• Korean Journal of Mathematics
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• v.19 no.2
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• pp.129-147
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• 2011

In this paper we discuss the zeta-determinants of harmonic oscillators having general quadratic potentials defined on $\mathbb{R}^2$. By using change of variables we reduce the harmonic oscillators having general quadratic potentials to the standard harmonic oscillators and compute their spectra and eigenfunctions. We then discuss their zeta functions and zeta-determinants. In some special cases we compute the zeta-determinants of harmonic oscillators concretely by using the Riemann zeta function, Hurwitz zeta function and Gamma function.

• Journal of Korean Society of Water and Wastewater
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• v.14 no.4
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• pp.343-349
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• 2000

Techniques such as dissolved air flotation and electroflotation, which utilize micro bubbles, are increasingly used for water and wastewater treatment. Most studies have concentrated on particle characteristics. Pretreatments that manipulate particle size and zeta potential were considered important. A recent study, which modeled the collision mechanism between micro bubbles and particles in dissolved air flotation, suggested bubble characteristics should also be important. Hydrogen micro bubbles were generated electrolytically and their zeta potentials measured under various conditions using a novel electrophoresis method. Effects of several parameters were investigated. Bubble zeta potentials were found to be pH dependent, and to have a negative value around neutral pH, becoming zero or positive at lower pH. The pH at zero zeta potential was 5.0 under study conditions. Using artificial solution and tap water, at fixed pH, bubble zeta potentials varied with solution composition. Zeta potentia]s of bubbles were affected by the types of cations and anions in solution but not by the voltage applied. These findings will help improve efficiencies of particle removal processes that utilize micro bubbles. As bubble zeta potential varies with solution composition, it needs to be measured for each composition to understand those effects, which increase removal efficiency.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.2
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• pp.242-247
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• 1987

Electrophysical phenomena at the silicon semiconductor-electrolyte solution interfaces were analyzed based on the zeta potential of the electrical double layer and microelectrophoresis. The suspensions were composed of the p or n-type silicon particles suspended in the KCI or pH buffer solutions. The approximate diameter of the prepared and sampled sioicon semiconductor pardticles was 1.5\ulcorner. The sign of the zeta poetntials of the p and n-type silicon particles in the KCl and pH buffer solution was positive. A range of electrophoretic mobilities of the p and n-type silicons in the KCl solutions was 5.5-8.9x10**-4 cm\ulcornerV-sec and 4.2-7.9x10**-4cm\ulcornerV-sec, respectively. The range of zeta potentials corresponding to the electrophoretic mobilities is 70.4-114.0mV nad 53.9-101.2mV, respectively. On the other hand, a range of electrophoretic mobilities of the p and n-type silicons in the pH buffer solutions was 1.1x10**-4-2.2x10**-3cm\ulcornerV-sec and 0-2.1x10**-3cm\ulcornerV-sec, respectively. The range of zeta potentials corresponding to the electrophoretic mobilities is 14.1-281.6mV and 0-268.8mV, respectively. The zeta potentials and electrical double layers of the doped silicon semiconductors are decisively influenced by the positively charged ions in the solutions. The maximum values of the zeta potentials in the KCl solutions appeared at a concentration of about 10-\ulcorner. The isoelectric point of the n-type silicon semiconductors appeared at about a pH 7. The effect of the space charge of the doped silicon semiconductors can be neglected compare with the effect of the surface charge.

• Carbon letters
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• v.8 no.4
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• pp.321-325
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• 2007

The oxygen and nitrogen enriched activated carbons were obtained from modification of commercial activated carbon by using nitric acid, sodium hydroxide and urea. Zeta-potentials of modified activated carbons were investigated in relation to copper ion adsorption. The structural properties of modified activated carbons were not so much changed, but the zeta-potentials and isoelectric points were considerably changed. The zeta-potential of nitric acid modified activated carbon was the most negative than other activated carbons in the entire pH region, and the $pH_{IEP}$ was shifted from pH 4.8 to 2.6, resulted in the largest copper ion adsorption capacities compare with other activated carbons in the range of pH 3~6.5. In case of urea modified activated carbon, copper ion adsorption was larger than that of the as-received activated carbon from pH 2 to pH 6.5 even though the $pH_{IEP}$ was shifted to pH 6.0, it was due to the coordination process operated between nitrogen functional groups and copper ion. The adsorption capacity of copper ion was much influenced by zeta-potential and $pH_{IEP}$ of carbon adsorbent.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.4
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• pp.640-645
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• 1987

Surface states and interfacial phenomena at the undoped polycrystalline semiconductor particale-electrolyte interfaces were qualitatively analyzed based on the zeta potentials which were measured with microelectrophoresis measurements. The suspensions were composed of the undoped polycrystaline silicon(Si) or gallium arsenide (GaAs) semiconductor particles stalline Si and GaAs particles in the KCl electrolytes was 3.73~6.2x10**-4 cm\ulcornerV.sec and -2.3~1.4x10**-4cm\ulcornerV.sec at the same conditions, respectively. The range of zeta potentials corresponding to the electrophoretic mobilities is 47.8~80.1mV and -30.1~17.9mV, respectively. The variation of the zeta potentials of the undoped polycrystalline Si was similar to the doped crystalline Si. On the other hand, two points of zeta potential reversal occurred at the undoped polycrystalline GaAs-KCl electrolyte interfaces. The surface states of the undoped polycrystalline Si and GaAs were dominated by positively charged donor surface states. These surface states are attributed to adsorbed ion surface states (slow states) at the semiconductor oxide layer-electrolyte interfaces.

