• Bulletin of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.589-597
• /
• 1999

Let G be a closed subspace of a Banach space X and let (S,$\Omega$,$\mu$) be a $\sigma$-finite measure space. It was known that $L_1$(S,G) is proximinal in $L_1$(S,X) if and only if $L_p$(S,G) is proximinal in $L_p$(S,X) for 1$\infty$. In this article we show that this result remains true when "proximinal" is replaced by "Chebyshev". In addition, it is shown that if G is a proximinal subspace of X such that either G or the kernel of the metric projection $P_G$ is separable then, for 0 < p $\leq$ $\infty$. $L_p$(S,G) is proximinal in $L_p$(S,X)

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.24 no.1
• /
• pp.16-25
• /
• 2012

To calculate the total mass flux that change in dry and flood season in the Yeomha Channel of Gyeonggi Bay, the 13 hour bottom tracking observation was performed from the southern extremity. The value of the total mass flux(Lagrange flux) was calculated as the sum of the Eulerian flux value and stroke drift value and the tidal residual flow was harmonically analyzed through the least-squares method. Moreover, the average during the tidal cycle is essential to calculate the mass flux and the tidal residual flow and there is the need to equate the grid of repeatedly observed data. Nevertheless, due to the great differences in the studied region, the number of vertical grid tends to change according to time and since the horizontal grid differs according to the transport speed of the ship as a characteristic of the bottom tracking observation, differences occur in the horizontal and vertical grid for each hour. Hence, the present study has vertically and horizontally normalized(sigma coordinate) to equate the grid per each hour. When compared to the z-level coordinate system, the Sigma coordinate system was evaluated to have no irrationalities in data analysis with 5% of error. As a result of the analysis, the tidal residual flow displayed the flow pattern of sagging in the both ends in the main waterway direction of dry season. During flood season, it was confirmed that the tidal residual flow was vertical 2-layer flow. As a result of the total mass flux, the ebb properties of 359 cm/s and 261 cm/s were observed during dry and flood season, respectively. The total mass flux was moving the intertidal region between Youngjong-do and Ganghwa-do.

• Bulletin of the Korean Mathematical Society
• /
• v.30 no.2
• /
• pp.179-185
• /
• 1993

In this article S is a topologically complete subspace of $R^{1}$i.e., the relativized topology on S may be metrized so as to make S complete. B(S) is the Borel .sigma.-field of S. For .GAMMA. one takes a set of measurable monotone (increasing or dereasing) functions on S into itself. Make the assumption of pp. There exists $x_{0}$ and a positive integer $n_{0}$ such that (Fig.) It is then shown that there exists a unique inveriant probability to which $p^{(n)}$ (x,dy) converges exponentially fast in a metric (stronger than the Kolmogorov distance); this convergence is uniform for all x .mem. S. This generalizes an earlier result of Bhattacharya and Lee (1988) who considered monotone nondecreasing maps on S.

• Journal of applied mathematics & informatics
• /
• v.32 no.1_2
• /
• pp.55-60
• /
• 2014

In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n={\Sigma}^n_{i=1}\;X_i$.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2007.05a
• /
• pp.285-288
• /
• 2007

The use of commercial finite element analysis software to perform the entire process analysis and springback analysis has increased fast for last decade. Pamstamp2G is one of commercial software to be used widely in the world but it has still not been perfected in the springback prediction accuracy. We must select the combination of input parameters for the highest springback prediction accuracy in Pamstamp2G because springback prediction accuracy is sensitive to input parameters. Then we study the affect of input parameters to use member part for acquiring high springback prediction accuracy in Pamstamp2G. First, we choose important four parameters which are adaptive mesh level at drawing stage and cam flange stage, Gauss integration point number through the thickness and cam offset on basis of experiment. Second, we make a orthogonal array table L82[(7)] which is consist of 8 cases to be combined 4 input parameters, compare to tryout result and select main factors after analyzing affect factors of input parameters by Taguchi's method in 6 sigma. Third, we simulate after changing more detail the conditions of parameters to have big affect. At last, we find the best combination of input parameters for the highest springback prediction accuracy in Pamstamp2G. The results of the study provide the selection of input parameters to Pamstamp2G users who want to Increase the springback prediction accuracy.

• Journal of the Korean Society for Nondestructive Testing
• /
• v.15 no.2
• /
• pp.371-377
• /
• 1995

By using ultrasonic waves, we obtained conclusion from the experiment for measuring joint axial force of high tension bolt. The conclusion is followed. : From the high tension bolts used at turbine of Thermoelectric Power Plant, we obtained the equation of calculating joint axial force that is ${\sigma}=\frac{{\Delta}BPD}{j{\times}{\Sigma}{\delta}}$. By using IBM PC, which is inputed by the equation for calculating joint axial force of high tension bolts, we got joint axial force of high tension bolts form beam path of ultrasonic waves. Furrther, we can identify that constitution of plant safety inspection system is possible.

