• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.325-331
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• 2010

Let a and b be nonnegative integers with 2 $\leq$ a < b, and let G be a Hamiltonian graph of order n with n > $\frac{(a+b-5)(a+b-3)}{b-2}$. An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F contains a Hamiltonian cycle. In this paper, it is proved that G has a Hamiltonian [a, b]-factor if $\delta(G)\;\geq\;\frac{(a-1)n+a+b-3)}{a+b-3}$ and $\delta(G)$ > $\frac{(a-2)n+2{\alpha}(G)-1)}{a+b-4}$.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.87-104
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• 2008

In this paper we investigate several properties and characteristics of the generalized Fibonacci sequence $\{g_n\}$={a, b, a+b, a+2b, 2a+3b, 3a+5b,...}. This concept is a generalization of the famous Fibonacci sequence. In particular we find the identities of sums and the nth term $g_n$ in detail. Also we find the generalizations of the Catalan's identity and A. Tagiuri's identity about the Fibonacci sequence, and investigate the relation between $g_n$ and Pascal's triangle, and how fast $g_n$ increases. Furthermore, we show that $g_n$ and $g_{n+1}$ are relatively prime if a b are relatively prime, and that the sequence $\{\frac{g_{n+1}}{g_n}\}$ of the ratios of consecutive terms converges to the golden ratio $\frac{1+\sqrt5}2$.

• Journal of Nutrition and Health
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• v.45 no.1
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• pp.94-102
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• 2012

There is a limitation to estimate vitamin $B_{12}$ intake due to a lack of data on vitamin $B_{12}$ content in many Korean foods. In this study, vitamin $B_{12}$ content was determined in some seaweeds, fish, and shellfish and their product that are consumed in Korea using a modified microbioassay with Lactobacillus delbruecki ATCC 7830. Dried laver and dried seasoned and toasted laver contained very high levels of vitamin $B_{12}$ (66.8 and $55.2-71.3\;{\mu}g$/100 g, respectively. Sea lettuce and seaweed fulvescene also contained high vitamin $B_{12}$ content of 5.47-9.41 and $6.46-7.20\;{\mu}g$/100 g, respectively, whereas sea mustard and sea tangle contained low levels of vitamin $B_{12}$; vitamin $B_{12}$ was not detected in seaweed fusifome. Pacific saury, trout, sea-bass, or squid contained 12.01, 2.00, 0.49 and $2.33\;{\mu}g$ vitamin $B_{12}$/100 g, respectively. Ochellatus octopus, and naked sand lance contained 0.72-1.43 and $3.68\;{\mu}g$ vitamin $B_{12}$/100 g, respectively. Dried Alaska pollack con-tained $0.19-2.64\;{\mu}g$ vitamin $B_{12}$/100 g. Shellfish such as little neck clam and small ark shellfish contained high levels of vitamin $B_{12}$ of $30.5-40.5\;{\mu}g$/100 g, and mussel and abalone contained 17.71 and $7.82\;{\mu}g$/100 g, respectively. Of unique Korean traditional fermented seafood products, salt-fermented products of squid ($2.91\;{\mu}g$/100 g), clams ($34.31\;{\mu}g$/100 g), Ala-ska pollack roe ($9.98-12.02\;{\mu}g$/100 g), hairtail guts ($4.58\;{\mu}g$/100 g) or small shrimp ($0.58-1.55\;{\mu}g$/100 g), and fish sauce from anchovies ($1.52-1.78\;{\mu}g$/100 mL), sand eel ($0.22-0.24\;{\mu}g$/100 mL) or small shrimp ($0.19-0.78\;{\mu}g$/100 mL) were analyzed. A few commercial brands of flying fish roe ($0.73-1.73\;{\mu}g$/100 g), canned tuna ($0.40\;{\mu}g$/100 g), and fried fish paste ($0.25-0.69\;{\mu}g$/100 g) were also analyzed. In conclusion, vitamin $B_{12}$ content in these foods, chosen considering the Korean food culture, should contribute to improve the present vitamin $B_{12}$ food database. It may be helpful to estimate vitamin $B_{12}$ intake more correctly than before, and provide additional information for dietary education related to vitamin $B_{12}$ and meal management.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.757-774
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• 2022

