共查询到20条相似文献,搜索用时 31 毫秒
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Kazaros Kazarian 《Comptes Rendus Mathematique》2004,339(5):335-337
A complete orthonormal system of functions is constructed such that converges almost everywhere on if and diverges a.e. for any . We also show that for any complete ONS of functions defined on there exists a fixed non decreasing subsequence of natural numbers such that for any and some sequence of coefficients , To cite this article: K. Kazarian, C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
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Guoyou Qian 《Comptes Rendus Mathematique》2017,355(11):1127-1132
Let be a strictly increasing sequence of positive integers ( if ). In 1978, Borwein showed that for any positive integer n, we have , with equality occurring if and only if for . Let be an integer. In this paper, we investigate the sum and show that for any positive integer n, where is a constant depending on r and n. Further, for any integer , we also give a characterization of the sequence such that the equality holds. 相似文献
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《Comptes Rendus Mathematique》2005,340(12):885-888
This Note presents a randomized method to approximate any vector v from some set . The data one is given is the set T, and k scalar products , where are i.i.d. isotropic subgaussian random vectors in , and . We show that with high probability any for which is close to the data vector will be a good approximation of v, and that the degree of approximation is determined by a natural geometric parameter associated with the set T. This extends and improves recent results by Candes and Tao. To cite this article: S. Mendelson et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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We present and analyze an iterative method for approximating the Karcher mean of a set of positive definite matrices , , defined as the unique positive definite solution of the matrix equation . 相似文献
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Let is an independent set of a graph G. In this paper, we give a low bound for the length of a longest cycle in a 4-connected graph and get the following result: If is a 4-connected graph on vertices, then the circumference . Moreover, we give graphs to show that the connectivity in our result is best possible with respect to the low bound and the low bound in our result is also best possible with respect to the connectivity. 相似文献
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We give all even perfect (resp. unitary perfect) polynomials over the prime field of the form , where each is a Mersenne irreducible polynomial, (resp. ) and . In particular, we characterize nine of the eleven known “sporadic” even perfect polynomials over that have the above form. 相似文献
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We study the Ramsey number for the 3-uniform loose path of length three, , and colors. We show that , for some explicit constant . 相似文献
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Let , be independent and identically distributed random variables with values in . We transform (‘prune’) the sequence , of discrete random samples into a sequence , of contiguous random sets by replacing with if . We consider the asymptotic behaviour of as . Applications include path growth in digital search trees and the number of tables in Pitmanʼs Chinese restaurant process if the latter is conditioned on its limit value. 相似文献