• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.31-39
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• 2009

Let $T_{\rho}$ be the generalized fractional integral operator associated to a function ${\rho}:(0,{\infty}){\rightarrow}(0,{\infty})$, as defined in [16]. For a function W on $\mathbb{R}^n$, we shall be interested in the boundedness of the multiplication operator $f{\mapsto}W{\cdot}T_{\rho}f$ on generalized Morrey spaces. Under some assumptions on ${\rho}$, we obtain an inequality for $W{\cdot}T_{\rho}$, which can be viewed as an extension of Olsen's and Kurata-Nishigaki-Sugano's results.

• Journal of Technologic Dentistry
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• v.32 no.4
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• pp.387-401
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• 2010

Purpose: The work of Dental technician which is part of national dental health, is more specialized recently. This research provides fundamental data from analyzing student's career consciousness according to needs of a career education. Here is the conclusion of the analysis about student's career consciousness, that is for a right choice of career. Methods: This study did questionnaire to a dental Laboratory Technology student who locate in Taegu. Question response student number was 570 people. Response contents analyzed to 506 people except imperfect questionnaire. Data used windows sas 8.0 program and did descriptive statistical analysis. Results: There is a meaningful difference in what they want to know about an occupation according to ages. (${\rho}$ < 0.01) All ages are similar to their occupational thinking, however they who are under twenties consider working environment. Most motives of an entrance are similar, there is a meaningful difference. (${\rho}$ < 0.05) According to a grade of college, there is a meaningful difference how to obtain informations of a career. (${\rho}$ < 0.05) Sophomores and juniors obtain information from seniors or family, however freshmen obtain from the internet because of an accessibility. There is a meaningful difference of a job meaning between men and women. (${\rho}$ < 0.01) Men are working for a means of living. But women give weight to a self-development. The older they grow, the more they know about their aptitude. Selecting subjects are different choosing time & motive. According to ages and where they are from, there is a meaningful difference how much know about their aptitude. (${\rho}$ < 0.05) Older Students know more than young students. Selecting subjects are different choosing time & motive. In accordance with a grade, ages, and where they are from, there are different degrees about how much know their interests. There is a meaningful difference of a choosing major period and choosing informations. (${\rho}$ < 0.01) And also there is a meaningful difference where they are from and why they enter to College. (${\rho}$ < 0.001) In accordance with a grade, ages, and where they are from, there are different degrees about how much know their aptitude. There is a meaningful difference of a choosing major period. (${\rho}$ < 0.01) And also there is a meaningful difference why they enter to College. (${\rho}$ < 0.001) Conclusion: Although we know that a career education is very important, however lots of students select a career without their aptitude & interest & character. We need to teach a career education systematically; considering students career consciousness, with a proper career guidance, cultivating career consciousness.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.797-804
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• 1998

A pair of multiobjective generalized symmetric dual non-linear programming problems and weak strong and converse dual-ity theorems for these problems are established under generalized $\rho-(\eta,0)$-invexity assumptions. Several known results are obtained as special cases.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2017.05a
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• pp.825-831
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• 2017

In this study, we perform the design of dome geometry for the composite pressure vessel with applying the equation of Fulton and Vasiliev considering external load(thrusts). Variables of the dome geometry are opening radius ratio(${\rho}_0$) from 0.1 to 0.5 and thrust level from 40kN to 200kN. We conduct Finite Element Analysis(FEA) by using ABAQUS. As a result, the strain of the composite pressure vessel has shown strain gradient from inner to outer of dome surface. And the strain gradient may cause crack of resin inside the composite laminate. Strain gradient of Fulton dome is monotonously decreased as the ${\rho}_0$ increases, but the strain gradient of Vasiliev dome bas shown some different trend. when ${\rho}_0{\leq}0.1$, strain gradient of Fulton's is higher than Vasiliev's. But when 0.1<${\rho}_0$<0.35, strain gradient of Vasiliev's becomes higher than Fulton's. And in the case of $0.35{\leq}{\rho}_0$, strain gradient of Vasiliev's is higher than Fulton's. So the Vasiliev dome is more effective in ${\rho}_0{\leq}0.1$ condition and Fulton dome is more effective in $0.35{\leq}{\rho}_0$ condition. So, it's important for dome design to consider the crack of resin cause of the strain gradient.

• Structural Engineering and Mechanics
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• v.13 no.6
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• pp.671-694
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• 2002

This paper presents theoretical investigation on the cross correlation between torsional vibration ($u_{\theta}$) and translation vibration ($u_x$) of asymmetrical structure under white noise excitation. The formula reveals that the cross correlation coefficient (${\rho}$) is a function of uncoupled frequency ratio (${\Omega}={\omega}_{\theta}/{\omega}_x$), eccentricity, and damping ratio (${\xi}$). Simulations involving acceleration records from fifteen different earthquakes show correlation coefficients results similar to the theoretical correlation coefficients. The uncoupled frequency ratio is the dominating parameter to ${\rho}$; generally, ${\rho}$ is positive for ${\omega}_{\theta}/{\omega}_x$ > 1.0, negative for ${\omega}_{\theta}/{\omega}_x$ < 1.0, and close to zero for ${\omega}_{\theta}/{\omega}_x$ = 1.0. When the eccentricity or damping ratio increases, ${\rho}$ increases moderately for small ${\Omega}$ (< 1.0) only. The relation among $u_x$, $u_{\theta}$ and corner displacement are best presented by ${\rho}$; a simple way to hand-calculate the theoretical dynamic corner displacements from $u_x$, $u_{\theta}$ and ${\rho}$ is proposed as an alternative to dynamic analysis.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1141-1158
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• 2017

In this paper, we study the value distribution of the derivative of a Dirichlet L-function $L^{\prime}(s,{\chi})$ at the a-points ${\rho}_{a,{\chi}}={\beta}_{a,{\chi}}+i{\gamma}_{a,{\chi}}$ of $L^{\prime}(s,{\chi})$. We give an asymptotic formula for the sum $${\sum_{{\rho}_{a,{\chi}};0<{\gamma}_{a,{\chi}}{\leq}T}\;L^{\prime}({\rho}_{a,{\chi}},{\chi})X^{{\rho}_{a,{\chi}}}\;as\;T{\rightarrow}{\infty}$$, where X is a fixed positive number and ${\chi}$ is a primitive character mod q. This work continues the investigations of Fujii [4-6], $Garunk{\check{s}}tis$ & Steuding [8] and the authors [12].

