• Journal of Environmental Health Sciences
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• v.24 no.1
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• pp.19-23
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• 1998

This study has designed to investigate the removal effect of sewage treatment effluent by ultrafilter membrane species and then to analyze the change of pH, bacteria and E. coli., the concentration of chlorides. Ultra filtration process did not effective to remove chloride, Ca and Mg. Spiral type ultrafiltration process was more effective to remove chemical oxygen demand of sewage treatment effluent than Hollow type ultrafiltration process. The flux of spiral wound ultrafilter was higher than the hollow fiber ultrafilter.

• Journal for History of Mathematics
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• v.15 no.2
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• pp.161-168
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• 2002

We show that if the Stone-Cech compactification of $\textit{AX}$ and the minimal basically disconnected cove. of $\beta$Χ we homeomorphic and every real $\sigma$$Z(X)^#$-ultrafilter on X has the countable intersection property, then there is a covering map from $\nu$(ΛΧ) to $\nu$Χ and every real $\sigma$$Z(X)^#$-ultrafilter on Χ has the countable intersection property if and only if there is a homeomorphism from the Hewitt realcompactification of ΛΧ to the minimal basically disconnected space of $\nu$Χ.

• Journal of environmental and Sanitary engineering
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• v.12 no.2
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• pp.65-74
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• 1997

The purpose of this study was to investigate the removal effect and variation of contaminated water by various water treatment processes using sediment filter, activated carbon, photocatalysis, reverse osmosis, ultra violet sterilizer and ultra filtration. The removal effect of chloride and trace metal was low by activated carbon and ultra filter but high in reverse osmosis. The removal effect of bacteria and E. coli was low by activated carbon and membrane filter system using activated carbon but high in impregnated activated carbon. The removal effect of TCE was low in sand and ultra filter system as compared with activated carbon. Ultra filtration process was effective for purify agricultural water without E.coli. Reverse osmosis was effective to remove heavy metal and activated carbon was effective to remove halogenated organic chemical compound. The flux and the removal effect of COD in spiral wound ultrafilter were higher than the hollow fiber ultrafilter.

• Membrane and Water Treatment
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• v.3 no.1
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• pp.51-62
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• 2012

The permeate flux declination along an ultrafilter membrane is due mainly to the concentration-polarization resistance increment and the decline in transmembrane pressure. It was found in previous works that the concentration polarization resistance could be reduced in a ring-rod tubular membrane ultrafilter using the turbulent behavior. In the present study, the performance was further improved by properly and gradually decreasing the baffled-ring distance along the cross-flow channel coupled with properly adjusting the number of baffled rings. This theoretical analysis is based on the mass and momentum balances as well as the application of the resistance-in-series model. The correlation predictions are confirmed with the experimental results for dextran T500 aqueous solution ultrafiltration.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.749-758
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• 2006

In [1], we introduced the notion of p-stacks. In this paper, by using p-stacks we characterize $S^*-continuous$ functions, separation axioms, supracompactness and some properties on supratopological spaces. We also introduce the notion of p-supracompactness and study some properties.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.41-47
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• 2004

We introduce the $K_0$-proximity space as a generalization of the Efremovi$\check{c}$-proximity space. We try to show every ultrafilter in $K_0$-proximity space generates a cluster and every Cauchy cluster is a point cluster.

• East Asian mathematical journal
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• v.23 no.2
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• pp.151-158
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• 2007

In this paper we introduce the concept of fuzzy ${\beta}-compact^*$ spaces. Besides giving some interesting properties of fuzzy ${\beta}-compact^*$ spaces we also give a characterization on fuzzy $\beta$-compact spaces by making use of newly introduced concept of fuzzy $\beta$-filters.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.221-229
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• 2013

We show that if X is a space such that ${\beta}QF(X)=QF({\beta}X)$ and each stable $Z(X)^{\sharp}$-ultrafilter has the countable intersection property, then there is a homeomorphism $h_X:vQF(X){\rightarrow}QF(vX)$ with $r_X={\Phi}_{vX}{\circ}h_X$. Moreover, if ${\beta}QF(X)=QF({\beta}X)$ and $vE(X)=E(vX)$ or $v{\Lambda}(X)={\Lambda}(vX)$, then $vQF(X)=QF(vX)$.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.37-43
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• 2014

In this paper, we show that for any ${\sigma}$-complete Boolean subalgebra $\mathcal{M}$ of $\mathcal{R}(X)$ containing $Z(X)^{\sharp}$, the Stone-space $S(\mathcal{M})$ of $\mathcal{M}$ is a basically diconnected cover of ${\beta}X$ and that the subspace {${\alpha}{\mid}{\alpha}$ is a fixed $\mathcal{M}$-ultrafilter} of the Stone-space $S(\mathcal{M})$ is the the minimal basically disconnected cover of X if and only if it is a basically disconnected space and $\mathcal{M}{\subseteq}\{\Lambda_X(A){\mid}A{\in}Z({\Lambda}X)^{\sharp}\}$.

• The Pure and Applied Mathematics
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• v.21 no.2
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• pp.113-120
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• 2014

In this paper, we first show that for any space X, there is a ${\sigma}$-complete Boolean subalgebra of $\mathcal{R}$(X) and that the subspace {${\alpha}{\mid}{\alpha}$ is a fixed ${\sigma}Z(X)^{\sharp}$-ultrafilter} of the Stone-space $S(Z({\Lambda}_X)^{\sharp})$ is the minimal basically disconnected cover of X. Using this, we will show that for any countably locally weakly Lindel$\ddot{o}$f space X, the set {$M{\mid}M$ is a ${\sigma}$-complete Boolean subalgebra of $\mathcal{R}$(X) containing $Z(X)^{\sharp}$ and $s_M^{-1}(X)$ is basically disconnected}, when partially ordered by inclusion, becomes a complete lattice.