Nonuniqueness of weak solutions to the Navier-Stokes equation

T Buckmaster, V Vicol - Annals of Mathematics, 2019 - projecteuclid.org
For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least
one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this …

[图书][B] Analysis in Banach spaces

Over the past fifteen years, motivated by regularity problems in evolution equations, there
has been tremendous progress in the analysis of Banach space-valued functions and …

[图书][B] An invitation to compressive sensing

S Foucart, H Rauhut, S Foucart, H Rauhut - 2013 - Springer
This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

[图书][B] Quantum information theory

MM Wilde - 2013 - books.google.com
Finally, here is a modern, self-contained text on quantum information theory suitable for
graduate-level courses. Developing the subject'from the ground up'it covers classical results …

[图书][B] Variable Lebesgue spaces: Foundations and harmonic analysis

DV Cruz-Uribe, A Fiorenza - 2013 - books.google.com
This book provides an accessible introduction to the theory of variable Lebesgue spaces.
These spaces generalize the classical Lebesgue spaces by replacing the constant exponent …

A mathematical theory of deep convolutional neural networks for feature extraction

T Wiatowski, H Bölcskei - IEEE Transactions on Information …, 2017 - ieeexplore.ieee.org
Deep convolutional neural networks (DCNNs) have led to breakthrough results in numerous
practical machine learning tasks, such as classification of images in the ImageNet data set …

[图书][B] The Navier-Stokes problem in the 21st century

PG Lemarié-Rieusset - 2018 - taylorfrancis.com
Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis
The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize …

[HTML][HTML] Neural network with unbounded activation functions is universal approximator

S Sonoda, N Murata - Applied and Computational Harmonic Analysis, 2017 - Elsevier
This paper presents an investigation of the approximation property of neural networks with
unbounded activation functions, such as the rectified linear unit (ReLU), which is the new de …

[图书][B] Lebesgue and Sobolev spaces with variable exponents

L Diening, P Harjulehto, P Hästö, M Ruzicka - 2011 - books.google.com
The field of variable exponent function spaces has witnessed an explosive growth in recent
years. The standard reference article for basic properties is already 20 years old. Thus this …

[图书][B] Morrey spaces: introduction and applications to integral operators and PDE's, Volume I

Y Sawano - 2020 - taylorfrancis.com
Title: Morrey spaces: introduction and applications to integral operators and PDE's/Yoshihiro
Sawano, Giuseppe Di Fazio, Denny Ivanal Hakim. Description: First edition.| Boca Raton …