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991.
992.
We investigate the ability of deep deep rectified linear unit (ReLU) networks to approximate multivariate functions. Specially, we establish the approximation error estimate on a class of bandlimited functions; in this case, ReLU networks can overcome the “curse of dimensionality.” 相似文献
993.
AbstractWe generalize the outer subdifferential construction suggested by Cánovas, Henrion, López and Parra for max type functions to pointwise minima of regular Lipschitz functions. We also answer an open question about the relation between the outer subdifferential of the support of a regular function and the end set of its subdifferential posed by Li, Meng and Yang. 相似文献
994.
《Indagationes Mathematicae》2022,33(6):1263-1296
We study the -th moment of central values of the family of primitive cubic and quartic Dirichlet -functions. We establish sharp lower bounds for all real unconditionally for the cubic case and under the Lindelöf hypothesis for the quartic case. We also establish sharp lower bounds for all real and sharp upper bounds for all real for both the cubic and quartic cases under the generalized Riemann hypothesis (GRH). As an application of our results, we establish quantitative non-vanishing results for the corresponding -values. 相似文献
995.
996.
Janne I. Kokkala Karen Meagher Reza Naserasr Kari J. Nurmela Patric R. J.
stergrd Brett Stevens 《组合设计杂志》2020,28(1):5-24
A covering array of strength is an array of symbols from an alphabet of size such that in every subarray, every ‐tuple occurs in at least one row. A covering array is optimal if it has the smallest possible for given , , and , and uniform if every symbol occurs or times in every column. Before this paper, the only known optimal covering arrays for were orthogonal arrays, covering arrays with constructed from Sperner's Theorem and the Erd?s‐Ko‐Rado Theorem, and 11 other parameter sets with and . In all these cases, there is a uniform covering array with the optimal size. It has been conjectured that there exists a uniform covering array of optimal size for all parameters. In this paper, a new lower bound as well as structural constraints for small uniform strength‐2 covering arrays is given. Moreover, covering arrays with small parameters are studied computationally. The size of an optimal strength‐2 covering array with and is now known for 21 parameter sets. Our constructive results continue to support the conjecture. 相似文献
997.
B. V. Pal’tsev 《Mathematical Notes》1999,65(5):571-581
Bounds uniform in the real argument and the index for the functionsa
ν
(x)=xI′
ν
(x)/I′
ν
(x) andb
ν
(x)=xK′
ν
(x)/K
ν
(x), as well as for the modified Bessel functionsI
ν(x) andK
ν(x), are established in the quadrantx>0, ν≥0, except for some neighborhoods of the pointx=0, ν=0.
Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 681–692, May, 1999. 相似文献
998.
In this paper we obtain a lower bound for the logarithmic Sobolev constant of the operator on C∞(M) given by LU f = Δ f - (?U|?f), where U ? C∞(M), M being a finite dimensional compact Riemannian manifold without boundary, in terms of the spectral gap of LU and the lowest eigenvalue of the operator -LU + V, where V is a function related to U and the Ricci curvature of M. Under suitable conditions and being U ≡ 0, this result improves a previous one by J.-D. DEUSCHEL and D.W. STROOCK (J. Funct. Anal. 92 (1990), 30–48). 相似文献
999.
Mark Krasnosel'Skii Reinhard Mennicken Dmitrii Rachinskii 《Mathematische Nachrichten》1999,207(1):133-155
We study quasilinear elliptic equations with strong nonlinear terms and systems of such equations. The methods developed by the authors in [1], [2] are used to prove the existence of solutions for boundary—value problems using some information on behavior of potential bounds for nonlinearities; the L–characteristics of elliptic operators and their fractional powers play an important role. New conditions are suggested for the existence of classical solutions of quasilinear second order elliptic equations. 相似文献
1000.
Debra J. Waugh 《Order》1999,16(1):77-87
Björner and Wachs proved that under the weak order every quotient of a Coxeter group is a meet semi-lattice, and in the finite case is a lattice. In this paper, we examine the case of an affine Weyl group W with corresponding finite Weyl group W
0. In particular, we show that the quotient of W by W
0 is a lattice and that up to isomorphism this is the only quotient of W which is a lattice. We also determine that the question of which pairs of elements of W have upper bounds can be reduced to the analogous question within a particular finite subposet. 相似文献