• Korean Journal of Food Science and Technology
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• v.16 no.2
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• pp.179-181
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• 1984

The present study was directed to define the triglyceride composition of pine nut oil. The triglycerides were separated from pine nut oil by thin layer chromatography, and fractionated by high performance liquid chromatography on the basis of partition numbers. Each of these collected fractions were fractionated again by gas liquid chromatography (GLC) according to the acyl carbon number of the triglyceride, and fatty acid composition of the triglyceride was also analyzed by GLC. The pine nut oil consisted of thirty two kinds of triglycerides, and the major triglycerides of pine nut oil were those of $(C_{18:2},\;C_{18:2},\;C_{18:3}\;;\;34.9%)$, $(C_{18:1},\;C_{18:2},\;C_{18:3}\;;\;10.8%)$, $(C_{18:1},\;C_{18:1},\;C_{18:2}\;;\;9.9%)$, $(C_{18:1},\;C_{18:1},\;C_{18:1}\;;\;6.5%)$, $(C_{18:1},\;C_{18:1},\;C_{18:2}\;;\;6.3%)$, $(C_{18:1},\;C_{18:1},\;C_{18:3}\;;\;4.8%)$, $(C_{16:0},\;C_{18:2},\;C_{18:3}\;;\;3.3%)$, $(C_{18:0},\;C_{18:1},\;C_{18:2}\;;\;2.7%)$, $(C_{16:0},\;C_{18:1},\;C_{18:2}\;;\;2.6%)$, $(C_{16:0},\;C_{18:2},\;C_{18:2}\;;\;2.2%)$, $(C_{16:0},\;C_{18:1},\;C_{18:3}\;;\;1.9%)$, $(C_{16:0},\;C_{18:2},\;C_{18:2}\;;\;1.7%)$, $(C_{16:0},\;C_{18:1},\;C_{18:1}\;;\;1.7%)$, $(C_{18:1},\;C_{18:3},\;C_{18:3}\;;\;1.5%)$.

• Korean Journal of Food Science and Technology
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• v.14 no.3
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• pp.226-231
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• 1982

In order to define triglyceride compositions in fat and oil triglycerides were separated by thin layer chromatography (TLC) from corn oil, and the separated triglycerides were graduated according to each partition number(PN) by high performance liquid chromatography (HPLC) using column of ${\mu}-Bondapack\;C_{18}$ and each graduation was graduated again according to acylcarbon number by gas liquid chromatography(GLC). Fatty acid compositions were analyzed by GLC after their graduation were methylated in according to PN. The triglyceride compositions were estimated by synthesizing the above three results. The estimated triglycerides consisted of 36 kinds in corn oil. The major triglyceride compositions of sample oil were as follows: 21.5%$(C_{18:2},\;C_{18:2},\;C_{18:1})$, 17.4%$(C_{18:1},\;C_{18:2},\;C_{18:1})$, 15.4%$(C_{18:1},\;C_{18:2},\;C_{16:0})$, 11.1%$(C_{16:0},\;C_{18:2},\;C_{18:2})$, 9.0%$(C_{18:1},\;C_{18:1},\;C_{18:1})$, 8.0%$(C_{18:2},\;C_18:2},\;C_{18:2})$, 5.7%$(C_{18:1},\;C_{18:1},\;C_{16:0})$, 2.2%$(C_{16:0},\;C_{16:0},\;C_{18:2})$, 1.6%$(C_{18:2},\;C_{18:2},\;C_{18:2})$, 1.1%$C_{18:2},\;C_{18:0},\;C_{16:0})$, 1.1%$(C_{16:0},\;C_{16:0},\;C_{18:1})$.

