共查询到20条相似文献,搜索用时 125 毫秒
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Mi Hee Park Byung Gyun Kang Phan Thanh Toan 《Journal of Pure and Applied Algebra》2018,222(8):2299-2309
Let be the power series ring over a commutative ring R with identity. For , let denote the content ideal of f, i.e., the ideal of R generated by the coefficients of f. We show that if R is a Prüfer domain and if such that is locally finitely generated (or equivalently locally principal), then a Dedekind–Mertens type formula holds for g, namely for all . More generally for a Prüfer domain R, we prove the content formula for all . As a consequence it is shown that an integral domain R is completely integrally closed if and only if for all nonzero , which is a beautiful result corresponding to the well-known fact that an integral domain R is integrally closed if and only if for all nonzero , where is the polynomial ring over R.For a ring R and , if is not locally finitely generated, then there may be no positive integer k such that for all . Assuming that the locally minimal number of generators of is , Epstein and Shapiro posed a question about the validation of the formula for all . We give a negative answer to this question and show that the finiteness of the locally minimal number of special generators of is in fact a more suitable assumption. More precisely we prove that if the locally minimal number of special generators of is , then for all . As a consequence we show that if is finitely generated (in particular if ), then there exists a nonnegative integer k such that for all . 相似文献
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D. Buraczewski E. Damek J. Zienkiewicz 《Stochastic Processes and their Applications》2018,128(9):2923-2951
We consider first passage times for the perpetuity sequence where are i.i.d. random variables with values in . Recently, a number of limit theorems related to were proved including the law of large numbers, the central limit theorem and large deviations theorems (see Buraczewski et al., in press). We obtain a precise asymptotics of the sequence , , which considerably improves the previous results of Buraczewski et al. (in press). There, probabilities were identified, for some large intervals around , with lengths growing at least as . Remarkable analogies and differences to random walks (Buraczewski and Ma?lanka, in press; Lalley, 1984) are discussed. 相似文献
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J.T. Stafford 《Comptes Rendus Mathematique》2013,351(11-12):429-432
Let R be a prime right Goldie ring. A useful fact is that, if are such that contains a regular element, then there exists such that is regular. We show that the analogous result holds for pairs of elements: if R contains a field of cardinality at least , and if are such that contains a regular element for , then there exists a single element such that is regular for each i. 相似文献
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An approximation scheme is a family of homogeneous subsets of a quasi-Banach space , such that , , and . Continuing the line of research originating at the classical paper [8] by Bernstein, we give several characterizations of the approximation schemes with the property that, for every sequence , there exists such that (in this case we say that satisfies Shapiro’s Theorem). If is a Banach space, as above exists if and only if, for every sequence , there exists such that . We give numerous examples of approximation schemes satisfying Shapiro’s Theorem. 相似文献
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B.A. Bailey 《Journal of Approximation Theory》2012,164(4):460-487
In this paper, an equivalence between existence of particular exponential Riesz bases for spaces of multivariate bandlimited functions and existence of certain polynomial interpolants for functions in these spaces is given. Namely, polynomials are constructed which, in the limiting case, interpolate for certain classes of unequally spaced data nodes and corresponding sampled data . Existence of these polynomials allows one to construct a simple sequence of approximants for an arbitrary multivariate bandlimited function which demonstrates and uniform convergence on to . A simpler computational version of this recovery formula is also given at the cost of replacing and uniform convergence on with and uniform convergence on increasingly large subsets of . As a special case, the polynomial interpolants of given data converge in the same fashion to the multivariate bandlimited interpolant of that same data. Concrete examples of pertinent Riesz bases and unequally spaced data nodes are also given. 相似文献
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《Annals of Pure and Applied Logic》2014,165(7-8):1243-1262
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Dawid Tarłowski 《Operations Research Letters》2018,46(1):33-36
Let be a continuous function with the minimal value , where is the compact metric space. Let be a Markov chain which represents the global optimization process on . We present sufficient conditions for very strong, geometric convergence mode of the form , where is some constant. This convergence mode is natural if the set of global minima is fat. 相似文献