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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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A Functional Extremal Criterion [PDF]
Journal of Mathematical Sciences, 2004 Let \({\mathcal N}=\{(t_k, X_k):\, k\geq 1\}\) be a point process with time space \([0, \infty)\) and state space \([0, \infty)^d\), where \(\{t_k\}\) are distinct nonrandom time points monotonically increasing to \(\infty\). \(\{X_k\}\) are independent and identically distributed random vectors on a given probability space with values in \([0,\infty ...
Jordanova, P. K., Pancheva, E. I.
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Extremal Functions for Morrey’s Inequality [PDF]
Archive for Rational Mechanics and Analysis, 2021 We give a qualitative description of extremals for Morrey's inequality. Our theory is based on exploiting the invariances of this inequality, studying the equation satisfied by extremals and the observation that extremals are optimal for a related convex minimization problem.
Ryan Hynd, Francis Seuffert
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Extremal plurisubharmonic functions [PDF]
Annales Polonici Mathematici, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cegrell, Urban, Thorbiörnson, Johan
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On an Optimal Quadrature Formula in a Hilbert Space of Periodic Functions
Algorithms, 2022 The present work is devoted to the construction of optimal quadrature formulas for the approximate calculation of the integrals ∫02πeiωxφ(x)dx in the Sobolev space H˜2m.
Kholmat Shadimetov +2 more
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Construction of optimal interpolation formula exact for trigonometric functions by Sobolev’s method
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2022 The paper is devoted to derivation of the optimal interpolation formula in W2(0,2)(0,1) Hilbert space by Sobolev’s method. Here the interpolation formula consists of a linear combination ΣNβ=0Cβφ(xβ) of the given values of a function φ from the space ...
Shadimetov, Kh.M. +2 more
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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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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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Entropy of an extremal electrically charged thin shell and the extremal black hole
Physics Letters B, 2015 There is a debate as to what is the value of the entropy S of extremal black holes. There are approaches that yield zero entropy S=0, while there are others that yield the Bekenstein–Hawking entropy S=A+/4, in Planck units.
José P.S. Lemos +2 more
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Reversed Hardy-Littlewood-Sobolev inequalities with weights on the Heisenberg group
Advances in Nonlinear Analysis, 2023 In this article, we establish some reverse weighted Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. We then show the existence of extremal functions for the above inequalities by combining the subcritical approach and the renormalization ...
Hu Yunyun
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