• Journal of Korean Ophthalmic Optics Society
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• v.6 no.2
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• pp.65-70
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• 2001

We obtained the sum of two curvature ($C_x+C_y$) in toric lens which two toroidal surface is the right angle each other. $$C_x+C_y=\frac{x^2+y^2}{2r_1}+\frac{x^2}{2}(\frac{1}{r_2}-\frac{1}{r_1})$$ and the sum of two curvature ($C_a+C_b$) in toric lens about the cross angle. $$(C_a+C_b)=\frac{x^2cos^2{\alpha}_1}{2r_1}+\frac{x^2cos^2{\alpha}_2}{2r_2}+\frac{y^2sin^2{\alpha}_1}{2r_1}+\frac{y^2sin^2{\alpha}_2}{2r_2}$$ and claculated the parameter S, C, ${\theta}$ of a combination power in toric lens of the cross angle including surface curvature ($C_x$, $C_y$) values. $$S=(n-1)\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]-\frac{C}{2},\;C=-\frac{2(n-1)}{sin2{\theta}}\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]$$ $${\theta}=\frac{1}{2}tan^{-1}\[-\frac{{C_xy^2sin2{\theta}_1}+{C_yx^2sin2{\theta}_2}}{{C_xy^2cos2{\theta}_1}+{C_yx^2cos2{\theta}_2}}\]$$.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.437-444
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• 2019

For c > -1, let ${\nu}_c$ denote a weighted radial measure on ${\mathbb{C}}$ normalized so that ${\nu}_c(D)=1$. For $c_1,c_2>-1$ and $f{\in}L^1(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$, we define the weighted Berezin transform $B_{c_1,c_2}f$ on $D^2$ by $$(B_{c_1,c_2})f(z,w)={\displaystyle{\smashmargin2{\int\nolimits_D}{\int\nolimits_D}}}f({\varphi}_z(x),\;{\varphi}_w(y))\;d{\nu}_{c_1}(x)d{\upsilon}_{c_2}(y)$$. This paper is about the space $M^p_{c_1,c_2}$ of function $f{\in}L^p(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$ ) satisfying $B_{c_1,c_2}f=f$ for $1{\leq}p<{\infty}$. We find the identity operator on $M^p_{c_1,c_2}$ by using invariant Laplacians and we characterize some special type of functions in $M^p_{c_1,c_2}$.

• Korean Journal of Food Science and Technology
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• v.14 no.3
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• pp.219-225
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• 1982

Triglycerides of cottonseed oil were separated by thin layer chromatography (TLC), and fractionated by high-performance liquid chromatography (HPLC) on the basis of partition numbers. From each fraction, it was fractionated again on the basis of acyl carbon numbers using gas liquid chromatography (GLC). The fatty acids of triglyceride for each partition number group were analyzed by GLC. From, these results, triglyceride constituents of cotton seed oil were estimated to be 37 kinds of triglycerides. The major triglycerides and their contents in cotton seed oil were as follows: 25.8%$(C_{16:0},\;C_{18:2},\;C_{18:2})$, 15.5%$(C_{18:2},\;C_{18:2},\;C_{18:2})$, 13.8%$(C_{16:0},\;C_{18:2},\;C_{16:0})$, 8.3%$(C_{18:2},\;C_{18:1},\;C_{18:2})$, 6.2%$(C_{18:2},\;C_{18:1},\;C_{18:1})$, 4.1%$(C_{18:1},\;C_{18:1},\;C_{14:0})$, 3.4%$(C_{16:0},\;C_{18:1},\;C_{16:0})$, 2.3%$(C_{18:1},\;C_{18:2},\;C_{16:0})$, 2.2%$(C_{18:1},\;C_{18:1},\;C_{18:1})$, 1.0%$(C_{14:0},\;C_{18:2},\;C_{18:1})$.

• Korean Journal of Food Science and Technology
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• v.15 no.1
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• pp.66-69
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• 1983

Triglyceride fraction was separated from olive oil by thin layer chromatography (TLC) and fractionated into four groups by high performance liquid chromatography (HPLC). Compositions of the triglycerides and fatty acids of four fractions were determined by gas liquid chromatography (GLC). The olive oil contained higher concentrations of C-52 and C-54 triglycerides having partition numbers of 48. The fatty acid compositions of these triglycerides were mainly composed of C18:1 and C18:2 fatty acids. From these results, the possible fatty acid combinations of major triglycerides of olive oil were estimated to be(3C18:1;50.6%), (1C16:0, 2C18:1;23.51%), (2C18:1, 1C18:2;5.48%), (1C18:0, 2 18:1;4.55%), (1C16:0, 1C18:1, 1C18:2;2.94%), (2C16:0, 1C18:1;2.35%), (1 C16:1, 2 C18:1;2.21%), (1C18:1, 2C18:2;1.06%), (1 C14:0, 2 C18:1;1.03%).

