• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.657-662
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• 2001

It is proved that if for each n, $1\leqp_n\leq2 \;and \;the(p_n, p’_n)$ Clarkson inequality holds in each Banach space X$_{n}$ then the (t, t’) Clarkson inequality holds in ($\sum^\infty_{n=1}\; X_n)_r, \;the \ell^r-sum \;of\; X_n’s,\; where\; 1\leqr<\infty,\; t=min{p, r, r’} \;and \;p = \;inf{p_n}.$ The (p, p’) Clarkson inequality is preserved by quotient maps and a new proof of a Takahashi-Kato theorem stating that the (p, p’) Clarkson inequality holds in a Banach space X if and only if it holds in its dual space $X_*$ is given.n.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.653-659
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• 2017

Let $p{\geq}1$ be a real number. A tuple $T=(T_1,{\ldots},T_n)$ of commuting bounded linear operators on a Banach space X is called an ${\ell}^p$-spherical isometry if ${\sum_{i=1}^{n}}{\parallel}T_ix{\parallel}^p={\parallel}x{\parallel}^p$ for all $x{\in}X$. The tuple T is called a toral isometry if each Ti is an isometry. By a result of Ansari, Hedayatian, Khani-Robati and Moradi, for every $n{\geq}1$, there is a supercyclic ${\ell}^2$-spherical isometric n-tuple on ${\mathbb{C}}^n$ but there is no supercyclic ${\ell}^2$-spherical isometry on an infinite-dimensional Hilbert space. In this article, we investigate the supercyclicity of ${\ell}^p$-spherical isometries and toral isometries on Banach spaces. Also, we introduce the notion of semicommutative tuples and we show that the Banach spaces ${\ell}^p$ ($1{\leq}p$ < ${\infty}$) support supercyclic ${\ell}^p$-spherical isometric semi-commutative tuples. As a result, all separable infinite-dimensional complex Hilbert spaces support supercyclic spherical isometric semi-commutative tuples.

• Journal of Korean Society for Atmospheric Environment
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• v.8 no.3
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• pp.191-197
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• 1992

In order to investigate the chemical components of acid precipitation at Kangwha near the Yellow Sea and Seoul in Korea, the precipitation samples were collected by wetonly precipitation sampler from February 1991 to January 1992, and pH, electric conductivity(E. C.) and major water-soluble ionic components were analyzed. Strong negative linear correlations were observed between the rainfall amount and the sum of major ionic components in $\mu eq/\ell$ at two sites. The sum of major ionic components also correlated negatively with rain intensity. The analytical results of precipitation samples at two sites were compared each other. Average values of volume-weighted pH were found to be 5.21 at Kangwha and 5.09 at Seoul. The cationic abundance($\mu eq/\ell$) in rainwater showed the general trend $NH_4^+ > Na^+ > Ca^{2+} > Mg^{2-+} > H^+ > K^+$ at Kangwah and $NH_4^+ > Ca^{2+} > Na^+ > H^+ > Mg^{2+} > K^+$ at Seoul. The anionic abundance showed the general trend $SO_4^{2-} > Cl^- > NO_3^-$ at Kangwha and $SO_4^{2-} > NO_3^- > Cl^-$ at Seoul. The concentrations of seasalt such as $Na^+ and Cl^-$ were higher at Kangwha than Seoul. The concentrations of $nss-SO_4^{2-}, nss-Cl^- and NO_3^-$ which are acid composition were higher at Seoul(96.3 $\mu eq/\ell$) than Kangwha(69.0 $\mu eq/\ell$). The contribution of seasalt to the composition of precipitation were higher at Kangwha(34.1%) than Seoul(15.7%). Ammonia and calcium species in rainwater at Kangwha and Seoul are interpreted to have 91% of neutralizing capacity of the original sulfuric and nitric acids. Provided that the precipitation acidity originates primarily from sulfate and nitrate, sulfate was found to contribute about 73-75% of the free precipitation acidity.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.53-56
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• 2002

Suppose { $X_{n}$}$_{n=1}$$^{\infty}$ sequence of finite dimensional Banach spaces and suppose that X is either a closed subspace of (equation omitted) or a closed subspace of (equation omitted) with p>2. We show that every bounded linear operator from X to a Banach space Y of cotype q(2$\leq$q〈p) is compact.t.t.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.715-720
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• 2004

Suppose X is a closed subspace of Z = ${({{\Sigma}^{\infty}}_{n=1}Z_{n})}_{p}$ (1 < p < ${\infty}$, dim $Z_{n}$ < ${\infty}$). We investigate an isometrically isomorphic embedding of L(X)/K(X) into L(X, Z)/K(X, Z), where L(X, Z) (resp. L(X)) is the space of the bounded linear operators from X to Z (resp. from X to X) and K(X, Z) (resp. K(X)) is the space of the compact linear operators from X to Z (resp. from X to X).

