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We prove the so-called conjecture: for every real-monic polynomial of degree there exists an n by n matrix with sign patternwhose characteristic polynomial is . The proof converts the problem of determining the nonsingularity of a certain Jacobi matrix to the problem of proving the non-existence of a nonzero matrix B that commutes with a nilpotent matrix with sign pattern and has zeros in positions , and for . 相似文献
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One dimensional Dirac operators considered with -potentials and subject to regular boundary conditions (), have discrete spectrum. For strictly regular , the spectrum of the free operator is simple while the spectrum of is eventually simple, and the corresponding normalized root function systems are Riesz bases. For expansions of functions of bounded variation about these Riesz bases, we prove the uniform equiconvergence property and point-wise convergence on the closed interval . Analogous results are obtained for regular but not strictly regular . 相似文献
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Sylvain Bonnot 《Comptes Rendus Mathematique》2005,340(4):291-294
In order to describe the dynamics of the complex Hénon map , where has an attractive fixed point, we build a topological model . In this model Y is the complement in of a cone over a solenoid lying in the unit 3-sphere, and is a map given in spherical coordinates by , where σ is a solenoidal map of degree two. Then we prove the existence of a constant such that any Hénon map with is conjugate to our model . To cite this article: S. Bonnot, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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Let F be a field of characteristic and G be a smooth finite algebraic group over F. We compute the essential dimension of G at p. That is, we show that 相似文献
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