• Polymer(Korea)
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• v.31 no.3
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• pp.206-214
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• 2007

The theoretical study is developed for predicting the thermal expansion changes of composites which include complex inclusion, which is used three-dimensional ellipsoid model ($a_1>a_2>a_3$), which has two aspect ratios (the primary aspect ratio, $\rho_{\alpha}=a_1/a_3$ and the secondary aspect ratio, $\rho_{\beta}=a_1/a_2$). We can predict the feature of general thermal expansion factors by theoretical approach of matrix with aligned ellipsoidal inclusion using the Eshelby's equivalent tensor. The coefficients of longitudinal linear thermal expansion ${\alpha}_{11}$ decrease to those of inclusions, ${\alpha}_f$, as both aspect ratios increase. The coefficients of transverse linear thermal expansion of composites ${\alpha}_{33}$ initially increase and show the parabolic corves with maximum values, as the concentrations of filler increase. The coefficient of thermal expansion, ${\alpha}_{22}$ in the transverse direction decreases, as $\rho_{\alpha}$ increases, however, ${\alpha}_{22}$ increases as $\rho_{\beta}$ increases. The coefficient of linear thermal expansion of composites, ${\alpha}_{33}$ in the normal direction increases, as $\rho_{\alpha}$ increases, while ${\alpha}_{33}$ decreases as $\rho_{\beta}$ increases.

• Korea-Australia Rheology Journal
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• v.14 no.3
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• pp.129-138
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• 2002

A cationic surfactant, cetyltrimethylammonium $\rho$-toluenesufonate (CTA$\rho$TS), forms long threadlike micelles in aqueous solution. The threadlike micelles make concentrated entanglement networks, so that the solution shows pronounced viscoelastic behavior as concentrated polymer systems do. However, a mechanism for a process responsible for the longest relaxation time of the threadlike micellar system is different from that of semi-dilute to concentrated polymer systems. The threadlike micellar system exhibits unique viscoelasticity described by a Maxwell model. The longest relaxation time of the threadlike micellar system is not a function of the concentration of CTA$\rho$TS, but changes with that of $\rho$-toluenesufonate ($\rho$$TS^{-}$) ions in the bulk aqueous phase supplied by adding sodium $\rho$-toluenesulfonate (NapTS). The rates of molecular motions in the threadlike micelles are not influenced by the concentration of $\rho$$TS^{-}$ anions, therefore, molecular motions in the threadlike micelles (micro-dynamics) are independent of the longest relaxation mechanism (macro-dynamics). A nonionic surfactant, oleyldimethylamineoxide (ODAO), forms long threadlike micelles in aqueous solution without any additives. The aqueous threadlike micellar system of ODAO also shows Maxwell type viscoelastic behavior. However, the relaxation mechanism for the longest relaxation process in the system should be different from that in the threadlike micellar systems of CTA$\rho$TS, since the system of ODAO does not contain additive anions. Because increase in the average degree of protonation of head groups of ODAO molecules in micelles due to adding hydrogen bromide causes the relaxation time remarkably longer, changes in micro-structure and micro-dynamics in the threadlike micelle are closely related to macro-dynamics in contrast with the threadlike micellar system of CTA$\rho$TS.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.27 no.2
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• pp.95-101
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• 2013

This paper presents the comparison of the earth resistivity obtained from the measurements made with the three-electrode and four-electrode fall-of-potential techniques. The ${\rho}-a$ curve obtained from Wenner four-electrode method in undisturbed earth is in good agreement with the ${\rho}-l$ curve obtained from the three-electrode method based on the fall-of- potential method. However, The ${\rho}-a$ curve in disturbed earth with moisture and freezing is significantly different with the ${\rho}-l$ curve. The ${\rho}-a$ curve is considerably sensitive to the freezing and the moisture present in the earth surface compared to the ${\rho}-l$ curve. Thus to determine the actual earth resistivity, it is necessary to take into account the earth surface conditions when measuring the earth resistivity.

• Journal of the Korean Chemical Society
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• v.32 no.5
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• pp.416-421
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• 1988

Kinetic studies for the nucleophilic substitution reactions of benzyl halides(para-substituted benzyl bromides and benzyliodide) with substituted pyridines in MeOH-MeCN mixtures have been carried out in order to elucidate the reaction mechanism. Cross interaction coefficient, ${\rho}_{XY}$ values suggested that the reactions between benzylhalides and substituted pyridines exhibit an dissocitive $S_N$2 mechanism. Hammett (${\rho}_X$, ${\rho}_Y$), Br${\o}$nsted ${\beta}_N$ and solvatochromic correlation coefficient a, s, a/s values were illustrated. Kinetic results were compared between potential energy surface model and quantum mechanical model. The quantum mechanical approach showed to be consistent with kinetic results.

