• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.977-986
• /
• 2015

Let G be a graph on the vertex set $V(G)=\{x_1,{\cdots},x_n\}$ with the edge set E(G), and let $R=K[x_1,{\cdots},x_n]$ be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials $x_i,x_j$ with $\{x_i,x_j\}{\in}E(G)$, and the vertex cover ideal $I_G$ generated by monomials ${\prod}_{x_i{\in}C}{^{x_i}}$ for all minimal vertex covers C of G. A minimal vertex cover of G is a subset $C{\subset}V(G)$ such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers $L_G$ and we explicitly describe the minimal free resolution of the ideal associated to $L_G$ which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice.

• Journal of Microbiology
• /
• v.45 no.4
• /
• pp.318-325
• /
• 2007

Glucose 6-phosphate dehydrogenase (G6PDH, EC 1.1.1.49) in Deinococcus radiophilus, an extraordinarily UV-resistant bacterium, was investigated to gain insight into its resistance as it was shown to be involved in a scavenging system of superoxide $(O_2^{-1})$ and peroxide $(O_2^{-2})$ generated by UV and oxidative stresses. D. radiophilus possesses two G6PDH isoforms: G6PDH-1 and G6PDH-2, both showing dual coenzyme specificity for NAD and NADP. Both enzymes were detected throughout the growth phase; however, the substantial increase in G6PDH-1 observed at stationary phase or as the results of external oxidative stress indicates that this enzyme is inducible under stressful environmental conditions. The G6PDH-1 and G6PDH-2 were purified 122- and 44-fold (using NADP as cofactor), respectively. The purified G6PDH-1 and G6PDH-2 had the specific activity of 2,890 and 1,033 U/mg protein (using NADP as cofactor) and 3,078 and 1,076 U/mg protein (using NAD as cofactor), respectively. The isoforms also evidenced distinct structures; G6PDH-1 was a tetramer of 35 kDa subunits, whereas G6PDH-2 was a dimer of 60kDa subunits. The pIs of G6PDH-1 and G6PDH-2 were 6.4 and 5.7, respectively. Both G6PDH-1 and G6PDH-2 were inhibited by both ATP and oleic acid, but G6PDH-1 was found to be more susceptible to oleic acid than G6PDH-2. The profound inhibition of both enzymes by ${\beta}-naphthoquinone-4-sulfonic$ acid suggests the involvement of lysine at their active sites. $Cu^{2+}$ was a potent inhibitor to G6PDH-2, but a lesser degree to G6PDH-1. Both G6PDH-1 and G6PDH-2 showed an optimum activity at pH 8.0 and $30^{\circ}C$.

• International Journal of Industrial Entomology and Biomaterials
• /
• v.2 no.1
• /
• pp.27-35
• /
• 2001

This study was carried out to investigate the mineral content in the regional, varietal and seasonal mulberry leaves. On average, mulberry leaf samples contained minerals in the order of potassiumi phosphorus, calcium, magnesium, iron and so on (2.494 g/100 g, 2.255 g/100 g, 1.835 g/100 g, 0.627 g/100 g, 0.0245 g/100 g DW, respectively). Calcium content was 19-fold and 4-fold higher than that of green tea and spinach, respectively, suggesting that mulberry loaves appear to be a calcium-rich food source. In the comparison of geographic samples of Cheongilppong variety, calcium bevel was highest in Youngchun sample (2.477 g/100 g) and highest potassium level in Suwon sample (2.962 g/100 g). In the geographic samples of YK209 variety, Jinju-City sample was highest in calcium content (1.509 g/100 g). Among wild mulberry loaves collected from Cheju Island and Tsushima, potassium level was highest in Bongge-dong, Cheiu City (3.865 g/100 g) and calcium level in Mitshshima Town, Tsushima (2.948 g/100 g). In the comparison of varietal samples collected in Suwon at the mulberry field of Dept. of Sericulture & entomology, Shinkwangppong variety was highest in the potassium levels although Keryangppong and Shinkwangppong were higher in calcium revel. In the comparison of seasonal samples of Cheongilppong, there was a rough trend of increase in some minerals up to July (e.g., calcium rind )potassium). Finding of the highest calcium and potassium contents in the wild mulberry (3.865 g/100 g and 2.948 g/100 g, respectively) rather than in the cultivated ones warrant that more focus should be paid to wild mulberry leaves to utilize their minerals effciently.

