• 대한수학회보
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• 제49권1호
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• pp.11-24
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• 2012

We characterize the class of inner uniform domains in terms of the quasihyperbolic metric and the quasihyperbolic geodesic. We also characterize uniform domains and inner uniform domains in terms of weak Bloch functions.

• 대한수학회보
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• 제50권6호
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• pp.1873-1886
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• 2013

In this paper, we characterize inner uniform domains in $\mathbb{R}^n$ in terms of Apollonian inner metric and the metric $j^{\prime}_D$ when D are Apollonian. As an application, a new characterization for A-uniform domains is obtained.

• East Asian mathematical journal
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• 제19권2호
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• pp.291-303
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• 2003

A result of Hardy and Littlewood relates Holder continuity of analytic functions in the unit disk with a bound on the derivative. Gehring and Martio extended this result to the class of uniform domains. In this paper we obtain a similar result to the class of uniformly John domains in terms of the inner diameter metric. We give several properties of a domain with the property. Also we show some results on the Holder continuity of conjugate harmonic functions in the above domains.

• 대한수학회논문집
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• 제19권1호
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• pp.53-62
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• 2004

A result of Hardy and Littlewood relates Holder continuity of analytic functions in the unit disk with a bound on the derivative. Gehring and Martio extended this result to the class of uniform domains. We call it the Hardy-Littlewood property. Langmeyer further extended their result to the class of John disks in terms of the inner length metric. We call it the Hardy-Littlewood property with the inner length metric. In this paper we give several properties of a domain which satisfies the Hardy-Littlewood property with the inner length metric. Also we show some results on the Holder continuity of conjugate harmonic functions in various domains.

• Macromolecular Research
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• 제15권3호
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• pp.211-215
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• 2007

Hybrid thin film nanostructures composed of metal nanoparticles (NPs) and self-assembled polymer films with different spatial distributions of NPs were analyzed by optical waveguide spectroscopy (OWS). Specifically, the dielectric constants were calculated using effective medium theory for the incorporation of 1 vol% Au NP into the block copolymer (BCP) films having a cylindrical nanodomain morphology. Three cases were considered: uniform distribution of NPs in the film; selective distribution of NPs only in the cylindrical domains; and segregation of NPs to the center of the cylindrical domains. The optical waveguide spectra derived from the calculated dielectric constants demonstrate the feasibility of experimentally distinguishing the composite nanostructures with different inner morphologies in the hybrid metal NP-BCP nanostructures, by the measurement of the dielectric constants using OWS.