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Uniqueness of near-horizon geometries of rotating extremal AdS(4) black holes [PDF]
, 2009 We consider stationary extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions. We determine all non-static axisymmetric near-horizon geometries and all static near-horizon geometries for ...
Lucietti, James, Kunduri, Hari K.
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Approximation by Extreme Functions
Journal of Approximation Theory, 1999 For a topological space \(T\) and a real normed space \(X\) let \(Y= C(T,X)\), the normed space of all \(X\)-valued bounded continuous functions on \(T\) endowed with the supremum norm. Let \(Y^{-1}=\{f\in Y:f\) does not vanish in any \(t\in T\}\). For \(f\in Y\), let \(\alpha(f)= d(f,Y^{-1})\) and let \(m(f)= \inf \{\|f(t)\|: t\in T\}\).
Jiménez-Vargas, A +2 more
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Functional extreme learning machine
Frontiers in Computational Neuroscience, 2023 IntroductionExtreme learning machine (ELM) is a training algorithm for single hidden layer feedforward neural network (SLFN), which converges much faster than traditional methods and yields promising performance. However, the ELM also has some shortcomings, such as structure selection, overfitting and low generalization performance.MethodsThis article ...
Xianli Liu +6 more
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On the homogeneous extremal function for the standard simplex [PDF]
, 2018 In this paper, an explicit formula for the homogeneous Siciak’s extremal function is computed in the case of standard simplex in RN. There are discussed some problems related to this result.
Baran, Mirosław
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An extremal harmonic function [PDF]
Proceedings of the American Mathematical Society, 1969 surface 3x=h-'(X) and D(u; X) for the Dirichlet integral over the region ix bounded by a and fi. The main result of this paper is the inequality: maxhJ|Qx=m(h; X)=D(h; X)
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Robin functions and extremal functions [PDF]
Annales Polonici Mathematici, 2003 Let \(L\) denote the set of plurisubharmonic functions \(u\) on \(\mathbb C^n\) of logarithmic growth, that is \(u(z) \leq \text{log }^+|z|+C\). For a bounded Borel set \(E\) in \(\mathbb C^n\), define \(V_E(z) = \sup\{u(z): u\in L, u\leq 0 \text{ on } E\}\).
Bloom, T., Levenberg, N., Ma'u, S.
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The extremal function for K9= minors [PDF]
Journal of Graph Theory, 2019 AbstractWe prove the extremal function for minors, where denotes the complete graph with two edges removed. In particular, we show that any graph with vertices and at least edges either contains a minor or is isomorphic to a graph obtained from disjoint copies of and by identifying cliques of size 5.
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Interpolation of Weighted Extremal Functions [PDF]
Arnold Mathematical Journal, 2021 AbstractAn approach to interpolation of compact subsets of$${{\mathbb {C}}}^n$$Cn, including Brunn–Minkowski type inequalities for the capacities of the interpolating sets, was developed in [8] by means of plurisubharmonic geodesics between relative extremal functions of the given sets.
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Revisiting leading quantum corrections to near extremal black hole thermodynamics
Journal of High Energy Physics, 2023 Computing the 4D Euclidean path integral to one-loop order we find the large quantum corrections that govern the behavior of a spherically symmetric non-supersymmetric near-extremal black hole at very low temperature.
Nabamita Banerjee, Muktajyoti Saha
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Equivalence of JT gravity and near-extremal black hole dynamics in higher derivative theory
Journal of High Energy Physics, 2022 Two derivative Jackiw-Teitelboim (JT) gravity theory captures the near-horizon dynamics of higher dimensional near-extremal black holes, which is governed by a Schwarzian action at the boundary in the near-horizon region.
Nabamita Banerjee +3 more
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