Let k be a real abelian number field with Galois group Δ and p an odd prime number. Assume that the order of Δ is not divisible by p. Let Ψ be an irreducible Q_p-character of Δ. Denote by λ_p(Ψ ) the Ψ-component of the λ-invariant associated to the cyclotomic Z_p-extension of k. Then Greenberg conjecture for the Ψ-components states that λ_p(Ψ ) is always zero for any Ψ and p. Although some efficient criteria for the conjecture to be true are given, very little is known about it except for k =Q or the trivial character case.
  There is another λ-invariant. Denote by λ_p^*(Ψ ) the λ-invariant associated to the p -adic L-function related to Ψ. One can know λ_p^*(Ψ ) by computing the Iwasawa power series attached to Ψ. The Iwasawa main conjecture proved by Mazur and Wiles says that the inequality λ_p(Ψ ) ≤ λ_p^*(Ψ ) holds. In this paper, we give a necessary and sufficient condition for this inequality to be strict in terms of special values of p -adic L-functions. This result enables us to obtain a criterion for Greenberg’s conjecture for Ψ-components to be true when the corresponding Iwasawa power series is irreducible.

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We study combinatorial Laplacians of graphs, and provide examples of isospectral graphs, including finite and infinite ones, as well as isospectral graphs with boundaries. Two general methods for the construction of isospectral graphs with boundaries are also presented.

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The following problems were raised in the workshop “Affine Differential Geometry and Related Topics” at Graduate School of Information Sciences, Tohoku University at December 16-18, 1996.

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An extension of the Steffensen iteration method for solving a single nonlinear equation is considered. The point is that the iteration function is defined by using the k -th Shanks transform. The convergence rate is shown to be of order k +1. The use of ε -algorithm avoids the direct calculation of Hankel determinants, which appear in the Shanks transform, and then diminishes the computational complexity. For a special case of the Kepler equation, it is shown that the numbers of mappings are actually decreased by the use of the extended Steffensen iteration.

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A harmonic wavelet analysis for a finite time sequence is presented. This is the discrete-time version of the wavelet analysis which was given in a preceding paper by Morita (1997) for a periodic function. As an application of the present analysis, we consider a time sequence of real numbers which were taken every five minutes in one day.

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The problem-solving ability of a human in manual control is considered. The purpose of the manual control is the positioning of the two-link arm with a free joint. This kind of manipulator are getting popular recently because of its simplicity. The control of the manipulator, however, is difficult because the motion is governed by a set of nonlinear equations. A real-time simulator is used to perform the experiment of manual control. It is concluded that a human can find some satisfactory control patterns after enough training. These results are interesting from the theoretical point of view, they suggest a possible theoretical approach to this difficult control problem.

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Two experiments were designed to examine the existence of lower versus upper visual field anisotropy in form perception based on shading and edge-based information. In the experiments, subjects were asked to judge the visual property of the stimulus defined by shading or edge. The results demonstrated that the lower visual field is specialized for the processing of shading information, whereas the upper field is specialized for the processing of edge-based information. These findings are consistent with Previc’s (1990) hypothesis that the processing of optically degraded images is linked to a peripersonal visual system which is biased to the lower visual field, while an extrapersonal visual system, which is biased toward the upper visual field, is used for the processing of details of form.

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Although the borderless broadcasting has been influencing the Chinese society, the studies of the changing society and communication policy in China have rarely done. In this dissertation, I review briefly the former and present situation of the borderless broadcasting and specially the satellite communication policy in Asia. To analyse the activity and influence of the STAR-TV, typical borderless broadcasting through the “Asia No. 1 Satellite”, I have implemented the survey research to the citizens of Nainkin City.

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Wrong: 
Right: 

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