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991.
《Mathematische Nachrichten》2018,291(1):55-85
We study minimal energy problems for strongly singular Riesz kernels , where and , considered for compact ‐dimensional ‐manifolds Γ immersed into . Based on the spatial energy of harmonic double layer potentials, we are motivated to formulate the natural regularization of such minimization problems by switching to Hadamard's partie finie integral operator which defines a strongly elliptic pseudodifferential operator of order on Γ. The measures with finite energy are shown to be elements from the Sobolev space , , and the corresponding minimal energy problem admits a unique solution. We relate our continuous approach also to the discrete one, which has been worked out earlier by D. P. Hardin and E. B. Saff. 相似文献
992.
Roman S. Gigoń 《代数通讯》2018,46(11):4884-4890
We show that an E-inversive semigroup S has a completely simple kernel KS if and only if it contains a primitive idempotent (in that case, KS is the set-theoretic union of the groups eSe, where e is a primitive idempotent of S). Along the way, some equivalent conditions for a semigroup to be E-inversive are given. Moreover, some applications of the above theorem will be pointed out. 相似文献
993.
In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the semi-recursive kernel estimator
of the regression in the multidimensional case. Under suitable conditions, we show that the rate function is a good rate function.
We thus generalize the results already obtained in the one-dimensional case for the Nadaraya-Watson estimator. Moreover, we
give a moderate deviations principle for these two estimators. It turns out that the rate function obtained in the moderate
deviations principle for the semi-recursive estimator is larger than the one obtained for the Nadaraya-Watson estimator.
相似文献
994.
The main objective of this paper is to prove Hilbert-type and Hardy-Hilbert-type inequalities with a product-type homogeneous kernel, thus generalizing a result obtained in [Z. Xie, Z. Zheng, A Hilbert-type integral inequality whose kernel is a homogeneous form of degree −3, J. Math. Anal. Appl. 339 (2008) 324-331]. In some cases the best possible constants obtained in these inequalities are expressed using the Schur polynomials. 相似文献
995.
This paper studies the model-robust design problem for general models with an unknown bias or contamination and the correlated errors. The true response function is assumed to be from a reproducing kernel Hilbert space and the errors are fitted by the qth order moving average process MA(q), especially the MA(1) errors and the MA(2) errors. In both situations, design criteria are derived in terms of the average expected quadratic loss for the least squares estimation by using a minimax method. A case is studied and the orthogonality of the criteria is proved for this special response. The robustness of the design criteria is discussed through several numerical examples. 相似文献
996.
This paper has analyzed the weights of the fifth‐order weighted essentially nonoscillatory scheme suggested by Jiang and Shu and a modified smoothness estimator is suggested to improve the accuracy. Using a function of the minimum and maximum of the original smoothness estimators, the new smoothness estimators have smaller variation among them than the original ones in smooth regions. Hence, as the new weights are closer to the optimal weights, the numerical accuracy is improved. Several numerical experiments are presented to demonstrate the accuracy and robustness of the new scheme. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
997.
998.
999.
We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study
the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a tool, we define
a new function of two complex variables, which is a natural generalization of the classical Gamma function for the setting
we consider.
D. Alpay thanks the Earl Katz family for endowing the chair which supports his research. 相似文献
1000.
The minimum covariance determinant (MCD) scatter estimator is a highly robust estimator for the dispersion matrix of a multivariate, elliptically symmetric distribution. It is relatively fast to compute and intuitively appealing. In this note we derive its influence function and compute the asymptotic variances of its elements. A comparison with the one step reweighted MCD and with S-estimators is made. Also finite-sample results are reported. 相似文献