Titlebook: Analysis at Large; Dedicated to the Lif Artur Avila,Michael Th. Rassias,Yakov Sinai Book 2022 The Editor(s) (if applicable) and The Author(

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The Continuous Formulation of Shallow Neural Networks as Wasserstein-Type Gradient Flows, for the weights for the error functional. In the limit, as the number of parameters tends to infinity, this gives rise to a family of parabolic equations. This survey aims to discuss this relation, focusing on the associated theoretical aspects appealing to the mathematical community and providing a list of interesting open problems.

CUMB

愤怒历史

Polynomial Equations in Subgroups and Applications,evious results of P. Corvaja and U. Zannier (2013). We also obtain a conditional improvement of recent results of J. Bourgain, A. Gamburd, and P. Sarnak (2016) and S. V. Konyagin, S. V. Makarychev, I. E. Shparlinski, and I. V. Vyugin (2019) on the structure of solutions to the reduction of the Markoff equation . + . + . = 3. modulo a prime ..

冷淡一切

Exponential Sums, Twisted Multiplicativity, and Moments,, and obtain evidence of un-correlation of exponential sums associated to different suitably unrelated and generic polynomials. The proofs combine analytic arguments with the algebraic interpretation of exponential sums and their monodromy groups.

哭得清醒了

Artur Avila,Michael Th. Rassias,Yakov SinaiA wide spectrum of subjects influenced by Bourgain’s monumental contributions to mathematics.Pays homage to the life and work of a true pioneer of mathematics.Contributions by leading experts present

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Derivate und Handlungsempfehlungen,r inequality. This is then applied to show that if . are finite sets and . is a subset of a “quasicube”, then .. This result is a key ingredient in forthcoming work of the fifth author and Pälvölgyi on the sum-product phenomenon.