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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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In this paper we study the existence of distributional solutions of Dirichlet problems whose simplest example is 相似文献
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The connection between geodesics on the modular surface and regular continued fractions, established by Series, is extended to a connection between geodesics on
and odd and grotesque continued fractions, where is the index two subgroup of generated by the order three elements and , and having an ideal quadrilateral as fundamental domain.A similar connection between geodesics on
and even continued fractions is discussed in our framework, where denotes the Theta subgroup of generated by and . 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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