Results 171 to 180 of about 1,183 (204)

Quantum Rate Distortion, Reverse Shannon Theorems, and Source-Channel Separation

IEEE Transactions on Information Theory, 2013
We derive quantum counterparts of two key theorems of classical information theory, namely, the rate-distortion theorem and the source-channel separation theorem.
Min-Hsiu Hsieh, Mark M Wilde
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Sharp growth and distortion theorems for a subclass of biholomorphic mappings

Computers and Mathematics With Applications, 2010
Let X be a complex Banach space with norm ‖⋅‖, and B be the unit ball in X. In this paper, we introduce a class of holomorphic mappings Mg on B. Let F(x) be a normalized locally biholomorphic mapping on B such that (DF(x))−1F(x)∈Mg.
Liu, Tai-Shun, Xu, Qing-Hua
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A note on the distortion theorem

Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials, 2017
The distortion theorem is a conditional statement that establishes the certain relations between the variation of the mean bond length and the variation of the valence of a central ion of a coordination polyhedron. It was found that in some principal cases the conditional part of the distortion theorem is not necessary.
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Some theorems on geometric measure of distortion [PDF]

Kybernetika, 1975
Yogeshwar Dayal Mathur, Jagdish Mitter
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The growth theorem and distortion theorem of spirallike mappings on B p

Acta Mathematica Sinica, English Series, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Hao, Lu, Ke Ping, Zhang, Fang Fang
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A Distortion Theorem for Univalent Gap Series

Siberian Mathematical Journal, 2003
Summary: We prove a distortion theorem for conformal mappings of the unit disk for which \(\log f'\) is representable as the Hadamard gap series. This theorem implies in particular that such conformal mapping is `almost' bounded, i.e., for every \(\varepsilon >0\), there is a positive constant \(C_\varepsilon\) such that \(|f(z)|\geq C_\varepsilon (1 ...
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DISTORTION THEOREMS FOR BOUNDED UNIVALENT FUNCTIONS

Analysis, 2003
Let be \[ D_hf(z) = \frac{1-| z| ^2}{1-| f(z)| ^2}f'(z) \] for a conformal map \(f(z)\) from the unit disk into itself. It was proved by \textit{W. Ma} and \textit{D. Minda} [Ann. Acad. Sci. Fenn., Math. 22, 425 - 444 (1997; Zbl 0908.30016)] \[ \Big(\Big(\frac{| D_hf(z_1)| }{1-| D_hf(z_1)| }\Big)^p + \Big(\frac{| D_hf(z_2)| }{1-| D_hf(z_2)| }\Big)^p ...
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Distortion theorems for polynomials on a circle

Sbornik: Mathematics, 2000
The author considers polynomials \[ P(z)= \sum^n_{k=0} c_kz^k, \quad c_n\neq 0, \] for points \(z=e^{i\varphi}\) on the unit circle. He proves new and interesting estimates for the derivatives \[ {\partial\text{Re} P(e^{i \varphi}) \over\partial \varphi},\;{\partial\bigl|P(e^{i\varphi}) \bigr |^2 \over\partial\varphi} \text{ and } {\partial\arg \bigl(P(
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Sharp Distortion Theorems Associated with the Schwarzian Derivative

Journal of the London Mathematical Society, 1993
Let \(f\) be meromorphic in the unit disk \(\mathbb{D}\) and let \(| Sf(z) | \leq 2t/(1-| z |^ 2)^ 2\) for \(| z |
Chuaqui, M., Osgood, B.
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An extension of the Ahlfors distortion theorem

Mathematical Proceedings of the Cambridge Philosophical Society, 1954
1. The conformal mapping of a strip domain in the z-plane on to a parallel strip— parallel, say, to the real axis of the ζ ( = ξ + iμ)-plane—brings about a certain distortion. More precisely: consider a cross-cut on the line ℜz = c joining the two sides of the frontier of the strip domain (in these introductory remarks we suppose for simplicity that ...
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