Let a and b be positive even integers. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), d_H(v) is even and a ≤ dH(v) ≤ b. Let κ(G) be the minimum size of a vertex set S such that G - S is disconnected or one vertex, and let σ₂(G) = min_uv∉E(G) (d(u)+d(v)). In 2005, Matsuda proved an Ore-type condition for an n-vertex graph satisfying certain properties to guarantee the existence of an even [2, b]-factor. In this paper, we prove that for an even positive integer b with b ≥ 6, if G is an n-vertex graph such that n ≥ b + 5, κ(G) ≥ 4, and σ₂(G) ≥ ${\frac{8n}{b+4}}$, then G contains an even [4, b]-factor; each condition on n, κ(G), and σ₂(G) is sharp.

• Korean Journal of Microbiology
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• v.49 no.2
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• pp.191-194
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• 2013

The fresh fruit bodies of Pleurotus eryngii var. ferulae was irradiated with ultraviolet (UV)-B (280-320 nm) in order to increase vitamin $D_2$ contents, which was assayed using HPLC (Waters 1525, USA). The vitamin $D_2$ contents were $3.5{\mu}g/g$ after 3 min UV-B irradiation ($21.6KJ/m^2$) and $6.02{\mu}g/g$ after 5 min UV-B irradiation ($36KJ/m^2$), respectively, which showed the significant increase considering the vitamin $D_2$ content ($0.01{\mu}g/g$) before UV-B irradiation. This increasing effect was confirmed also for other edible mushrooms; Pleurotus eryngii, from $0.09{\mu}g/g$ to $2.75{\mu}g/g$ (3 min) and $5.21{\mu}g/g$ (5 min); Lentinus edodes, from $0.021{\mu}g/g$ to $3.02{\mu}g/g$ (3 min) and $3.78{\mu}g/g$ (5 min); Pleurotus ostreatus, from $0.19{\mu}g/g$ to $9.63{\mu}g/g$ (3 min) and $11.6{\mu}g/g$ (5 min). Although the original content of vitamin $D_2$ was the highest in P. ostreatus, the extent of increase by UV irradiation was remarkably high in P. eryngii var. ferulae.

• KSBB Journal
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• v.19 no.4
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• pp.331-334
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• 2004

In vivo characterization of FadB homologous enzymes including PaaG, YdbU and YgfG for medium-chain-length (MCL) polyhydroxyalkanoate (PHA) biosynthesis was carried out in fadB mutant Escherichia coli. Previously, it was reported that amplification of FadB homologous enzymes such as PaaG and YdbU in fadB mutant E. coli resulted in enhanced biosynthesis of MCL-PHA by greater than two fold compared with control strain. In this study, we constructed paaG fadB double mutant E. coli WB114 and ydbU fadB double mutant E. coli WB115 to investigate the roles of PaaG and YdbU in biosynthesis of MCL-PHA. Inactivation of paaG and ydbU genes in fadB mutant E. coli harboring Pseudomonas sp. 61-3 phaC2 gene reduced the MCL-PHA production to 0.16 and 0.16 PHA g/L, respectively from 2 g/L of sodium decanoate, which are much lower than 0.43 PHA g/L obtained with fadB mutant E. coli WB101 harboring the phaC2 gene. Also, we identified new FadB homologous enzyme YgfG, and examined its roles by overexpression of ygfG and construction of ygfG fadB double mutant E. coli WB113.

• Proceedings of the Korean Society of Applied Pharmacology
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• 1995.10a
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• pp.107-113
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• 1995