• Journal of The Korean Astronomical Society
• /
• v.42 no.3
• /
• pp.61-69
• /
• 2009

Transverse velocity vectors can be determined from a pair of images successively taken with a time interval using an optical flow technique. We have tested the performance of the new technique called NAVE (non-linear affine velocity estimator) recently implemented by Chae & Sakurai using real image data taken by the Narrowband Filter Imager (NFI) of the Solar Optical Telescope (SOT) aboard the Hinode satellite. We have developed two methods of estimating the errors in the determination of velocity vectors, one resulting from the non-linear fitting ${\sigma}_{\upsilon}$ and the other ${\epsilon}_u$ resulting from the statistics of the determined velocity vectors. The real error is expected to be somewhere between ${\sigma}_{\upsilon}$ and ${\epsilon}_u$. We have investigated the dependence of the determined velocity vectors and their errors on the different parameters such as the critical speed for the subsonic filtering, the width of the localizing window, the time interval between two successive images, and the signal-to-noise ratio of the feature. With the choice of $v_{crit}$ = 2 pixel/step for the subsonic filtering, and the window FWHM of 16 pixels, and the time interval of one step (2 minutes), we find that the errors of velocity vectors determined using the NAVE range from around 0.04 pixel/step in high signal-to-noise ratio features (S/N $\sim$ 10), to 0.1 pixel/step in low signa-to-noise ratio features (S/N $\sim$ 3) with the mean of about 0.06 pixel/step where 1 pixel/step corresponds roughly to 1 km/s in our case.

• Bulletin of the Korean Chemical Society
• /
• v.35 no.7
• /
• pp.2135-2138
• /
• 2014

A kinetic study is reported for the SNAr reaction of 1-Y-substituted-phenoxy-2,4-dinitrobenzenes (1a-1h) with OH- in 80 mol % $H_2O$/20 mol % DMSO at $25.0{\pm}0.1^{\circ}C$. The second-order rate constant ($k_{OH^-}$) increases as the substituent Y in the leaving group changes from an electron-donating group (EDG) to an electronwithdrawing group (EWG). The Br${\o}$nsted-type plot for the reactions of 1a-1h is linear with ${\beta}_{lg}$ = -0.16, indicating that the reactivity of substrates 1a-1h is little affected by the leaving-group basicity. A linear Br${\o}$nsted-type plot with ${\beta}_{lg}=-0.3{\pm}0.1$ is typical for reactions reported previously to proceed through a stepwise mechanism in which formation of a Meisenheimer complex is the rate-determining step (RDS). The Hammett plot correlated with ${\sigma}_Y{^{\circ}}$ constants results in a much better correlation than that correlated with ${\sigma}_Y{^-}$constants, implyng that no negative charge is developing on the O atom of the leaving group (or expulsion of the leaving group is not advanced at all in the TS). This excludes a possibility that the $S_NAr$ reaction of 1a-1h with $OH^-$ proceeds through a concerted mechanism or via a stepwise pathway with expulsion of the leaving group being the RDS. Thus, the current reactions have been concluded to proceed through a stepwise mechanism in which expulsion of the leaving group occurs rapidly after the RDS.

• Journal of the Korea Safety Management & Science
• /
• v.11 no.1
• /
• pp.103-113
• /
• 2009

Motorola which had developed and commercialized wireless telephone and mobile phone for the first time in the world made a decision on the separation of the mobile unit from the Motorola due to the continuous bad performance turn. In addition, the Korean company named Raincom which had developed and commercialized MP3 player have been disappeared since Raincom failed to compete with iPod of Apples. What is the main cause the companies that have been top of the world level weed out of IT product market? For less product life cycle and globalization of market, the company's competitiveness tends to be determined based on company's creative capability, rather than process implementation capability. Thus, companies spent a great amount of time and effort in the introduction of creativity management and R&D activities. However, as company's continuous investment on R&D and innovation activities did not lead to business performance, they starts to pay much attention on the effective R&D and innovation activities. Therefore, this paper tries to solve the limitation of the effectiveness of R&D activities by introducing the concept of 'creative quality'. The creative quality is executed by the creative process, which is designed for getting over the limitation of the traditional brainstorming method. This paper presents the concept so called 'creative quality management' and expects it to be an alternative to conquest the limitation of six sigma management.

• Bulletin of the Korean Chemical Society
• /
• v.32 no.1
• /
• pp.179-182
• /
• 2011

Second-order rate constants ($k_{OH^-}$) have been measured spectrophotometrically for reactions of Y-substituted phenyl phenyl thionocarbonates (4a-i) with $OH^-$ in 80 mol % $H_2O$/20 mol % DMSO at $25.0{\pm}0.1^{\circ}C$. The $k_{OH^-}$ values for the reactions of 4a-i have been compared with those reported previously for the corresponding reactions of Y-substituted phenyl phenyl carbonates (3a-i) to investigate the effect of changing the electrophilic center from C=O to C=S on reactivity and mechanism. Thionocarbonates 4a-i are less reactive than the corresponding carbonates 3a-i although 4a-i are expected to be more reactive than 3a-i. The Bronsted-type plot for reactions of 4a-i is linear with $\beta_{lg}$ = -0.33, a typical $\beta_{lg}$ value for reactions reported to proceed through a stepwise mechanism with formation of an intermediate being the rate-determining step (RDS). Furthermore, the Hammett plot correlated with $\sigma^o$ constants results in much better linearity than that correlated with $\sigma^-$ constants, indicating that expulsion of the leaving group is not advanced in the RDS. Thus, alkaline hydrolysis of 4a-i has been concluded to proceed through a stepwise mechanism with formation of an intermediate being RDS, which is in contrast to the forced concerted mechanism reported for the corresponding reactions of 3a-i. Enhanced stability of the intermediate upon modification of the electrophilic center from C=O to C=S has been concluded to be responsible for the contrasting mechanisms.