• Honam Mathematical Journal
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• v.31 no.4
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• pp.591-599
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• 2009

For given ${\alpha},{\omega}\;{\in}\;{\mathbb{R}}$ and ${\beta}$ > 1, let $T_{{\beta},{\alpha},{\omega}}$ be the skew-product transformation on the torus, [0, 1) ${\times}$ [0, 1) defined by (x, y) ${\longmapsto}\;({\beta}x,y+{\alpha}x+{\omega})$ (mod 1). In this paper, we give a criterion of ergodicity and weakly mixing for the transformation $T_{{\beta},{\alpha},{\omega}}$ when the natural extension of the given ${\beta}$-transformation can be viewed as a generalized baker's transformation, i.e., they flatten and stretch and then cut and stack a two-dimensional domain. This is a generalization of theorems in [10].

• Journal of the Korean Society of Food Science and Nutrition
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• v.35 no.10
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• pp.1363-1370
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• 2006

This study was designed to evaluate the effect of Agaricus blazei $\beta-glucan$ and egg shell calcium complex on bone metabolism in ovariectomized (OVX) rats. Forty Sprague-Dewley female rats, 10 weeks of age $(248{\pm}1.7g)$, were divided into 4 groups and fed on the experimental diets for 6 weeks: sham operated control treated with normal diet containing 0.5% calcium (Sham-C), OVX-control treated with normal diet containing 0.5% calcium (OVX-C), $OVX-\beta-glucan$ group treated with $\beta-glucan$ diet containing 0.5% calcium (OVX-G), and $OVX-\beta-glucan$ egg shell calcium complex treated with $OVX-\beta-glucan$ egg shell calcium complex containing 0.5% calcium (OVX-GE). Bone weight of femur was higher in the OVX-GE group than in the other OVX groups. Bone mineral density of femur was significantly different (p<0.05) among the experimental groups and showed the highest level in the OVX-GE group. Calcium absorption rate and retention were higher in the $\beta-glucan$ supplement groups than in the other groups (p<0.05). Alkaline phosphatase activities and osteocalcin levels of serum showed lower in the $\beta-glucan$ supplement groups than in the OVX-C group. Deoxypyridinoline crosslink values of urine, indicator of bone absorption, showed the lowest in the OVX-GE group. The $\beta-glucan$ supplemented groups had a lower bone resorption ratio than in the OVX-C group. We concluded that bioavailability of calcium is higher in $\beta-glucan$ supplement groups compared to those in OVX rats. From the above results, these findings suggest the possibility of using $\beta-glucan$ egg shell calcium complex as a functional food material related to bone metabolism, even though there is no significant difference between the groups of $\beta-glucan$ and $\beta-glucan-egg$ shell calcium complex supplementation.

• Natural Product Sciences
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• v.2 no.1
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• pp.19-23
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• 1996

A mixture of sterols containing ${\beta}-sitosterol$ and stigmasterol (1), and sterol glycosides containing $3-O-{\beta}-D-glucopyranosyl$ ${\beta}-sitosterol$ and $3-O-{\beta}-D-glucopyranosyl$ stigmasterol (2) were isolated from the leaves of Gynura procumbens. After acetylation of 2 with pyridine-acetic anhydride, $3-0-{\beta}-D-tetra-O-acetylglucopyranosyl$ ${\beta}>-sitosterol$ (3) was isolated.

• Korean Journal of Microbiology
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• v.54 no.2
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• pp.136-139
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• 2018

The inhibitory compound (Compound S) against Ralstonia solanacearum and its conversion product (Compound S') were isolated from the culture filtrate of Bacillus subtilis JW-1 using a series of chromatography procedures. The structures were elucidated as alanyl-L-${\beta}$-(2,3-epoxycyclohexyl-4-one)alanine and alanyl-L-${\beta}$-(2,3-dihydroxycyclohexyl-4-one)alanine, respectively on the basis of nuclear magnetic resonance spectral data, including $^1H$, $^{13}C$, $^1H-^1H$ correlation spectroscopy and heteronuclear multiple bond correlation spectroscopy. The compound S exhibited a broad antimicrobial activity against $G^+$, $G^-$ bacteria, Saccharomyces cerevisiae and Candida albicans. The activity loss of the conversion product revealed that the epoxy function was essential for activity of Compound S.

• Biotechnology and Bioprocess Engineering:BBE
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• v.3 no.2
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• pp.78-81
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• 1998

Cyclodextrin glucanotransferase [CGTase, E.C.2.4.1.19] is an extracellular enzyme, which catalyzes he formation of ${\alpha}$-, ${\beta}$-, ${\gamma}$- CDs from starch. Their proportions of formations depend on enzyme sources and reaction conditions. To understand what determines the product specificity of CGTases, we examined the alteration of product specificity of CGTase from Bacillus macerans by organic solvent sand pH. At acidic pH range less than pH 6 where the enzyme was unstable, the ratio of ${\alpha}$-/ ${\beta}$-CD production was increased 4 times more than that at neutral pH range. As we increased the concentration of 2-butanol, ${\alpha}$-/ ${\beta}$-CD ratio was proportionally increased but / ratio remained constant. The ${\alpha}$-/ ${\beta}$-CD ratio of products was increased in the reaction media which yielded low products.

