• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.365-371
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• 1997

We prove some relation of volume with the covering radius of Riemannian manifolds and reprove well-known sphere rigidity theorems by using it.

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.87-93
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• 1999

A holomorphic function f on D = {z : │z│ ＜ 1} is called uniformly locally univalent if there exists a positive constant $\rho$ such that f is univalent in every hyperbolic disk of hyperbolic radius $\rho$. We establish a characterization of uniformly locally univalent functions and investigate uniform local univalence of holomorphic universal covering projections.

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.137-144
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• 1997

In this paper we consider covering problems in spherical geometry. Let $cov_q{S_1}^n$ be the smallest radius of q equal metric balls that cover n-dimensional unit sphere ${S_1}^n$. We show that $cov_q{S_1}^n\;=\;\frac{\pi}{2}\;for\;2\leq\;q\leq\;n+1$ and $\pi-arccos(\frac{-1}{n+1})$ for q = n ＋ 2. The configuration of centers of balls realizing $cov_q{S_1}^n$ are established, simultaneously. Moreover, some properties of $cov_{q}$X for the compact metric space X, in general, are proved.

• Proceedings of the KWS Conference
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• v.43
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• pp.275-277
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• 2004

Fictitious notch radius approach is based on the Neuter's microstructural support hypothesis which assumes that fatigue crack is governed by highly stressed volume of the material right on the weld toe area rather than the surface stress at a pin point of weld toe area. Variety of successes have been achieved in applying this methodology to the fatigue of welded joint, hence, it became one of recommended design procedure in IIW's recommendation as well as many ship classification societies. 1mm fictitious notch radius approach was applied to the various fatigue problems of welded joints in this study covering the effect of weld size, notch stress calculation for 3D geometry and low cycle fatigue problem. It was found that fictitious notch radius approach fumed out to be very effective and accurate in dealing with fatigue strength of welded joint.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.449-461
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• 2001

The purpose of this paper is to study several geometric properties for the new class $G_{\kappa}(\beta)$ including geometric interpretation, coefficient estimates, radius of convexity, distortion property and covering theorem.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.12 s.243
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• pp.1605-1614
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• 2005

For the last four decades, tension test of notched bars has been performed to investigate the effect of stress triaxiality on ductile fracture. To quantify the effect of the notch radius on stress triaxiality, the Bridgman equation is typically used. However, recent works based on detailed finite element analysis have shown that the Bridgman equation is not correct, possibly due to his assumption that strain is constant in the necked ligament. Up to present, no systematic work has been performed on fully plastic stress fields for notched bars in tension. This paper presents fully plastic results for tension of notched bars and plates in plane strain, via finite element limit analysis. The notch radius is systematically varied, covering both un-cracked and cracked cases. Comparison of plastic limit loads with existing solutions shows that existing solutions are accurate for notched plates, but not for notched bars. Accordingly new limit load solutions are given for notched bars. Variations of stress triaxiality with the notch radius and depth are also given, which again indicates that the Bridgman solution for notched bars is not correct and inaccuracy depends on the notch radius and depth.

• Membrane and Water Treatment
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• v.13 no.4
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• pp.167-172
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• 2022

The analytical results are presented for the mass transfer in a cylindrical pore covering from the macroscale, multiscale to nanoscale owing to the variation of the inner diameter of the pore. When the thickness h_bf of the physically adsorbed layer potentially fully formed on the pore wall is comparable to but less than the inner radius R₀ of the pore, the multiscale flow occurs consisting of both the nanoscale non-continuum adsorbed layer flow and the macroscopic continuum liquid flow; When R₀ ≤ h_bf, the flow in the whole pore is essentially non-continuum; When R₀ is far greater than h_bf, the flow in the whole pore can be considered as macroscopic and continuum and the adsorbed layer effect is negligible.

• Journal of the Korean Chemical Society
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• v.41 no.8
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• pp.427-436
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• 1997

A simple relation exists between electronegativities of cations and their oxidation states and ionic radii. An empirical law is proposed: X = 0.274 z-0.15 z r - 0.01 r+1+${\alpha}$, z being oxidation number, r ionic radius in $\AA$ and ${\alpha}$ a term related to the atomic number. this relation permits to calculate an electronegativity scale covering a large set of electronic and crystallographic situations. An application to the calculation of acid strengths of cations is presented.

• Nuclear Engineering and Technology
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• v.46 no.2
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• pp.217-224
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• 2014

The present work used the efficiency transfer method used to calculate the full energy peak efficiency (FEPE) curves of the (2"*2" & 3"*3") NaI (Tl) detectors based on the effective solid angle subtended between the source and the detector. The study covered the effect of the self attenuation coefficient of the source matrix (with a radius greater than the detector's radius) on the detector efficiency. $^{152}$ An Eu aqueous radioactive source covering the energy range from 121.78 keV up to 1408.01 keV was used. In this study an empirical formula was deduced to calculate the difference between the measured and the calculated efficiencies [without self attenuation] at low and high energy regions. A proper balance between the measured and calculated efficiencies [with self attenuation] was achieved with discrepancies less than 3%, while reaching 39% for calculating values [without self attenuation] due to working with large sources, or for low photon energies.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.881-893
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• 1997

E. M. Silvia introduced the class $S^\lambda_\alpha$ of $\alpha$-spirallike functions f(z) satisfying the condition $$ (A) Re[(e^{i\lambda} - \alpha) \frac{zf'(z)}{f(z)} + \alpha \frac{(zf'(z))'}{f'(z)}] > 0, $$ where $\alpha \geq 0, $\mid$\lambda$\mid$ < \frac{\pi}{2}$ and $$\mid$z$\mid$ < 1$. We will generalize Silvia class of functions by formally replacing f(z) in the denominator of (A) by a spirallike function g(z). We denote the new class of functions by $Y(\alpha,\lambda)$. In this note we obtain some results for the class $Y(\alpha,\lambda)$ including integral representation formula, relations between our class $Y(\alpha,\lambda)$ and Ziegler class $Z_\lambda$, the radius of convexity problem, a few coefficient estimates and a covering theorem for the class $Y(\alpha,\lambda)$.