Results 11 to 20 of about 8,616 (247)
Non-Lipschitz differentiable functions on slit domains [PDF]
Revista Matemática Complutense, 2017 It is proved the existence of large algebraic structures –including large vector subspaces or infinitely generated free algebras– inside the family of non-Lipschitz differentiable real functions with bounded gradient defined on special non-convex plane ...
Bernal González, Luis +3 more
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Stochastic Mean-Field Limit: Non-Lipschitz Forces \& Swarming
Mathematical Models and Methods in Applied Sciences, 2010 We consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the system is close to the solution of a kinetic PDE.
Bolley, François +2 more
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Assigning probabilities to non-Lipschitz mechanical systems [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021 We present a method for assigning probabilities to the solutions of initial value problems that have a Lipschitz singularity. To illustrate the method, we focus on the following toy example: d2r(t)dt2=ra, r(t=0)=0, and dr(t)dt∣r(t=0)=0, with a∈]0,1[. This example has a physical interpretation as a mass in a uniform gravitational field on a frictionless,
Danny E. P. Vanpoucke, Sylvia Wenmackers
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Prevalence of non-Lipschitz Anosov foliations [PDF]
Electronic Research Announcements of the American Mathematical Society, 1997 We give sharp regularity results for the invariant subbundles of hyperbolic dynamical systems and give open dense sets of codimension one systems where this regularity is not exceeded as well as open dense sets of symplectic, geodesic, and codimension one systems where the analogous regularity results of Pugh, Shub, and Wilkinson are optimal.
Hasselblatt, Boris, Wilkinson, Amie
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Non-Lipschitz Attack: A More Sparse Adversarial Attack via Non-Lipschitz $ℓ_p$ Regularization
CSIAM Transactions on Applied Mathematics, 2023 Summary: Deep neural networks are considerably vulnerable to adversarial attacks. Therein, sparse attacks mislead image classifiers with a sparse, pixel-level perturbation that alters few pixels, and have much potential in physical world applications. The existing sparse attacks are mostly based on \(\ell_0\) optimization, and there are few theoretical
Lin, Xuan +3 more
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Hyperbolic operators with non-Lipschitz coefficients [PDF]
Duke Mathematical Journal, 1995 In a joint paper of some years ago [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 6, 511-559 (1979; Zbl 0417.35049)], the first author, \textit{E. De Giorgi} and the reviewer investigated the solvability of a strictly hyperbolic Cauchy problem of the form \[ \partial^2_t u= \sum \partial_i(a_{ij}, \partial_j u),\quad u(0, x)= u_0(x),\quad \partial_t u(
COLOMBINI, FERRUCCIO, N. LERNER
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Terrace Solutions for Non-Lipschitz Multistable Nonlinearities
SIAM Journal on Mathematical Analysis, 2022 Traveling wave solutions of reaction-diffusion equations are well-studied for Lipschitz continuous monostable and bistable reaction functions. These special solutions play a key role in mathematical biology and in particular in the study of ecological invasions.
Thomas Giletti +2 more
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The Martin boundary in non-Lipschitz domains [PDF]
Transactions of the American Mathematical Society, 1993 The Martin boundary with respect to the Laplacian \(\Delta\) and with respect to a uniformly elliptic operator \(L\) in divergence form is considered for a wider class than the Lipschitz domains in \(\mathbb{R}^ d\), \(d \geq 3\). For a so-called bounded \(C^ \gamma\) domain \(D\) it is shown that the Martin boundary of \(D\) and its Euclidean boundary
Burdzy, Krzysztof, Bass, Richard F.
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Strong solutions for stochastic differential equations with jumps [PDF]
, 2010 General stochastic equations with jumps are studied. We provide criteria for the uniqueness and existence of strong solutions under non-Lipschitz conditions of Yamada-Watanabe type.
Li, Zenghu, Mytnik, Leonid
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Mathematical Modelling and Analysis, 2022 In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces.
Bing Tan, Xiaolong Qin
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