Results 121 to 130 of about 20,152 (160)

The Modulus as a Set Function

2020
Let E and F be compact disjoint non-empty sets in \(\overline {\mathbb {R}}^n\) and \(\mathsf {M}( \Delta _{EF})=\mathsf {M}\bigl (\Delta (E,F)\bigr )\).
Parisa Hariri, Riku Klén, Matti Vuorinen   +2 more
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Modulus of Continuity of Piecewise Analytic Functions

Mathematical Notes, 2003
Conditions under which the modulus of continuity \(\omega(f; \delta)\) of a piece-wise real-analytic function \(f : [a, b] \rightarrow {\mathbb R}\) becomes analytic at zero are found. The results obtained are of the following type. Theorem 1. Let \(f\) be piece-wise real-analytic on \([a, b]\). If \[ \sup_{x\in D_{N}} d(x) < \sup_{x\in M\setminus D_{N}
Dovgosheĭ, A. A., Potemkina, L. L.
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On the Maximum Modulus and the Mean Modulus of an Entire Function

Canadian Mathematical Bulletin, 1969
Let be an entire function, but not a polynomial.
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Derivatives of the maximum modulus of a starlike function

Analysis Mathematica, 1981
Let \(f\) be analytic in the unit disk \(D\) and \(M(r,f)=\max\{| f(z)|\mid| z|= r\}\) for \(r\in (0,1)\). In this paper the author describes the very delicate construction of a function \(f\) and a sequence \((r_ n)_{n\in\mathbb{N}}= (r_ n(f))_{n\in\mathbb{N}}\) with the following properties: 1) \(f(0)= f'(0)- 1=0\), \(f\) is starlike in \(D\), 2 ...
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The maximum modulus function of a polynomial

Complex Variables, Theory and Application: An International Journal, 1990
We establish certain relationships between pairs of polynomials which have the same maximum modulus on an infinite set of concentric circles.
George Csordas, Marvin Ortel, Wayne Smith   +2 more
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On the Maximum and Minimum Modulus of Rational Functions

Canadian Journal of Mathematics, 2000
AbstractWe show that if m, n ≥ 0, λ > 1, and R is a rational function with numerator, denominator of degree ≤ m, n, respectively, then there exists a set ⊂ [0, 1] of linear measure such that for r ∈ ,Here, one may not replace , for any ε > 0.
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Lower Bounds for the Modulus of Analytic Functions

Bulletin of the London Mathematical Society, 1990
Let 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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Majorization of the Modulus of Continuity of Analytic Functions

Computational Methods and Function Theory, 2007
Let \(G\) be an open set in the complex plane, \(f\) analytic in \(G\) and continuous in \(\overline G\). Let \(\mu\) is a majorant in the sense that \(\mu(t)\) is a nonnegative, nondecreasing function defined for \(t\geq 0\) with \(\mu(2t)\leq 2\mu(t)\) for all \(t\geq 0\) and \[ |f(z_1)- f(z_2)|\leq \mu(|z_1- z_2|)\tag{1} \] for \(z_1\) and \(z_2 ...
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Equivalence of K-functional and modulus of smoothness of functions on the sphere

Mathematical Notes, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Comments on the electric modulus function

Journal of Non-Crystalline Solids, 2005
Arguments in favor of the electric modulus formalism are reviewed, and several misunderstandings and misrepresentations are corrected. It is argued that different representations of the same experimental data provide additional, rather then subtractive, insights into the difficult problem of understanding ionic conductivity in melts, glasses and ...
I.M. Hodge, K.L. Ngai, C.T. Moynihan
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