Basement membrane laminin is a multidomain glycoprotein that interacts with itself, heparin and cells. The distal long arm plays major cell and heparin interactive roles. The long arm consists of three subunits (A, B1, B2) joined in a coiled-coil rod attached to a terminal A chain globule (G). The globule is in turn subdivided into five subdomains (Gl-5). In order to analyze the functions of this region, recombinant G domains (rG, rAiG, rG5, rGΔ2980-3028) were expressed in Sf9 insect cells using a baculovirus expression vector. A hybrid molecule (B-rAiG), consisting of recombinant A chain(rAiG) and the authentic B chains (E8-B)was assembled in vitro. The intercalation of rAiG into E8-B chains suppressed a heparin binding activity identified in subdomain Gl-2. By the peptide napping and ligand blotting, the relative affinity of each subeomain to heparin was assigned as Gl> G2= G4> G5> G3, such that G1 bound strongly and G3 not at all. The active heparin binding site of G domain in intact laminin appears to be located in G4 and proximal G5. Cell binding was examined using fibrosarcoma Cells. Cells adhered to E8, B-rAiG, rAiG and rG, did not bind on denatured substrates, poorly bound to the mixture of E8-B and rG. Anti-${\alpha}$6 and anti-${\beta}$1 integrin subunit separately blocked cell adhesion on E8 and B-rAiG, but not on rAiG. Heparin inhibited cell adhesion on rAiG, partially on B-rAiG, and not on E8. In conclusion, 1) There are active and cryptic cell and heparin binding activities in G domain. 2) Triple-helix assembly inactivates cell and heparin binding activities and restores u6131 dependent cell binding activities.

• Journal of the Korean Society of Food Science and Nutrition
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• v.46 no.8
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• pp.944-951
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• 2017

This study aimed to determine and examine the contents of vitamins $B_1$, $B_2$, and $B_3$ using the high-performance liquid chromatography method in traditional holiday foods in Korea. All analyses were under the quality control chart of vitamins $B_1$, $B_2$, and $B_3$. The z-scores for vitamins $B_1$, $B_2$, and $B_3$ were 1.3, 0.0, and 0.6, respectively, in food analysis performance assessment scheme proficiency tests assuring reliability of analytical performance. Vitamin $B_1$, $B_2$, and $B_3$ contents were analyzed in a total of 31 samples. Vitamin $B_1$, $B_2$, and $B_3$ contents ranged from 0.000 to 0.973 mg/100 g, from 0.037 to 0.264 mg/100 g, and from 0.000 to 1.223 mg/100 g in Korean traditional holiday foods, respectively. The highest contents of vitamins $B_1$, $B_2$, and $B_3$ were 0.973 mg/100 g in Yukwon-jeon, 0.264 mg/100 g in Dongtae-jeon, and 1.223 mg/100 g in Yukwon-jeon sample, respectively. However, compared to vitamins $B_2$ and $B_3$, vitamin $B_1$ was not detected, generally. Therefore, these results can be used as basic data for a food composition table and improvement of national health for Koreans.

• Journal of Communications and Networks
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• v.3 no.4
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• pp.361-364
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• 2001

Over an additive abelian group G of order g and for a given positive integer $\lambda$, a generalized Hadamard matrix GH(g, $\lambda$) is defined as a gλ$\times$gλ matrix[h(i, j)], where 1 $\leq i \leqg\lambda and 1 \leqj \leqg\lambda$, such that every element of G appears exactly $\lambd$atimes in the list h($i_1, 1) -h(i_2, 1), h(i_1, 2)-h(i_2, 2), …, h(i_1, g\lambda) -h(i_2, g\lambda), for any i_1\neqi_2$. In this paper, we propose a new method of expanding a GH(g^m, \lambda_1) = B = [B_{ij}] over G^m$ by replacing each of its m-tuple B_{ij} with B_{ij} + GH(g, $\lambda_2) where m = g\lambda_2. We may use g^m/\lambda_1 (not necessarily all distinct) GH(g, \lambda_2$)s for the substitution and the resulting matrix is defined over the group of order g.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.669-676
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• 2013

Let $a$ and $b$ be two even integers with $2{\leq}a<b$, and let k be a nonnegative integer. Let G be a graph of order $n$ with $n{\geq}\frac{(a+b-1)(a+b-2)+bk-2}{b}$. A graph G is called an ($a,b,k$)-critical graph if after deleting any $k$ vertices of G the remaining graph of G has an [$a,b$]-factor. In this paper, it is proved that G is an ($a,b,k$)-critical graph if $${\mid}N_G(X){\mid}&gt;\frac{(a-1)n+{\mid}X{\mid}+bk-2}{a+b-1}$$ for every non-empty independent subset X of V (G), and $${\delta}(G)>\frac{(a-1)n+a+b+bk-3}{a+b-1}$$. Furthermore, it is shown that the result in this paper is best possible in some sense.