• Communications of the Korean Mathematical Society
• /
• v.10 no.4
• /
• pp.881-887
• /
• 1995

Let f be a measurable function on the unit ball B in $C^n$, then we define a maximal function $M_p(f), 1 \leq p < \infty$, by $$ M_p(f)(\zeta ) = \sup_{\delta > 0}(\frac{1}{\sigma(\beta(\zeta, \delta))} \int_{T(\beta(\zeta, \delta))} $\mid$f(z)$\mid$^p \frac{d\nu(z)}{(1-$\mid$z$\mid$^n})^{1/p} $$ where $\sigma$ denotes the surface area measure on S, the boundary of B, and $T(\beta(\zeta, \delta))$ denotes the tent over the ball $\beta(\zeta, \delta)$. We prove that the maximal operator $M_p$ belongs to the Muckenhoupt class $A_1$.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.4
• /
• pp.1087-1098
• /
• 2013

We find a $C^{\infty}$-continuous path of Riemannian metrics $g_t$ on $\mathbb{R}^k$, $k{\geq}3$, for $0{\leq}t{\leq}{\varepsilon}$ for some number ${\varepsilon}$ > 0 with the following property: $g_0$ is the Euclidean metric on $\mathbb{R}^k$, the scalar curvatures of $g_t$ are strictly decreasing in $t$ in the open unit ball and $g_t$ is isometric to the Euclidean metric in the complement of the ball. Furthermore we extend the discussion to the Fubini-Study metric in a similar way.

• Journal of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.313-326
• /
• 2018

The paper studies some new ${\mathbb{C}}^n$-generalizations of Bergman type operators introduced by Shields and Williams depending on a normal pair of weight functions. We find the values of parameter ${\beta}$ for which these operators are bounded on mixed norm spaces L(p, q, ${\beta}$) over the unit ball in ${\mathbb{C}}^n$. Moreover, these operators are bounded projections as well, and the images of L(p, q, ${\beta}$) under the projections are found.

• International Journal of Precision Engineering and Manufacturing
• /
• v.7 no.3
• /
• pp.39-46
• /
• 2006

This paper presents an elastic deformation model of a spindle unit (S/U), which takes into account the non-linear properties of high-speed ball bearings (particularly the effect of high rotational speed). For this, a software for the estimation of the S/U elastic deformation properties was developed and intended for use by S/U designers. A computer aided analysis of the model using the developed software was carried out and experiments showed the significant effect of rotational speed, cutting load and bearing axial preload, and showed some new phenomena, from which the criteria for the choice of bearing axial preload is given.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.581-588
• /
• 2012

We find a $C^{\infty}$ one-parameter family of Riemannian metrics $g_t$ on $\mathbb{R}^3$ for $0{\leq}t{\leq}{\varepsilon}$ for some number ${\varepsilon}$ with the following property: $g_0$ is the Euclidean metric on $\mathbb{R}^3$, the scalar curvatures of $g_t$ are strictly decreasing in t in the open unit ball and $g_t$ is isometric to the Euclidean metric in the complement of the ball.

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

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1996.11a
• /
• pp.434-438
• /
• 1996

In this paper we present the multi-agent robot system and the vision system developed for participating in micro robot soccer tournament. The multi-agent robot system consists of micro robot, a vision system, a host computer and a communication module. Micro robot are equipped with two mini DC motors witf encoders and gearboxes, a R/F receiver, a CPU and infrared sensors for obstacle detection. A vision system is used to recognize the position of the ball and opponent robots, position and orientation of our robots. The vision system is composed of a color CCD camera and a vision processing unit(AISI vision computer). The vision algorithm is based on morphological method. And it takes about 90 msec to detect ball and 3-our robots and 3-opponent robots with reasonable accuracy

• Journal of the Korean Society for Precision Engineering
• /
• v.20 no.3
• /
• pp.187-193
• /
• 2003

This paper presents an on-machine measurement method of flatness error fur surface machining processes. There are two kinds of on-machine measurement methods available to measure flatness errors in workpieces: i.e., surface scanning method and sensor scanning method. However, motion errors are often engaged in both methods. This paper proposes an idea to realize a measurement system of flatness errors and its rigorous application for estimation of motion errors of the positioning system. The measurement system is made by modifying the straightness measurement system, which consists of a laser, a CCD camera and processing system, a sensor head, and some optical units. The sensor head is composed of a retroreflector, a ball and ball socket, a linear motion guide unit and adjustable arms. The experimental .results show that the proposed method is useful to identify flatness errors of machined workpieces as well as motion errors of positioning systems.

• Journal of Institute of Control, Robotics and Systems
• /
• v.21 no.1
• /
• pp.65-69
• /
• 2015

A vision-based blank alignment unit for a press automation line is introduced in this paper. A press is a machine tool that changes the shape of a blank by applying pressure and is widely used in industries requiring mass production. In traditional press automation lines, a mechanical centering unit, which consists of guides and ball bearings, is employed to align a blank before a robot inserts it into the press. However it can only align limited sized and shaped of blanks. Moreover it cannot be applied to a process where more than two blanks are simultaneously inserted. To overcome these problems, we developed a press centering unit by means of vision sensors for press automation lines. The specification of the vision system is determined by considering information of the blank and the required accuracy. A vision application S/W with pattern recognition, camera calibration and monitoring functions is designed to successfully detect multiple blanks. Through real experiments with an industrial robot, we validated that the proposed system was able to align various sizes and shapes of blanks, and successfully detect more than two blanks which were simultaneously inserted.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.30 no.4
• /
• pp.246-252
• /
• 2017

Pulverized $FeS_2$ (pyrite) gives different discharge test results with as-received $FeS_2$ electrodes. The as-received $FeS_2$ electrode shows three voltage plateaus during the discharge test. However, the ball-milled $FeS_2$ electrode shows two voltage plateaus. To interpret this result, the effect of $FeS_2$ particle size on electrochemical reactions is investigated by unit cell discharge tests, SEM and XRD. As a result, it is found that the transition reaction product ($Li_2+xFe+xS_2$) of $FeS_2$ explains the difference. The as-received $FeS_2$ reacts according to three reaction steps ($FeS_2{\rightarrow}Li_3Fe_2S_4{\rightarrow}Li_2+xFe_1+xS_2{\rightarrow}LiFe_2S_4$). However, ball-milled $FeS_2$ reacts without the $Li_2+xFe_1+xS_2$ stage. In this study, this result is explained by the difference in electrochemical reaction mechanism. The as-received $FeS_2$ has a larger radius than the ball-milled $FeS_2$. Therefore, the lithium ion has to diffuse into the $FeS_2$ unreacted core, and $Li_2+xFe_1+xS_2$, the transition reaction product of as-received $FeS_2$, is formed during this stage.