scholarly journals Lipschitzian selections in approximation from nonconvex sets of bounded functions

1989 ◽  
Vol 56 (2) ◽  
pp. 217-224 ◽  
Author(s):  
Vasant A Ubhaya
Keyword(s):  
Nonconvex Sets ◽  
Bounded Functions

scholarly journals Fractional Ostrowski type inequalities for bounded functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Samet Erden ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya ◽  
Sabah Iftikhar ◽  
Poom Kumam
Keyword(s):  
Bounded Functions

scholarly journals Pairings between bounded divergence-measure vector fields and BV functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Graziano Crasta ◽  
Virginia De Cicco ◽  
Annalisa Malusa
Keyword(s):  
Vector Field ◽  
Conservation Laws ◽  
Bounded Variation ◽  
Vector Fields ◽  
Hyperbolic Conservation Laws ◽  
Divergence Measure ◽  
Compensated Compactness ◽  
Hyperbolic Conservation ◽  
Bv Functions ◽  
Bounded Functions

AbstractWe introduce a family of pairings between a bounded divergence-measure vector field and a function u of bounded variation, depending on the choice of the pointwise representative of u. We prove that these pairings inherit from the standard one, introduced in [G. Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. (4) 135 1983, 293–318], [G.-Q. Chen and H. Frid, Divergence-measure fields and hyperbolic conservation laws, Arch. Ration. Mech. Anal. 147 1999, 2, 89–118], all the main properties and features (e.g. coarea, Leibniz, and Gauss–Green formulas). We also characterize the pairings making the corresponding functionals semicontinuous with respect to the strict convergence in \mathrm{BV}. We remark that the standard pairing in general does not share this property.

Quantitative Voronovskaya-Type Results for Polynomially Bounded Functions

2016 ◽  
Vol 70 (3-4) ◽  
pp. 313-324 ◽  
Author(s):  
Ali Aral ◽  
Heiner Gonska ◽  
Margareta Heilmann ◽  
Gancho Tachev
Keyword(s):  
Bounded Functions

Wavelets as activation functions in Neural Networks

2021 ◽  
pp. 1-11
Author(s):  
Oscar Herrera ◽  
Belém Priego
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
High Performance ◽  
Research Area ◽  
Experimental Results ◽  
Activation Functions ◽  
Hyperbolic Tangent ◽  
Open Research ◽  
Bounded Functions

Traditionally, a few activation functions have been considered in neural networks, including bounded functions such as threshold, sigmoidal and hyperbolic-tangent, as well as unbounded ReLU, GELU, and Soft-plus, among other functions for deep learning, but the search for new activation functions still being an open research area. In this paper, wavelets are reconsidered as activation functions in neural networks and the performance of Gaussian family wavelets (first, second and third derivatives) are studied together with other functions available in Keras-Tensorflow. Experimental results show how the combination of these activation functions can improve the performance and supports the idea of extending the list of activation functions to wavelets which can be available in high performance platforms.

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