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Displaying 681 –
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A number of approaches for discretizing partial differential equations with random data
are based on generalized polynomial chaos expansions of random variables. These constitute
generalizations of the polynomial chaos expansions introduced by Norbert Wiener to
expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We
present conditions on such measures which imply mean-square convergence of generalized
polynomial...
Recently, Tripathy - Jour. Ind. Math. Soc., 32 (1960), 141-154 - has proved some results on absolute Hausdorff summability of some series associated with Fourier series and its allied series, which generalise the results proved by Mohanty on absolute Cesaro summability. Proceeding on the similar lines, the author has generalised the results of Cheng - Duke Math. Jour., 15 (1948), 17-27 - by proving them on absolute Hausdorff summability.
For any Borel ideal ℐ we describe the ℐ-Baire system generated by the family of quasi-continuous real-valued functions. We characterize the Borel ideals ℐ for which the ideal and ordinary Baire systems coincide.
In the paper, some kind of independence between upper metric dimension and natural order of converging sequences is shown — for any sequence converging to zero there is a greater sequence with an arbitrary () upper dimension. On the other hand there is a relationship to summability of series — the set of elements of any positive summable series must have metric dimension less than or equal to .
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