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LetF be a totally real number field and [ a product of some real primes ofF. J. Brinkhuis gave a necessary condition for a finite abelian extension ofF which is unramified outside [ to have a normal integral basis. We consider the converse of his result and give a necessary and sufficient condition. Furthermore, we concretely express it whenF is a real quadratic field or a cyclic cubic field.  相似文献
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In this paper, we extend a result by H. Takagi on the non-existence of mutually commuting and linearly independent Killing vector fields on positively curved Riemannian manifolds. Further, a kind of “Compact Leaf Theorem” is proved for metric foliations of closed manifolds with positive sectional curvature. Received: 26 May 2000 / Revised version: 28 February 2001  相似文献
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For 1/2<<1 fixed, letE (T) denote the error term in the asymptotic formula for . We obtain some new bounds forE (T), and an _-result which is the analogue of the strongest _-result in the classical Dirichlet divisor problem.  相似文献
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Summary We consider extensible beam equations, Timoshenko beam equations and the system of coupled beam equations. We show that, under suitable conditions, there are bounded domains in which every solution satisfying certain end conditions has a zero. End conditions to be considered are hinged ends and hinged-sliding ends. The results are based on the conditions for the nonexistence of positive solutions of ordinary differential inequalities.  相似文献
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In this paper, we study nonlinear analytic methods for linear contractive semigroups in Banach spaces and apply them to the splitting theorem of Jacobs–de Leeuw–Glicksberg. Using these results, we obtain the extension of Lin’s proposition for a group of linear operators to a semigroup.  相似文献
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We consider the Allen-Cahn equation in Rn (with n?2) and study how a planar front behaves when arbitrarily large (but bounded) perturbation is given near the front region. We first show that the behavior of the disturbed front can be approximated by that of the mean curvature flow with a drift term for all large time up to t=+∞. Using this observation, we then show that the planar front is asymptotically stable in L(Rn) under spatially ergodic perturbations, which include quasi-periodic and almost periodic ones as special cases. As a by-product of our analysis, we present a result of a rather general nature, which states that, for a large class of evolution equations, the unique ergodicity of the initial data is inherited by the solution at any later time.  相似文献
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Sequential pattern mining is a crucial but challenging task in many applications, e.g., analyzing the behaviors of data in transactions and discovering frequent patterns in time series data. This task becomes difficult when valuable patterns are locally or implicitly involved in noisy data. In this paper, we propose a method for mining such local patterns from sequences. Using rough set theory, we describe an algorithm for generating decision rules that take into account local patterns for arriving at a particular decision. To apply sequential data to rough set theory, the size of local patterns is specified, allowing a set of sequences to be transformed into a sequential information system. We use the discernibility of decision classes to establish evaluation criteria for the decision rules in the sequential information system.  相似文献
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