• Applied Biological Chemistry
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• v.27 no.4
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• pp.278-284
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• 1984

The triglyceride compositions of peach kernel and apricot kernel oil have been investigated by a combination of high performance liquid chromatography (HPLC) and gas liquid chromatography(GLC). The triglycerides of peach kernel and apricot kernel oil were first separated by thin layer chromatography(TLC), and fractionated on the basis of their partition number(PN) by HPLC on a C-18 ${\mu}-Bondapak$ column with methanol-chloroform solvent mixture. Each of these fractionated groups was purely collected and analyzed by GLC according to acyl carbon number(CN) of triglyceride. Also the fatty acid compositions of these triglycerides were determined by GLC. From the consecutive analyses of these three chromatography techniques, the possible triglyceride compositions of peach kernel and apricot kernel oil were combinated into fifteen and thirteen kinds of triglycerides, respectively. The major triglycerides of peach ternel oil were those of $(3{\times}C_{18:1}\;30.9%)$, $(2{\times}C_{18:1},\;C_{18:2},\;21.2%)$, $(C_{18:1},\;2{\times}C_{18:2}\;10.6%)$, $(3{\times}C_{18:2}\;3.8%)$, $(C_{18:0},\;2{\times}C_{18:1},\;1.8%)$, $(C_{16:0},\;C_{18:1},\;C_{18:2},\;1.5%)$, $(C_{18:0},\;C_{18:1},\;C_{18:2},\;1.1%)$ and those of apricot kernel oil were $(3{\times}C_{18:1},\;39.5%)$, $(2{\times}C_{18:1},\;C_{18:2},\;24.5%)$, $(C_{18:0},\;2{\times}C_{18:2},\;14.2%)$, $(3{\times}C_{18:2},\;2.0%)$.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.17 no.4
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• pp.291-298
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• 1984

The extracted hagfish (Eptatretus burgeri) flesh lipid was separated into following fractions by column chromatography on Bio-beads SX-2 and Sephadex LH-20 prior to gab chromatographic analysis of their fatty acid compositions: polar lipid, triglyceride and free fatty acid. The major fatty acids of total lipid and triglyceride in hagfish were $C_{16:0},\;C_{16:1},\;and\;C_{18:1}$. The ratio of $C_{18:0}/C_{18:1}$ in the total lipid and triglyceride of hagfish was 0.1. The polar lipid of the hagfish muscle was mainly composed of phosphatidyl choline ($65.5\%$) and phosphatidyl ethanolamine ($28.0\%$). The triglyceride obtained was fractionated into four fractions by HPLC on the basis of partition numbers. Both the fatty acid composition and triglyceride composition on the basis of the total carbon number in the acyl chains of the triglyceride were analysed by the GLC. From the information obtained on triglyceride compositions based on the total carbon number by GLC and the partition number by HPLC and fatty acid composition by GLC, the combination of fatty acid in each triglycerides was estimated. A computer was used for estimation of the fatty acid combination in the triglyceride because hagfish lipid triglyceride was composed of various kinds of fatty acids. Fortyfour kinds of triglyceride were estimated. The major triglycerides in hagfish flesh lipid were found to those of ($1{\times}C_{16:0},\;2{\times}C_{18:1};\;13.5\%$), ($1{\times}C_{16:0},\;1{\times}C_{18:0},\;1{\times}C_{18:1};\;7.2\%$), ($1{\times}C_{16:1},\;2{\times}C_{18:1};\;5.4\%$), ($2{\times}C_{16:0},\;1{\times}C_{22:5};\;5.2\%$), ($1{\times}C_{14:0},\;2{\times}C_{18:1};\;4.5\%$), ($2{\times}C_{18:1},\;1{\times}C_{22:5};\;3.6\%$), ($1{\times}C_{14:0},\;1{\times}C_{18:0},\;1{\times}C_{18:1};\;2.7\%$) and ($1{\times}C_{14:0},\;1{\times}C_{16:0},\;1{\times}C_{18:2};\;2.2\%$).

