نتایج جستجو برای: lipschitz function
تعداد نتایج: 1218581 فیلتر نتایج به سال:
Rademacher and Gaussian complexities are successfully used in learning theory for measuring the capacity of the class of functions to be learned. One of the most important properties for these complexities is their Lipschitz property: a composition of a class of functions with a fixed Lipschitz function may increase its complexity by at most twice the Lipschitz constant. The proof of this prope...
We show that local minimizers of functionals of the form Z Ω [f(Du(x)) + g(x , u(x))] dx, u ∈ u0 + W 1,p 0 (Ω), are locally Lipschitz continuous provided f is a convex function with p − q growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.
Keywords: Hurwitz–Lerch Zeta function Lipschitz–Lerch Zeta function Lerch Zeta function Hurwitz Zeta function Riemann Zeta function Legendre chi function Bernoulli polynomials Bernoulli numbers Discrete Fourier transform a b s t r a c t It is shown that there exists a companion formula to Srivastava's formula for the Lipschitz–Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bern...
Motivated by applications to (directionally) Lipschitz functions, we provide a general result on the almost everywhere Gâteaux differentiability of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone with nonempty interior. This seemingly arduous restriction is useful, since it covers the case of directionally Lips...
We prove that every bounded Lipschitz function F on a subset Y of a length space X admits a tautest extension to X, i.e., a unique Lipschitz extension u : X → R for which LipUu = Lip∂Uu for all open U ⊂ X r Y . This was previously known only for bounded domains in Rn, in which case u is infinity-harmonic, that is, a viscosity solution to ∆∞u = 0, where
We develop a. new feedforward neuralnet.work represent.ation of Lipschitz functions from [0, p]n into [0,1] ba'3ed on the level sets of the function. We show that ~~ + ~€r + ( 1 + h) (:~) n is an upper bound on the number of nodes needed to represent f to within uniform error Cr, where L is the Lipschitz constant. \Ve also show that the number of bits needed to represent the weights in the netw...
Let g:Ω=[0,1] d →ℝ denote a Lipschitz function that can be evaluated at each point, but the price of heavy computational time. X stand for random variable with values in Ω such one is able to simulate, least approximately, according restriction law any subset Ω. For example, thanks Markov chain Monte Carlo techniques, this always possible when admits density known up normalizing constant. In co...
A grounded M -Lipschitz function on a rooted d-ary tree is an integer-valued map on the vertices that changes by at most M along edges and attains the value zero on the leaves. We study the behavior of such functions, specifically, their typical value at the root v0 of the tree. We prove that the probability that the value of a uniformly chosen random function at v0 is more than M + t is doubly...
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