• Bulletin of the Korean Chemical Society
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• v.26 no.1
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• pp.107-114
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• 2005

Molecular aggregates of surfactant molecules consisting of one or more bilayers arranged in a hollow, closed, usually spherical geometry are termed “esicles”or “iposomes” In recent years it has been found that in certain systems the vesicular structure forms spontaneously and is long lived, and it has been suggested that these structures may in fact constitute the equilibrium state in these cases (as is true of micelles) This paper deals with the mixed CMC, vesicles, phase behavior, phase transition, geometrical structure, their formation and characterization in the aqueous solutions of mixed cationic/anionic surfactants systems. TEM micrographs revealed that the vesicles were of spherical shape and that their size was of around 180 nm. The zeta potentials are positive at CGS1-rich regions and negative at SLES-rich regions. In the region where SLES/CGS1 (6/4), the zeta potentials are very small, implying that the vesicles at this surfactant ratio may be less stable. At other surfactant ratios, the vesicles are thought to be stable, supported by large absolute values of zeta potentials and little change in UV absorbance for several months.

• Journal of the Society of Cosmetic Scientists of Korea
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• v.33 no.2
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• pp.105-110
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• 2007

The stability of titanium dioxide dispersion was evaluated by zeta ($\zeta$) potential and we intended to apply it for improvement of dispersion stability. Both theories related to $\zeta$ potential (electric double layer, electrophoresis, isoelectric point and electroosmosis) and a method to measure $\zeta$ potential were explained in this study. The change in $\zeta$ potential of $TiO_2$ dispersion was measured by means of Henry's function of Helmholtz-Smoluchowski's equation (H-S equation). The $\zeta$ potentials of $TiO_2$ dispersion were negative in all measured pH values ($3.0{\sim}9.0$), and absolute values of $\zeta$ potentials of $TiO_2$ increased as pH values increased. $TiO_2$ dispersion was maintained in pH 8.0 and 9.0 respectively. From these results, we suggest that $\zeta$ potentials have an effect on $TiO_2$ dispersion and absolute value of $\zeta$ potentials played an important role in the stability of $TiO_2$ dispersion in aqeous medium.

• 한국생물공학회:학술대회논문집
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• 2001.11a
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• pp.890-893
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• 2001

Zeta potential measurement not only can provide surface information on colloidal biomaterials but more importantly can be used in bioprocess control and products quality control. In this study, zeta potentials for intracrystalline proteins of each layers from oyster shell prepared in 1mM NaCl at different pH were measured. Also, in forming calcite crystals with intracrystalline proteins as an additive extracted from oyster shell, the zeta potentials were measured. These studies were performed to verify the primary role of intracrystalline proteins in controlling the formation, morphological development and crystallography of the biocomposite.

• Bulletin of the Korean Chemical Society
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• v.26 no.7
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• pp.1083-1089
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• 2005

Most experimental studies available in the literature on filtration are based on observed average zeta potential of particles (usually 10 measurements). However, analyses of data using the average zeta potential alone can lead to misleading and erroneous conclusions about the attachment behavior because of the variation of particle zeta potentials and the heterogeneous distribution of the collector surface charge. To study characteristics of zeta potential, zeta potential distributions (ZPDs) of silica particles under 9 different chemical conditions were investigated. Contrary to many researchers’ assumptions, most of the ZPDs of silica particles were broad. The solids concentration removal was better near the isoelectric point (IEP) as many researchers have noticed, thus proper destabilization of particles is very important to achieve better particle removal in particle separation processes. While, the mean zeta potential of silica particles at a given coagulant dose was a function of particle concentration; the amount of needed coagulant for particle destabilization was proportional to the total surface charge area of particles in the suspension.

• Journal of Korean Society of Environmental Engineers
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• v.37 no.8
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• pp.441-449
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• 2015

Studies on the flocculation of algae using various metal ions were carried out by measurements of optical density(OD) and zeta potential. Cyanobacteria were used as algaes. Flocculation efficiencies of cyanobacteria by an addition of metal ions were determined from OD values, and the effect of metal ions was greater in the order of $Al^{3+}$>$La^{3+}$>$Ho^{3+}$>$Fe^{2+}$>$Ca^{2+}$. Especially for trivalent metal ions, percentages of metal removed from cyanobacteria solutions on flocculation were measured, showing the same order as in flocculation efficiencies. Zeta potentials of cyanobacteria alone were measured with increasing the concentration, found to be all negative voltages, and were increased with increasing the concentration. The effect of pH on zeta potential of cyanobacteria solution was investigated. Below pH 5.5, the zeta potentials were steeply decreased with increasing pH, whereas in the range of $5.5{\leq}pH{\leq}10$ they were almost constant ($-46{\pm}1mV$) even with increasing pH. At a constant concentration of cyanobacteria ($A_{730}=0.25$), an increase in concentration of metal ions caused an increase in zeta potential of cyanobacteria solution, showing that the effect was greater in the order of $Al^{3+}$>$Ho^{3+}$>$La^{3+}{\gg}Mg^{2+}{\geq}Ca^{2+}{\gg}K^+$. At a constant metal concentration, zeta potentials were measured with increasing cyanobacteria concentration, showing that zeta potentials for $K^+$, $Mg^{2+}$ and $Ca^{2+}$ ions were negligibly changed, whereas those of $Ho^{3+}$ and $La^{3+}$ ions were decreased. Moreover, the effect of $Ho^{3+}$ ion on decreasing zeta potential was smaller than that of $La^{3+}$ ion. $Al^{3+}$ ions showed quite a different behavior that with increasing cyanobacteria concentration the zeta potentials increased and decreased thereafter. Hydrolysis of $Al^{3+}$ ions caused a difficulty to investigate coagulation or flocculation of cyanobacteria by measurement of zeta potential.