Results 51 to 60 of about 1,369 (167)
Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2135-2160, 15 March 2026.ABSTRACT It is an elementary fact in the scientific literature that the Lipschitz norm of the realization function of a feedforward fully connected rectified linear unit (ReLU) artificial neural network (ANN) can, up to a multiplicative constant, be bounded from above by sums of powers of the norm of the ANN parameter vector.
Arnulf Jentzen, Timo Kröger
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Boundary Value Problems, 2009 We consider a nonlinear elliptic equation driven by the -Laplacian with a nonsmooth potential (hemivariational inequality) and Dirichlet boundary condition.
Filippakis MichaelE +3 more
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Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 1, March 2026.ABSTRACT In this paper, we present a regularization of the set‐valued Coulomb friction law based on a regularized projection. The regularized projection is used to formulate differentiable equations encoding a set‐valued friction law that can be used in typical optimal control frameworks.
Giuseppe Capobianco, Sigrid Leyendecker
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The Influence of Grain Crushing and Pore Collapse on the Formation of Faults
Journal of Geophysical Research: Solid Earth, Volume 131, Issue 3, March 2026.Abstract During an earthquake, slip occurs in a localized shear zone that features a heavily granulated fault core that can be characterized as a shear band. We study the formation of this fault core in a granular rock such as sandstone by developing a model of crushable granular media within the framework of Breakage Mechanics. This model accounts for
N. A. Collins‐Craft +3 more
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International Journal for Numerical Methods in Engineering, Volume 127, Issue 4, 28 February 2026.ABSTRACT Wave propagation effects such as resonance and interference effects complicate the design of many acoustic devices, particularly when the dimensions of the device are in the order of the operating wavelength. At the same time, these complications also offer an opportunity for numerical optimization schemes to outperform designs achieved using ...
Martin Berggren +4 more
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Minimization of nonsmooth integral functionals
International Journal of Mathematics and Mathematical Sciences, 1992 In this paper we examine optimization problems involving multidimensional nonsmooth integral functionals defined on Sobolev spaces. We obtain necessary and sufficient conditions for optimality in convex, finite dimensional problems using techniques from ...
Nikolaos S. Papageorgiou +1 more
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MathematicsThis paper develops a mathematical approach to the analysis of the stability of economic equilibria in nonsmooth models. The λ-Hölder apparatus of subdifferentials is used, which extends the class of systems under study beyond traditional smooth ...
Anna V. Aleshina +3 more
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Some Existence Theorems for Nonconvex Variational Inequalities Problems
Abstract and Applied Analysis, 2010 By using nonsmooth analysis knowledge, we provide the conditions for existence solutions of the variational inequalities problems in nonconvex setting. We also show that the strongly monotonic assumption of the mapping may not need for the existence of ...
Narin Petrot
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A Unified Convergence Analysis for Some Two-Point Type Methods for Nonsmooth Operators
Mathematics, 2019 The aim of this paper is the approximation of nonlinear equations using iterative methods. We present a unified convergence analysis for some two-point type methods.
Sergio Amat +4 more
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Applied Bionics and Biomechanics, 2016 Fish-like, dolphin-like, and bionic nonsmooth surfaces were employed in a hydraulic torque converter to achieve drag reduction and performance improvement, which were aimed at reducing profile loss, impacting loss and friction loss, respectively. YJSW335,
Liu Chunbao +4 more
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