• Solar Energy
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• v.18 no.2
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• pp.123-135
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• 1998

The effect of the thermal conductivity of a centered, square, heat-conducting body on natural convection In a square enclosure was examined numerically. Numerical simulations was carried out for Pr=0.17, $Ra=1.0{\times}10^4,\;1.0{\times}10^5,\;1.0{\times}10^6$, $K^*$=1.0, 6.6, 34.0 and t=0.5, 1.0, 2.0. The results were reported in terms of streamlines, isotherms, Nusselt number. As the results, the mean Nusselt number increases with the increasing of ${\zeta}$ at a constant Ra and $K^*$. In the case of ${\zeta}=1.0$(obstruction shape ratio), the mean Nusselt numbers were decreased as increasing of $K^*$(obstruction thermal conductivity ratio) with regardless of the Rayleigh number. When the constant obstruction size and thermal conductivity ratio, convective heat transfer effect was more enhanced at ${\zeta}=2.0$ than ${\zeta}=0.5$.

• Journal of Korean Society of Water and Wastewater
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• v.23 no.3
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• pp.353-362
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• 2009

A new method and equipment for measuring the zeta potential of the external surface of hollow fiber (HF) membranes is reported. An existing commercial streaming potential analyzer in conjunction with home-made test cells was used to determine the electrokinetic surface characteristics of various HF membranes. It was shown that measurements of the external surface of HF membrane using the home-made test cells designed in this study were easy and reliable. The zeta potential values were quite accurate and reproducible. By varying the physical shape of the test cells to adjust hydrodynamics inside the test cells, several upgrade versions of home-made test cells were obtained. It was shown that the zeta potential of the external surface of HF membranes was most influenced by membrane materials as well as the way of surface modification. However, the overall surface charge of tested HF membranes were much less than that of commercial polyamide thin-film-composite (TFC) reverse osmosis (RO) membranes due to the lack of surface functional groups. For the HF membranes with the same material, the effect of pore size on the zeta potential was not significant, implying the potential of accurate zeta potential measurements for various HF membranes. The results obtained in this study are expected to be useful for better understating of electrokinetic surface characteristics of the external surface of HF membranes.

• 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.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1107-1116
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• 2001

In this paper, we study the rationality of the Reidemeister zeta function of an endomorphism of a group extension. As an application, we give sufficient conditions for the rationality of the Reidemeister and the Nielsen zeta functions of selfmaps on an exponential solvmanifold or an infra-nilmanifold or the coset space of a compact connected Lie group by a finite subgroup.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.561-568
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• 2017

Hurwitz zeta function occurs in various parts of mathematics. In particular, it plays an important role in some area of number theory. In this paper, using a certain transformation formula, we find some identities of relations between ${\zeta}(2n+1)$ and ${\zeta}(2n+1,{\alpha})$ for special values of ${\alpha}$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1219-1224
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• 2011

In this paper we give a determinant formula for congruent zeta functions of real Abelian function fields. We also give some example of congruent zeta functions when the conductor of real Abelian function field is monic irreducible.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.757-766
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• 1996

The purpose of this paper is to study a real hypersurface of $M_n(c)$ where structure vector $\zeta$ is principal and satisfying $\bigtriangledown_\zeta S = (\bigtriangledown S)\zeta$ (section 2) and also satisfying $\bigtriangledown_\zeta S = a(S \phi - \phi S)$ (section 3) where a is constant.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.435-443
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• 1998

Some mathematical constants have been used in evaluating series involving the Zeta function, the origin of which can be traced back to an over two centries old theorem of Christian Goldbach. We show some of the series involving the Zeta function can be evaluated in terms of the Catalan's constant by using the theory of the double Gamma function.

• East Asian mathematical journal
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• v.18 no.2
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• pp.219-224
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• 2002

Recently the theory of the multiple Gamma functions, which were studied by Barnes and others a century ago, has been revived in the study of determinants of Laplacians. Here we are aiming at evaluating the values of the multiple Gamma functions ${\Gamma}_n(\frac{1}{2})$ in terms of the Hurwitz or Riemann Zeta functions.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1291-1304
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• 2014

In 2005 Kadiri proved that the Riemann zeta function ${\zeta}(s)$ does not vanish in the region $$Re(s){\geq}1-\frac{1}{R_0\;{\log}\;{\mid}Im(s){\mid}},\;{\mid}Im(s){\mid}{\geq}2$$ with $R_0=5.69693$. In this paper we will show that $R_0$ can be taken $R_0=5.68371$ using Kadiri's method together with Platt's numerical verification of Riemann Hypothesis.