 to 20 of about 285,483 (304)
Total positivity, Schubert positivity, and geometric Satake [PDF]
Journal of Algebra, 2016 Let G be a simple and simply-connected complex algebraic group, and let X \subset G^\vee be the centralizer subgroup of a principal nilpotent element. Ginzburg and Peterson independently related the ring of functions on X with the homology ring of the affine Grassmannian Gr_G.
Lam, Thomas, Rietsch, Konstanze
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Hyperdeterminantal Total Positivity
Symmetry, Integrability and Geometry: Methods and ApplicationsFor a given positive integer $m$, the concept of <I>hyperdeterminantal total positivity</I> is defined for a kernel $K\colon {\mathbb R}^{2m} \to {\mathbb R}$, thereby generalizing the classical concept of total positivity. Extending the fundamental example, $K(x,y) = \exp(xy)$, $x, y \in \mathbb{R}$, of a classical totally positive kernel,
Johnson, Kenneth W. +1 more
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Total Positivity and Convexity Preservation
Journal of Approximation Theory, 1999 In this paper the author introduces a concept of \(d\)-convexity of curves in the \(d\)-dimensional space and characterizes totally positive blending systems in terms of \(d\)-convexity. He shows that for certain systems total positivity and rational convexity preservation are equivalent.
Floater, Michael S.
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Positive Hankel Matrices, Eigenvalues and Total Positivity
MathematicsFor positive Hankel matrices, an interval containing all eigenvalues is obtained. With a stronger condition, we also construct two sharper intervals for the eigenvalue localization. The total positivity of positive Hankel matrices is analyzed.
Juan Manuel Peña
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Linear Algebra and its Applications, 2004 The authors consider the important descriptors: totally positive, and the related terms (totally nonnegative and oscillatory). They define the concept of the total positivity interval of such matrices. They seek concretely this interval and investigate some properties of this.
Gladwell, G.M.L., Ghanbari, K.
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Total positivity and dependence of order statistics [PDF]
, 2023 In this comprehensive study, we delve deeply into the concept of multivariate total positivity, defining it in accordance with a direction. We rigorously explore numerous salient properties, shedding light on the nuances that characterize this notion ...
Amo Artero, Enrique de +4 more
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Total Positivity in Springer Fibres [PDF]
The Quarterly Journal of Mathematics, 2020 Abstract Let u be a unipotent element in the totally positive part of a complex reductive group. We consider the intersection of the Springer fibre at u with the totally positive part of the flag manifold. We show that this intersection has a natural cell decomposition which is part of the cell decomposition (Rietsch) of the totally ...
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Combinatorics of Positroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Recently Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroids.
Suho Oh
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Totally positive matrices and totally positive hypergraphs
Linear Algebra and its Applications, 2001 This paper characterizes (0,1)-matrices which are totally positive, that is, all their minors are totally positive. First the case of \(1\times 1\) and \(2\times 2\) minors is characterized in terms of interval hypergraphs and then the general case is characterized in terms of a chain of cliques \(C_i\), \(C_i\cap C_j = \emptyset \Leftrightarrow |i-j ...
Kubicki, Grzegorz +2 more
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Association between Inhaled Corticosteroid Use and SARS-CoV-2 Infection: A Nationwide Population-Based Study in South Korea [PDF]
Tuberculosis and Respiratory Diseases, 2022 Background Although it is known that inhaled corticosteroid (ICS) use may increase the risk of respiratory infection, its influence on the risk of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection remains unknown.
Sang Chul Lee +4 more
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