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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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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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LeRoy B. Beasley 《Linear algebra and its applications》2012,436(9):3469-3474
Let be the binary Boolean algebra. The Boolean rank, or factorization rank, of a matrix A in is the smallest k such that A can be factored as an times a matrix. The isolation number of a matrix, A, is the largest number of entries equal to 1 in the matrix such that no two ones are in the same row, no two ones are in the same column, and no two ones are in a submatrix of A of the form . It is known that the isolation number of A is always at most the Boolean rank. This paper investigates for each k, if the isolation number of A is k what are some of the possible values of the Boolean rank of A. 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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Michael Winkler 《Journal of Differential Equations》2018,264(10):6109-6151
A class of chemotaxis-Stokes systems generalizing the prototype is considered in bounded convex three-dimensional domains, where is given.The paper develops an analytical approach which consists in a combination of energy-based arguments and maximal Sobolev regularity theory, and which allows for the construction of global bounded weak solutions to an associated initial-boundary value problem under the assumption that
(0.1)
Moreover, the obtained solutions are shown to approach the spatially homogeneous steady state in the large time limit.This extends previous results which either relied on different and apparently less significant energy-type structures, or on completely alternative approaches, and thereby exclusively achieved comparable results under hypotheses stronger than (0.1). 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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Daniel Pragel 《Discrete Mathematics》2012,312(10):1844-1847