• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.559-572
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• 2021

It is well known that every invariant harmonic function on the unit ball of the multi-dimensional complex space has the volume version of the invariant mean value property. In 1993 Ahern, Flores and Rudin first observed that the validity of the converse depends on the dimension of the underlying complex space. Later Lie and Shi obtained the analogues on the unit ball of multi-dimensional real space. In this paper we obtain the half-space analogues of the results of Liu and Shi.

• Transactions of the Korean Society of Automotive Engineers
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• v.3 no.5
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• pp.38-46
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• 1995

In this paper, an experimental study on the effects of the impact damage and the perforation characteristic of CFRP laminates with different fiber stacking orientation and ply number was done through an observation of interrelations between the impact energy vs. transmitted energy and the impact energy vs. absorbed energy per unit volume. The velocities of the ball before or after impact are measured by the high-speed camera. And when CFRP laminates are subjected to tranverse impact by a steel ball(${\phi}10$), the delamination shapes generated by impact damage are observed by using SAM (Scanning acoustic Microscope).

• East Asian mathematical journal
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• v.34 no.5
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• pp.577-585
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• 2018

For the purpose of characterizing subharmonic or ${\mathcal{M}}$-subharmonic Hardy classes in the unit ball of ${\mathbb{C}}^n$, we establish fundamental identities between integral means in terms of volume integrals and Green's functions.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.89-99
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• 2009

Let $\mu$ be a finite positive Borel measure on the unit ball $B{\subset}\mathbb{C}^n$ and $\nu$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, $\sigma$ is the rotation-invariant measure on S such that ${\sigma}(S)=1$. Let $\mathcal{P}[f]$ be the invariant Poisson integral of f. We will show that there is a constant M > 0 such that $\int_B{\mid}{\mathcal{P}}[f](z){\mid}^{p}d{\mu}(z){\leq}M\;{\int}_B{\mid}{\mathcal{P}}[f](z)^pd{\nu}(z)$ for all $f{\in}L^p({\sigma})$ if and only if ${\parallel}{\mu}{\parallel_r}\;=\;sup_{z{\in}B}\;\frac{\mu(E(z,r))}{\nu(E(z,r))}\;<\;\infty$.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.195-200
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• 2010

Let C be a closed convex set in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$. Assume that ${\Sigma}$ is an n-dimensional compact minimal submanifold outside C such that ${\Sigma}$ is orthogonal to ${\partial}C$ along ${\partial}{\Sigma}{\cap}{\partial}C$ and ${\partial}{\Sigma}$ lies on a geodesic sphere centered at a fixed point $p{\in}{\partial}{\Sigma}{\cap}{\partial}C$ and that r is the distance in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$ from p. We make use of a modified volume $M_p({\Sigma})$ of ${\Sigma}$ and obtain a sharp relative isoperimetric inequality $$\frac{1}{2}n^n{\omega}_nM_p({\Sigma})^{n-1}{\leq}Vol({\partial}{\Sigma}{\sim}{\partial}C)^n$$, where ${\omega}_n$ is the volume of a unit ball in ${\mathbb{R}}^n$ Equality holds if and only if ${\Sigma}$ is a totally geodesic half ball centered at p.

• Journal of the Korean Recycled Construction Resources Institute
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• v.2 no.1
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• pp.46-51
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• 2014

In this study, strength development properties of high volume fly ash concrete was evaluated through compressive strength of concrete with reduction of unit water content. And concrete specimens were prepared according to target strength 3 level and variation of unit water content. As a result, the improved fluidity were obtained as a result of the ball bearing action of the spherical, the electrostatic repulsion and the particle size distribution of fly ash particles in case of using more than 50% fly ash. Through this, the mixture of fly ash has been shown to reduce the amount of water required in concrete. Also, the early strength of high volume fly ash concrete with reduction of unit water content was improved more about 66% than general concrete mixture.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.12 s.189
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• pp.30-37
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• 2006

In this work, the surface integrity smoothened with a ball end mill was investigated. Because surface integrity mainly affects the manual finishing process, $RV_{AM}$(Remaining Volume After Machining) was introduced, and it gives the relation between machining process and finishing process. Runout and phase shift which adversely affect surface integrity were considered in the generation of surface topography. Cutting points in ball end milling were identified with positional vectors and a set of vectors which have the minimum height in unit area was selected for the generation of surface and $RV_{AM}$. $RV_{AM}$ variation according to runout and phase shift was calculated and experimentally verified in proposed HSM conditions for mold machining. From the simulations and the experiments, a desirable High Speed Machining condition was suggested.

• Journal of the Korea Institute of Building Construction
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• v.6 no.3 s.21
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• pp.107-114
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• 2006

In this study, the experiment was carried out to investigate and analyze the engineering properties of concrete using fine aggregate of PS bal slagl. The main experimental variables were water/cement ratio 30, 40, 50(%), water content $170kg/m^3$, replacement ratio of slag fine aggregate 0, 25, 50, 75(%) in experiment I and water/cement ratio 30, 40, 50(%), water content 165, 170, 175($kg/m^3$), replacement ratio of fine aggregate of PS ball 0, 50 in experiment II. According to the test results, the principle conclusions are summarized as follows (1) The workability of slag fine aggregate-mixed concrete tends to improve, as the replacement rate increases. (2) The air content of slag fine aggregate-mixed concrete tends to decrease, as the replacement rate increases. (3) The unit volume weight of slag fine aggregate-mixed concrete tends to significantly increase, as the replacement rate increases. (4) The compressive strength of slag fine aggregate-mixed concrete tends to show more increasing propensity, in case the curing period is relatively long, as the replacement rate increases.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-667
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• 2011

A class of functions involving divided differences of the psi and tri-gamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving the ratio of two gamma functions and originating from the establishment of the best upper and lower bounds in Kershaw's double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in $\mathbb{R}^{n-1}$ and $\mathbb{R}^n$ respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized.

• Korean Journal of Materials Research
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• v.30 no.7
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• pp.350-358
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• 2020

A variety of composite powders having different aluminum and carbon contents are prepared using various organic solvents having different amounts of carbon atoms in unit volume as ball milling agents for titanium and aluminum ball milling. The effects of substrate temperature and post-heat treatment on the texture and hardness of the coating are investigated by spraying with this reduced pressure plasma spray. The aluminum part of the composite powder evaporates during spraying, so that the film aluminum content is 30.9 mass%~37.4 mass% and the carbon content is 0.64 mass%~1.69 mass%. The main constituent phase of the coating formed on the water-cooled substrate is a non-planar α₂ phase, obtained by supersaturated carbon regardless of the alloy composition. When these films are heat-treated at 1123 K, the main constituent phase becomes γ phase, and fine Ti₂AlC precipitates to increase the film hardness. However, when heat treatment is performed at a higher temperature, the hardness is lowered. The main constitutional phase of the coating formed on the preheated substrate is an equilibrium gamma phase, and fine Ti₂AlC precipitates. The hardness of this coating is much higher than the hardness of the coating in the sprayed state formed on the water-cooled substrate. When hot pressing is applied to the coating, the porosity decreases but hardness also decreases because Ti₂AlC grows. The amount of Ti₂AlC in the hot-pressed film is 4.9 vol% to 15.3 vol%, depending on the carbon content of the film.