• Journal of the Korean Chemical Society
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• v.34 no.6
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• pp.517-526
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• 1990

The crystal structures of two alditol acetates, D-glucitol hexaacetate and xylitol pentaacetate, have been determined by diffraction methods with Mo-K$\alpha$radiation, using direct methods for phase determinations. The crystal data are: for D-glucitol hexaacetate, P2$_1$, with a = 10.275 (2), b = 8.363 (1), c = 12.560 (5) $\AA;\beta$ = 95.97 $(2)^{\circ}$, Z = 2; for xylitol pentaacetate, P2$_1$/C with a = 18.126 (1), b = 11.422 (2), c = 8.649 (1) $\AA$, $\beta = 95.03 (1)^{\circ}$, Z = 4. Both molecules have extended zigzag carbon chain conformations which differ from previous studies of the structures of D-glucitol and xylitol and also differ from NMR studies on alditol acetates. The bond lengths and angles are normal, with mean values over both structures of C($sp^3)-C(sp^3): 1.514 (10),\; C(sp^3)-O: 1.444 (6),\; C(sp^2)-O: 1.347 (9),\; C(sp^2)=O: 1.197 (6),\; C(sp^2)-C(sp^3): 1.479(9){\AA},\; C(sp^3)-C(sp^3)-C(sp^3): 114.6 (17),\; O-C(sp^3)-C(sp^3): 109.4 (23),\; C(sp^2)-O-C(sp^3): 117.4 (6),\; O=C(sp^2)-O: 122.6 (6),\; C(sp^3)-C(sp^2)-O: 111.8 (7),\; C(sp^3)-C(sp^2)=O: 125.5 (4)^{\circ}$. The atoms of acetate groups are in coplanar. There are no particularly short intermolecular contacts and the molecules are held together by van der Waals force only.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.781-791
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• 2016

Let $d_*(1,w)^2 ={\mathbb{R}}^2$ with the octagonal norm of weight w. It is the two dimensional real predual of Lorentz sequence space. In this paper we classify the smooth points of the unit ball of the space of symmetric bilinear forms on $d_*(1,w)^2$. We also show that the unit sphere of the space of symmetric bilinear forms on $d_*(1,w)^2$ is the disjoint union of the sets of smooth points, extreme points and the set A as follows: $$S_{{\mathcal{L}}_s(^2d_*(1,w)^2)}=smB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}extB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}A$$, where the set A consists of $ax_1x_2+by_1y_2+c(x_1y_2+x_2y_1)$ with (a = b = 0, $c={\pm}{\frac{1}{1+w^2}}$), ($a{\neq}b$, $ab{\geq}0$, c = 0), (a = b, 0 < ac, 0 < ${\mid}c{\mid}$ < ${\mid}a{\mid}$), ($a{\neq}{\mid}c{\mid}$, a = -b, 0 < ac, 0 < ${\mid}c{\mid}$), ($a={\frac{1-w}{1+w}}$, b = 0, $c={\frac{1}{1+w}}$), ($a={\frac{1+w+w(w^2-3)c}{1+w^2}}$, $b={\frac{w-1+(1-3w^2)c}{w(1+w^2)}}$, ${\frac{1}{2+2w}}$ < c < ${\frac{1}{(1+w)^2(1-w)}}$, $c{\neq}{\frac{1}{1+2w-w^2}}$), ($a={\frac{1+w(1+w)c}{1+w}}$, $b={\frac{-1+(1+w)c}{w(1+w)}}$, 0 < c < $\frac{1}{2+2w}$) or ($a={\frac{1=w(1+w)c}{1+w}}$, $b={\frac{1-(1+w)c}{1+w}}$, $\frac{1}{1+w}$ < c < $\frac{1}{(1+w)^2(1-w)}$).