• Korean Journal of Environmental Agriculture
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• v.24 no.4
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• pp.326-333
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• 2005

To enhance groundwater quality and soil nutrient management in fertigated plastic film house, groundwater samples from Jinju 52, Sacheon 3, Changnyeong 3, Sancheong 4 and Namhae 2 sites and soil samples from Jinju 23 sites were collected from September to November in 2004. The average concentration of $NO_3-N$ in groundwater was $12.0mg{\ell}^{-1}$ and 20% of survey sites exceeded the limiting level $(20mg{\ell}^{-1})$ of agricultural goundwater quality. The amount of ions in groundwater was in the order of $Ca^{2+}>Na^+>Mg^{2+}>NH_4-N>K^+$ in cations and ${HCO_3}^->{SO_4}^{2-}>NO_3-N>Cl^-$ in anions. Electrical conductivity of groundwater was positively correlated with $Ca^{2+},\;Cl^-,\;Mg^{2+},\;{SO_4}^{2-},\;NO_3-N\;and\;Na^+$ concentrations. In addition, it had significantly positive correlation with sum cations and anions, respectively $({\Sigma}cations\;(me{\ell}^{-1})$ = EC values $(dS\;m^{-1}){\times}4.65,\;{\Sigma}anions\;(me{\ell}^{-1})$ = EC values $(dS\;m^{-1}){\times}7.63\;and\;{\Sigma}\;(cations+anions,\;me{\ell}^{-1})$ = EC values $(dS\;m^{-1}){\times}11.1)$. The proportions of soil chemical properties over the critical levels for crop production in fertigated plastic film house were 56.5% in pH, 47.8% in OM, 95.7% in available $P_2O_5$, 78.3% in exchangeable K, 87% in exchangeable Ca, 56.5% in exchangeable Mg and 43.5% in EC. Soil pH was positively correlated with pH $(r=0.540^{**})$ and ${HCO_3}^-$ concentration $(r=0.523^{**})$ of groundwater.

• Journal of the Korean Society of Food Science and Nutrition
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• v.32 no.2
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• pp.269-277
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• 2003

Effects of soy protein concentrate (SPC) containing isoflavone and casein diets on plasma phospholipid (PLs)-fatty acid patterns were investigated in 7-& 40- wk old female rats. Diets containing 16% SPC (soy/young:SY, soy/old: SO) and casein (casein/young : CY, casein/ old: CO) supplemented with 0.5% cholesterol were fed for 4 wks. Fatty acid compositions of plasma PLs were determined by TLC and GLC. Compared to the dietary protein effects, age effects on serum lipids were more profound. The levels of total cholesterol (Chol.), triglyceride, HDL-Chol., (LDL+VLDL)-Chol. and atherogenic index (AI) were higher in older groups (OC & OS) than younger groups (YC &. YS). Soy groups had higher Ell)L-Chol. level and lower (LDL+ VLDL)-Chol. and AI, compared with casein groups. The compositions of C22:0, Cl8:1 $\omega$9 and sum of MUFA in plasma PLs were significantly higher in casein group (CY & CO) than soy group (SY & SO), but those of sum of SFA were higher in soy group. The compositions of C22:0, Cl8:1 $\omega$9, C22:1, Cl8:3$\omega$3 and C22:4$\omega$6 were higher and those of C22:6$\omega$3, sum of $\omega$3, Cl8: 2$\omega$6 C20:4$\omega$6, sum of $\omega$6 and sum of PUFA were lower in plasma PLs of younger rats. The average P/S and $\omega$3/$\omega$6 ratio in older group was higher. The $\Delta$-7 desaturation index (16:0⇒16:1$\omega$7) and $\Delta$-9 desaturation index (18:0⇒18:1$\omega$9) were lower in soy group than casein group, while $\Delta$-6 and $\Delta$-5 desaturation index were not affected by dietary protein. The $\Delta$-4 desaturation index (22:4$\omega$6⇒22:5$\omega$6) were higher and elongation index (20:4$\omega$6⇒22:4$\omega$6) were lower in older group. The ratio of the products of $\omega$3 fatty acid series (Cl8:3) was significantly higher in older group, which indicated that age affected the plasma PUFA metabolism. On the other hand, older rats had higher serum cholesterol level compared with younger rats. Taken together, these changes in fatty acid composition might cause minimal changes in tile membrane fluidity induced by the increase serum cholesterol level.