The Self-Similarity of the Josephus Problem and its Variants
Masakazu Naito, Sohtaro Doro, Daisuke Minematsu, Ryohei Miyadera (2009)
Visual Mathematics
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Masakazu Naito, Sohtaro Doro, Daisuke Minematsu, Ryohei Miyadera (2009)
Visual Mathematics
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R. U. Verma (1971)
Annales Polonici Mathematici
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Yūki Naito, Takashi Suzuki (2008)
Colloquium Mathematicae
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We consider a system which describes the scaling limit of several chemotaxis systems. We focus on self-similarity, and review some recent results on forward and backward self-similar solutions to the system.
Rehder, Wulf (1982)
International Journal of Mathematics and Mathematical Sciences
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Heydar Radjavi, Ping-Kwan Tam, Kok-Keong Tan (2003)
Studia Mathematica
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A characterization of compactness of a given self-adjoint bounded operator A on a separable infinite-dimensional Hilbert space is established in terms of the spectrum of perturbations. An example is presented to show that without separability, the perturbation condition, which is always necessary, is not sufficient. For non-separable spaces, another condition on the self-adjoint operator A, which is necessary and sufficient for the perturbation, is given.
McClure, M., Vallin, R.W. (2000)
Acta Mathematica Universitatis Comenianae. New Series
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Leopold Herrmann (1988)
Aplikace matematiky
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The operator , , , is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types and , respectively.
Hertel, Eike (2000)
Beiträge zur Algebra und Geometrie
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R. Kenyon (1996)
Geometric and functional analysis
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Robert Stańczy (2009)
Banach Center Publications
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This paper contains some results concerning self-similar radial solutions for some system of chemotaxis. This kind of solutions describe asymptotic profiles of arbitrary solutions with small mass. Our approach is based on a fixed point analysis for an appropriate integral operator acting on a suitably defined convex subset of some cone in the space of bounded and continuous functions.
Reiner Berntzen (1996)
Studia Mathematica
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The problem of approximation by accretive elements in a unital C*-algebra suggested by P. R. Halmos is substantially solved. The key idea is the observation that accretive approximation can be regarded as a combination of positive and self-adjoint approximation. The approximation results are proved both in the C*-norm and in another, topologically equivalent norm.