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On the Maximum Modulus and the Mean Modulus of an Entire Function
Canadian Mathematical Bulletin, 1969Let be an entire function, but not a polynomial.
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1990
The author defines the class of modulus monotonic functions \((MM(r,\alpha))\) as follows: \(f(z)=z+a_ 2z^ 2+a_ 3z^ 3+\cdots\) is analytic in the unit disk. There is an \(\alpha\in\left(-{\pi\over 2},{\pi\over 2}\right)\) such that \(| f(re^{i\theta})|\) decreases for \(\theta\in[\alpha,\pi-\alpha]\) and increases for \(\theta\in[\pi-\alpha,2\pi+\alpha]
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The author defines the class of modulus monotonic functions \((MM(r,\alpha))\) as follows: \(f(z)=z+a_ 2z^ 2+a_ 3z^ 3+\cdots\) is analytic in the unit disk. There is an \(\alpha\in\left(-{\pi\over 2},{\pi\over 2}\right)\) such that \(| f(re^{i\theta})|\) decreases for \(\theta\in[\alpha,\pi-\alpha]\) and increases for \(\theta\in[\pi-\alpha,2\pi+\alpha]
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Lower Bounds for the Modulus of Analytic Functions
Bulletin of the London Mathematical Society, 1990Let f be an analytic function in \(| z| 0)\) with \(f(0)=1\). If f has no zeros there are well known estimates from below in terms of the maximum modulus function \[ M(t)=\max_{| z| \leq t}| f(z)|,\quad 0\leq t0\) such that for all ...
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3D Printing Nanostructured Solid Polymer Electrolytes with High Modulus and Conductivity
Advanced Materials, 2022Valentin A Bobrin +2 more
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Stretchable ultrasonic arrays for the three-dimensional mapping of the modulus of deep tissue
Nature Biomedical Engineering, 2023, Xuejun Qian
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