Touché Rouché
نویسنده
چکیده
There seems to be a love-hate relationship between Brouwer's fixed point theorem and the fundamental theorem of algebra; in this note we offer one more tweak at it, and give a version of Rouchés theorem.
منابع مشابه
touché Is required for touch-evoked generator potentials within vertebrate sensory neurons.
The process by which light touch in vertebrates is transformed into an electrical response in cutaneous mechanosensitive neurons is a largely unresolved question. To address this question we undertook a forward genetic screen in zebrafish (Danio rerio) to identify mutants exhibiting abnormal touch-evoked behaviors, despite the presence of sensory neurons and peripheral neurites. One family, sub...
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Rouché’s theorem and winding numbers are standard tools for counting solutions of holomorphic equations in the complex plane. We explore counterparts to these tools for smooth systems of two real equations in two real unknowns. In the process, we outline the implementation of a system solver which makes use of this topological information. AMS subject classifications. 26B99, 58K15, 65H10, 65H20...
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In analytic queueing theory, Rouch e's theorem is frequently used, and when it can be applied, leads quickly to tangible results concerning ergodicity and performance analysis. For more complicated models it is sometimes diicult to verify the conditions needed to apply the theorem. The natural question that arises is: Can one dispense with this theorem, in particular when the ergodicity conditi...
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The GSR theorem generalizes the classical Rouché theorem of complex analysis, concerning the stability of the total multiplicity of “roots minus poles” for finitely meromorphic functions taking values in the space of Fredholm operators on a Hilbert space. This theorem has been a very useful tool in the stability analysis of nonlinear waves. Proofs based on logarithmic integrals are usually cons...
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