• Bulletin of the Korean Chemical Society
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• v.35 no.11
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• pp.3224-3226
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• 2014

A new androstane derivative, $4{\beta}$-methyl-15-oxa-$14{\beta}$-androstane-7-ene-$4{\alpha}$-carboxylic acid (1) and a known one $4{\beta}$-methyl-15-oxa-$14{\beta}$-androstane-7-ene-$4{\alpha}$-hydroxyl (2) were isolated from the EtOAc extract of the cultures of the fungus Marasmiellus ramealis (Bull.) Singer. Their structures were elucidated on the basis of 1D and 2D NMR as well as MS spectroscopic data analysis. The inhibitory activity of two isolates against acetylcholinesterase (AChE) revealed that compound 1 exhibited definitely inhibitory activity.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.253-260
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• 2002

For an outer action $\alpha$ of a finite group G on a factor M, it was proved that H is a, normal subgroup of G if and only if there exists a finite group F and an outer action $\beta$ of F on the crossed product algebra M $\times$$_{\alpha}$ G = (M $\times$$_{\alpha}$ F. We generalize this to infinite group actions. For an outer action $\alpha$ of a discrete group, we obtain a Galois correspondence for crossed product algebras related to normal subgroups. When $\alpha$ satisfies a certain condition, we also obtain a Galois correspondence for fixed point algebras. Furthermore, for a minimal action $\alpha$ of a compact group G and a closed normal subgroup H, we prove $M^{G}$ = ( $M^{H}$)$^{{beta}(G/H)}$for a minimal action $\beta$ of G/H on $M^{H}$.f G/H on $M^{H}$.TEX> H/.

• Journal of the Korean Ceramic Society
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• v.29 no.5
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• pp.347-356
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• 1992

Various kaolin samples with different alumina content were prepared from calcined admixture of kaolin and ammonium sulfate by varying the treatment time in sulfuric acid. Samples were nitridated under N2 or N2-H2 atmosphere with changing the amount of added carbon, the reaction time and temperature. As the alumina content lowered, the size of kaolin particles decreased and the specific surface area increased. XRD analysis indicated that ${\alpha}$-quartz remained by decomposition of halloysite and meta-halloysite. Experimental results of nitridation behavior are summerized as follows; 1) Nitridation under N2 atmosphere. With the increase of C/SiO2 ratio and with the decrease of Al2O3 content, disappearance of XRD pattern peaks of mullite, ${\alpha}$-quartz and ${\alpha}$-Al2O3 were accelerated at 1300$^{\circ}C$. SiC was the main phase in the reaction product of acid-treated kaolin samples nitridated at 1300$^{\circ}C$ for 10 hours regardless of C/SiO2 ratio. But the XRD peak intensities of ${\beta}$-Si3N4, ${\beta}$-sialon and SiC did not show much difference when untreated raw kaolin was fired at the same condition. When the ratio of C/SiO2 was 3.5, ${\beta}$-sialon and ${\beta}$-Si3N4 existed in the reaction product of about 22% alumina containing kaolin sample fired at 1350$^{\circ}C$ for 7 hours. Only ${\beta}$-sialon existed in the same sample fired at 1400$^{\circ}C$ for 10 hours. ${\beta}$-sialon was obtained from all of the acid-treated kaolin samples fired at 1400$^{\circ}C$ for 40 hours, but AlN and SiC remained in the untreated kaolin sample. Z value of the ${\beta}$-sialon obtained from the 22% alumina containing kaolin sample fired at 1400$^{\circ}C$ for 40 hours was about 1.3(XRD) and 1.5(EDS). 2) Nitridation under 80N2+2OH2 mixed gas atmosphere with the C/SiO2 ratio of 1 Mullite was not found, but ${\alpha}$-Si3N4, and ${\beta}$-sialon were present in the reaction product of about 22% alumina containing kaolin sample fired at 1300$^{\circ}C$ for 10 hours. When untreated kaolin sample was nitridated at the same condition, mullite remained. AlN and SiC were not found in the reaction product of about 22% alumina containing kaolin sample fired at 1350$^{\circ}C$ for 5 hours. On the other hand, AlN and SiC remained in the product of untreated kaolin fired at the same condition.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.283-290
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• 2024

In this article, a new operation on product fuzzy graphs (PFGs) is provide; namely β-product. We give sufficient conditions for the β-product of two PFGs to be strong and we prove if the β-product of two PFGs is complete, then one of them is strong. We also study the unbiased notion of the class of PFGs and necessary and sufficient conditions for the β-product to be unbiased are given.

• Journal of the Korean Chemical Society
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• v.26 no.2
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• pp.99-106
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• 1982

The ketone chromophore of 1-Acetyl-1-methyl-2-cyclopentene (1) was replaced by nitrile, carboxylic acid and acetamide group, and their photochemical reactions were investigated. While the ${\beta},\;{\gamma}$-unsaturated ketone 1 afforded 1,2 ar 1,3-Acyl shift product, these replaced chromophores did not afford any monomeric rearranged products. 1-Cyano-1-methyl-2-cyclohexene also afforded no product anology of the 1,2-acyl shift reaction. The replacement of the ketone chromophore by nitrile, carboxylic acid and carboxamide has greatly altered the photochemistry of ${\beta},\;{\gamma}$-unsaturated ketones.