• Polymer(Korea)
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• v.36 no.2
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• pp.229-234
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• 2012

This paper studied the effects of the content and the orientation of the disk shape fillers on the modulus of PP composites. The experimental results were compared with the theoretical calculations which included the three dimensional ellipsoids and analyzed by two aspect ratios, ${\rho}_{\alpha}=a_1/a_3$and ${\rho}_{\beta}=a_1/a_2$proposed by Lee and his researchers. Mica and talc were used as disk shape fillers in the composites. The shapes of mica and talc were observed by SEM and aspect ratios were statistically calculated. For the case of mica, the average aspect ratios were ${\rho}_{\alpha}=13.5$ and ${\rho}_{\beta}=1.8$, and for the case of talc, they were ${\rho}_{\alpha}=3.8$ and ${\rho}_{\beta}=1.4$. Also, the effects of two aspect ratios and the content of filler on the mechanical properties were studied: For 30 wt% of mica, $E_{11}$ increased up to about 2.7 times, and for the other case of talc, $E_{11}$ increased up to about 2.3 times, respectively.

• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.243-251
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• 2017

In this paper, we solve the additive ${\rho}-functional$ equations (0.1) $f(x+y)+f(x-y)-2f(x)={\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x))$, and (0.2) $2f(\frac{x+y}{2})+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$, where ${\rho}$ is a fixed (complex) number with ${\rho}{\neq}1$, Using the direct method, we prove the Hyers-Ulam stability of the additive ${\rho}-functional$ equations (0.1) and (0.2) in ${\beta}-homogeneous$ (complex) F-spaces.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.235-246
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• 2015

In this paper, a vector optimization problem over cones is considered, where the functions involved are $\eta$-semidifferentiable. Necessary and sufficient optimality conditions are obtained. A dual is formulated and duality results are proved using the concepts of cone $\rho$-semilocally preinvex, cone $\rho$-semilocally quasi-preinvex and cone $\rho$-semilocally pseudo-preinvex functions.

• Bulletin of the Korean Chemical Society
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• v.33 no.11
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• pp.3805-3809
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• 2012

Results for molecular dynamics simulation method of small liquid drops of argon (N = 1200-14400 molecules) at 94.4 K through a Lennard-Jones intermolecular potential are presented in this paper as a preliminary study of drop systems. We have calculated the density profiles ${\rho}(r)$, and from which the liquid and gas densities ${\rho}_l$ and ${\rho}_g$, the position of the Gibbs' dividing surface $R_o$, the thickness of the interface d, and the radius of equimolar surface $R_e$ can be obtained. Next we have calculated the normal and transverse pressure tensor ${\rho}_N(r)$ and ${\rho}_T(r)$ using Irving-Kirkwood method, and from which the liquid and gas pressures ${\rho}_l$ and ${\rho}_g$, the surface tension ${\gamma}_s$, the surface of tension $R_s$, and Tolman's length ${\delta}$ can be obtained. The variation of these properties with N is applied for the validity of Laplace's equation for the pressure change and Tolman's equation for the effect of curvature on surface tension through two routes, thermodynamic and mechanical.

• Korean Journal of Mathematics
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• v.6 no.1
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• pp.127-135
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• 1998

Let ${\rho}(A)$ and ${\rho}(B)$ denote the orders of entire functions $A(z)$ and $B(z)$ respectively. Suppose that ${\rho}(A)$ > 1 and 0 < ${\rho}(B){\leq}\frac{1}{2}$, and that ${\rho}$(A) is not an integer. Then it is shown that every nonconstant solution $f$ of $f^{{\prime}{\prime}}+A(z)f^{\prime}+B(z)f=0$ is of infinite order if all the zeros of $A(z)$ lie in a certain angular sector depending on its genus. In addition, we investigate some growth properties of $A(z)$.

• BMB Reports
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• v.30 no.5
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• pp.337-341
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• 1997

In order to investigate the role of a small GTP-binding protein RhoA in lysophosphatidic acid (LPA)-induced stress fiber formation, C3 ADP-ribosyltransferase was prepared by expressing in E. coli and then applied to Rat-2 fibroblasts. C3 transferase isolated from E. coli was as effective as the toxin from Clostridium botulinum in ADP-ribosylation of RhoA. Incubation of the cells with C3 transferase for 2 days induced ADP-ribosylation of RhoA by a dose-dependent manner, with a sub-maximal induction at $25\;{\mu}g/ml$. As expected, LPA-induced stress fiber formation was completely blocked by pre-incubation with C3 transferase for 2 days. However, exogenously added C3 transferase had no significant effect on the formation of phosphatidylethanol by LPA. These results suggested that phospholipase D was not activated by RhoA in the LPA-induced stress fiber formation.