• Bulletin of the Korean Chemical Society
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• v.32 no.10
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• pp.3743-3747
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• 2011

Kinetic studies on the reactions of Y-S-aryl phenyl phosphonochloridothioates with X-pyridines have been carried out in MeCN at $55.0^{\circ}C$. The Hammett and Bronsted plots for substituent X variations in the nucleophiles are biphasic concave upwards with a break point at X = H. The Hammett plots for substituent Y variations in the substrates are biphasic concave upwards with a break point at Y = H, and the sign of ${\rho}_Y$ is changed from unusual negative (${\rho}_Y$ < 0) with the weaker electrophiles to positive (${\rho}_Y$ > 0) with the stronger electrophiles. The stepwise mechanism is proposed on the basis of the ${\rho}_X$, ${\beta}_X$, and ${\rho}_{XY}$ values as follows: a ratelimiting leaving group departure from the intermediate involving a frontside attack and product-like TS for the stronger nucleophiles and weaker electrophiles; a rate-limiting leaving group departure from the intermediate involving a backside attack and product-like TS for the weaker nucleophiles and electrophiles; a rate-limiting bond formation involving a frontside attack for the stronger nucleophiles and electrophiles; a rate-limiting bond formation involving a backside attack for the weaker nucleophiles and stronger electrophiles. The substituent effects of X and Y on the pyridinolysis mechanisms of $R_1R_2P$(=S)Cl-type substrates are discussed.

• Elastomers and Composites
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• v.38 no.3
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• pp.235-242
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• 2003

A vulcanization reaction characteristics of an isoprene rubber (IR)-modified natural rubber/carbon black (NR/CB) composite was studied using in-situ electrical property measuring technique. Since the electrical conductivity of the sample composite would be changed continuously during the vulcanization reaction by rearranging of the carbon black particles within the sample, volume resistivity (${\rho}$) might be obtained as a function or reaction time. A stabilization time ($t_i$), maximum reaction speed time ($t_p$), and volume resistivity at that time(${\rho}_p$) were defined from the data for the Arrhenius analysis. Volume resistivity ${\rho}$ showed a comparatively high value of ${\sim}10^8$ order before the reaction started, and dramatically decreased to be stabilized within $1{\sim}2$ minutes as soon as the reaction started. As the more time elapsed, thereafter, ${\rho}$ decreased monotonously to a certain constant value through a peak, ${\rho}_p$ at time $t_p$, which was considered as the maximum reaction rate. As a result, while $t_i$ values were comparatively constant as $1{\sim}2$ minutes, $t_p$ values showed to become shorter and shorter as the reaction temperature.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.667-680
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• 2004

We generalize a theorem of W. Benz by proving the following result: Let $H_{\theta}$ be a half space of a real Hilbert space with dimension $\geq$ 3 and let Y be a real normed space which is strictly convex. If a distance $\rho$ > 0 is contractive and another distance N$\rho$ (N $\geq$ 2) is extensive by a mapping f : $H_{\theta}$ \longrightarrow Y, then the restriction f│$_{\theta}$ $H_{+}$$\rho$/2// is an isometry, where $H_{\theta}$＋$\rho$/2/ is also a half space which is a proper subset of $H_{\theta}$. Applying the above result, we also generalize a classical theorem of Beckman and Quarles.

• Journal of Korean Society of Water and Wastewater
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• v.33 no.2
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• pp.111-119
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• 2019

Electro-coagulation process has been gained an attention recently because it could overcome the membrane fouling problems in MBR(Membrane bio-reactor). Effect of the key operational parameters in electro-coagulation, current density(${\rho}_i$) and contact time(t) on membrane fouling reduction was investigated in this study. A kinetic model for ${\rho}_i$ and t required to reduce the membrane fouling was suggested under different MLSS(mixed liquor suspended solids) concentration. Total 48 batch type experiments of electro-coagulations under different sets of current densities(2.5, 6, 12 and $24A/m^2$), contact times(0, 2, 6 and 12 hr) and MLSS concentration(4500, 6500 and 8500mg/L) were carried out. After each electro-coagulation under different conditions, a series of membrane filtration was performed to get information on how much of membrane fouling was reduced. The membrane fouling decreased as the ${\rho}_i$ and t increased but as MLSS decreased. Total fouling resistances, Rt (=Rc+Rf) were calculated and compared to those of the controls (Ro), which were obtained from the experiments without electro-coagulation. A kinetic approach for the fouling reduction rate (Rt/Ro) was carried out and three equations under different MLSS concentration were suggested: i) ${\rho}_i^{0.39}t=3.5$ (MLSS=4500 mg/L), ii) ${\rho}_i^{0.46}t=7.0$ (MLSS=6500 mg/L), iii) ${\rho}_i^{0.74}t=10.5$ (MLSS=8500 mg/L). These equations state that the product of ${\rho}_i$ and t needed to reduce the fouling in certain amounts (in this study, 10% of fouling reduction) is always constant.