The Experts below are selected from a list of 45 Experts worldwide ranked by ideXlab platform
José Manuel Benítez - One of the best experts on this subject based on the ideXlab platform.
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neural networks with a continuous squashing Function in the output are universal approximators
Neural Networks, 2000Co-Authors: Juan Castro, Carlos Javier Mantas, José Manuel BenítezAbstract:Abstract In 1989 Hornik as well as Funahashi established that multilayer feedforward networks without the squashing Function in the output layer are universal approximators. This result has been often used improperly because it has been applied to multilayer feedforward networks with the squashing Function in the output layer. In this paper, we will prove that also this kind of neural networks are universal approximators, i.e. they are capable of approximating any Borel Measurable Function from one finite dimensional space into (0,1) n to any desired degree of accuracy, provided sufficiently many hidden units are available.
Juan Castro - One of the best experts on this subject based on the ideXlab platform.
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neural networks with a continuous squashing Function in the output are universal approximators
Neural Networks, 2000Co-Authors: Juan Castro, Carlos Javier Mantas, José Manuel BenítezAbstract:Abstract In 1989 Hornik as well as Funahashi established that multilayer feedforward networks without the squashing Function in the output layer are universal approximators. This result has been often used improperly because it has been applied to multilayer feedforward networks with the squashing Function in the output layer. In this paper, we will prove that also this kind of neural networks are universal approximators, i.e. they are capable of approximating any Borel Measurable Function from one finite dimensional space into (0,1) n to any desired degree of accuracy, provided sufficiently many hidden units are available.
Hofmanová Martina - One of the best experts on this subject based on the ideXlab platform.
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Ergodic theory for energetically open compressible fluid flows
2020Co-Authors: Fanelli Francesco, Feireisl Eduard, Hofmanová MartinaAbstract:The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier--Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a stationary statistical solution, which is interpreted as a stochastic process with continuous trajectories supported by the family of weak solutions of the problem. The abstract Birkhoff--Khinchin theorem is applied to obtain convergence (in expectation and a.s.) of ergodic averages for any bounded Borel Measurable Function of state variables associated to any stationary solution. Finally, we show that validity of the ergodic hypothesis is determined by the behavior of entire solutions (i.e. a solution defined for any $t\in R$). In particular, the ergodic averages converge for any trajectory provided its $\omega-$limit set in the trajectory space supports a unique (in law) stationary solution.Comment: Submitte
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Ergodic theory for energetically open compressible fluid flows
HAL CCSD, 2020Co-Authors: Fanelli Francesco, Feireisl Eduard, Hofmanová MartinaAbstract:The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier-Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a stationary statistical solution, which is interpreted as a stochastic process with continuous trajectories supported by the family of weak solutions of the problem. The abstract Birkhoff-Khinchin theorem is applied to obtain convergence (in expectation and a.s.) of ergodic averages for any bounded Borel Measurable Function of state variables associated to any stationary solution. Finally, we show that validity of the ergodic hypothesis is determined by the behavior of entire solutions (i.e. a solution defined for any t ∈ R). In particular, the ergodic averages converge for any trajectory provided its ω−limit set in the trajectory space supports a unique (in law) stationary solution
Imed Bachar - One of the best experts on this subject based on the ideXlab platform.
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estimates on the green s Function and existence of positive solutions of nonlinear singular elliptic equations in the half space
Positivity, 2005Co-Authors: Imed Bachar, Habib MaâgliAbstract:We establish a new 3G-Theorem for the Green’s Function for the half space \(\mathbb{R}^{n}_{+} := \{x = (x_{1},\ldots,x_{n}) \in \mathbb{R}^{n} : x_{n} > 0\}, (n \geq 3).\) We exploit this result to introduce a new class of potentials \(K(\mathbb{R}^{n}_{+})\) that we characterize by means of the Gauss semigroup on \(\mathbb{R}^{n}_{+}\). Next, we define a subclass \(K^{\infty}(\mathbb{R}^{n}_{+})\) of \(K(\mathbb{R}^{n}_{+})\) and we study it. In particular, we prove that \(K^{\infty}(\mathbb{R}^{n}_{+})\) properly contains the classical Kato class \(K^\infty_n (\mathbb{R}^{n}_{+})\). Finally, we study the existence of positive continuous solutions in \(\mathbb{R}^{n}_{+}\) of the following nonlinear elliptic problem $$\left\{\begin{array}{ll} \Delta u + h(., u) = 0,\\hbox{in}\mathbb{R}^{n}_{+} \ \hbox{(in the sense of distributions)},&\\ u|_{\partial\mathbb{R}^{n}_{+}} = 0, &\end{array}\right.$$ where h is a Borel Measurable Function in \(\mathbb{R}^{n}_{+} \times (0,\infty),\) satisfying some appropriate conditions related to the class \(K^{\infty}(\mathbb{R}^{n}_{+})\).
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estimates on the green Function and existence of positive solutions of nonlinear singular elliptic equations
Communications in Contemporary Mathematics, 2003Co-Authors: Imed Bachar, Habib Maâgli, Noureddine ZeddiniAbstract:We establish a 3G-Theorem for the Green's Function for an unbounded regular domain D in ℝn(n ≥ 3), with compact boundary. We exploit this result to introduce a new class of potentials K(D) that properly contains the classical Kato class . Next, we study the existence and the uniqueness of a positive continuous solution u in of the following nonlinear singular elliptic problem where φ is a nonnegative Borel Measurable Function in D × (0, ∞), that belongs to a convex cone which contains, in particular, all Functions φ(x, t) = q(x)t-σ, σ ≥ 0 with q ∈ K(D). We give also some estimates on the solution u.
Carlos Javier Mantas - One of the best experts on this subject based on the ideXlab platform.
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neural networks with a continuous squashing Function in the output are universal approximators
Neural Networks, 2000Co-Authors: Juan Castro, Carlos Javier Mantas, José Manuel BenítezAbstract:Abstract In 1989 Hornik as well as Funahashi established that multilayer feedforward networks without the squashing Function in the output layer are universal approximators. This result has been often used improperly because it has been applied to multilayer feedforward networks with the squashing Function in the output layer. In this paper, we will prove that also this kind of neural networks are universal approximators, i.e. they are capable of approximating any Borel Measurable Function from one finite dimensional space into (0,1) n to any desired degree of accuracy, provided sufficiently many hidden units are available.