• Bulletin of the Korean Mathematical Society
• /
• v.50 no.6
• /
• pp.1873-1886
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.11-24
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.19 no.1
• /
• pp.53-62
• /
• 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.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.4 no.3
• /
• pp.291-301
• /
• 2012

A scalar metric for the assessment of hull surface producibility was known to be useful in estimating the complexity of a hull form of ships or large offshore structures by looking at their shape. However, it could not serve as a comprehensive measuring tool due to its lack of important components of the hull form such as longitudinals, stiffeners, and web frames attached to the hull surface. To have a complete metric for cost estimation, these structural members must be included. In this paper, major inner structural members are considered by measuring the complexity of their geometric shape. The final scalar metric thus consists of the classes containing inner members with various curvature magnitudes as well as the classes containing curved plates with single and double curvature distribution. Those two distinct metrics are merged into a complete scalar metric that accounts for the total cost estimation of complex structural bodies.

• Journal of applied mathematics & informatics
• /
• v.9 no.2
• /
• pp.859-867
• /
• 2002

In this paper, we get a necessary and sufficient condition for an inner automorphism between compact connected semisimple Lie groups to be an atone transformation, and obtain atone transformations of (SU(n),g) with some left invariant metric g.

• East Asian mathematical journal
• /
• v.19 no.2
• /
• pp.291-303
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.397-420
• /
• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.

• Smart Structures and Systems
• /
• v.28 no.6
• /
• pp.761-777
• /
• 2021

This study presents a numerical investigation on the sensitivity of electromechanical (EM) impedance responses to inner damaged concrete of a prestressed anchorage zone. Firstly, the Ottosen yield criterion is selected to simulate the plasticity behavior of the concrete anchorage zone under the compressive loading. Secondly, several overloading cases are selected to analyze inner damage formations in the concrete of the anchorage zone. Using a finite element (FE) model of the anchorage zone, the relationship between applied forces and stresses is analyzed to illustrate inner plasticity regions in concrete induced by the overloading. Thirdly, EM impedance responses of surface-mounted PZT (lead-zirconate-titanate) sensors are numerically acquired before and after concrete damage occurrence in the anchorage zone. The variation of impedance responses is estimated using the RMSD (root-mean-square-deviation) damage metric to quantify the sensitivity of the signals to inner damaged concrete. Lastly, a novel PZT skin, which can measure impedance signatures in predetermined frequency ranges, is designed for the anchorage zone to sensitively monitor the EM impedance signals of the inner damaged concrete. The feasibility of the proposed method is numerically evaluated for a series of damage cases of the anchorage zone. The results reveal that the proposed impedance-based method is promising for monitoring inner damaged concrete in anchorage zones.

• Communications of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.1215-1231
• /
• 2023

The present article contains the study of D-homothetically deformed f-Kenmotsu manifolds. Some fundamental results on the deformed spaces have been deduced. Some basic properties of the Riemannian metric as an inner product on both the original and deformed spaces have been established. Finally, applying the obtained results, soliton functions, Ricci curvatures and scalar curvatures of almost Riemann solitons with several kinds of potential vector fields on the deformed spaces have been characterized.

• Journal of Communications and Networks
• /
• v.18 no.2
• /
• pp.261-269
• /
• 2016

In this paper, the impact of energy constraints on a two-hop network with a source, a relay and a destination under random medium access is studied. A collision channel with erasures is considered, and the source and the relay nodes have energy harvesting capabilities and an unlimited battery to store the harvested energy. Additionally, the source and the relay node have external traffic arrivals and the relay forwards a fraction of the source node's traffic to the destination; the cooperation is performed at the network level. An inner and an outer bound of the stability region for a given transmission probability vector are obtained. Then, the closure of the inner and the outer bound is obtained separately and they turn out to be identical. This work is not only a step in connecting information theory and networking, by studying the maximum stable throughput region metric but also it taps the relatively unexplored and important domain of energy harvesting and assesses the effect of that on this important measure.