• Communications of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.455-468
• /
• 2020

An element in a ring R with identity is called invo-clean if it is the sum of an idempotent and an involution and R is called invoclean if every element of R is invo-clean. Let C(R) be the center of a ring R and g(x) be a fixed polynomial in C(R)[x]. We introduce the new notion of g(x)-invo clean. R is called g(x)-invo if every element in R is a sum of an involution and a root of g(x). In this paper, we investigate many properties and examples of g(x)-invo clean rings. Moreover, we characterize invo-clean as g(x)-invo clean rings where g(x) = (x-a)(x-b), a, b ∈ C(R) and b - a ∈ Inv(R). Finally, some classes of g(x)-invo clean rings are discussed.

• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.603-616
• /
• 2008

A generalized n-dimensional Riemannian manifold $X_n$ on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$, satisfying certain conditions, through the $^*g$-ME-connection which is both Einstein's equation and of the form(3.1) is called $^*g$-ME-manifold and we denote it by $^*g-MEX_n$. In this paper, we prove a necessary and sufficient condition for the existence of $^*g$-ME-connection and derive a surveyable tensorial representation of the $^*g$-ME-connection and the $^*g$-ME-vector in $^*g-MEX_n$.

• The Journal of Advanced Prosthodontics
• /
• v.13 no.5
• /
• pp.269-280
• /
• 2021

PURPOSE. The objective of this study was to evaluate the effect of thickness reduction and fatigue on the failure load of monolithic zirconia crowns. MATERIALS AND METHODS. 140 CAD-CAM fabricated crowns (3Y-TZP, inCorisTZI, Dentsply-Sirona) with different ceramic thicknesses (2.0, 1.5, 1.0, 0.8, 0.5 mm, respectively, named G2, G1.5, G1, G0.8, and G0.5) were investigated. Dies of a mandibular first molar were made of composite resin. The zirconia crowns were luted with a resin composite cement (RelyX Unicem 2 Automix, 3M ESPE). Half of the specimens (n = 14 per group) were mouth-motion-fatigued (1.2 million cycles, 1.6 Hz, 200 N/ 5 - 55℃, groups named G2-F, G1.5-F, G1-F, G0.8-F, and G0.5-F). Single-load to failure was performed using a universal testing-machine. Fracture modes were analyzed. Data were statistically analyzed using a Weibull 2-parameter distribution (90% CI) to determine the characteristic strength and Weibull modulus differences among the groups. RESULTS. Three crowns (21%) of G0.8 and five crowns (36%) of G0.5 showed cracks after fatigue. Characteristic strength was the highest for G2, followed by G1.5. Intermediate values were observed for G1 and G1-F, followed by significantly lower values for G0.8, G0.8-F, and G0.5, and the lowest for G0.5-F. Weibull modulus was the lowest for G0.8, intermediate for G0.8-F and G0.5, and significantly higher for the remaining groups. Fatigue only affected G0.5-F. CONCLUSION. Reduced crown thickness lead to reduced characteristic strength, even under failure loads that exceed physiological chewing forces. Fatigue significantly reduced the failure load of 0.5 mm monolithic 3Y-TZP crowns.

• Bulletin of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.45-56
• /
• 1995

D. H. Gottlieb [1, 2] studied the subgroups $G_n(X)$ of homotopy groups $\pi_n(X)$. In [5, 7, 10], the authors introduced subgroups $G_n(X, A)$ and $G_n^{Rel}(X, A) of \pi_n(X)$ and $\pi_n(X, A)$ respectively and showed that they fit together into a sequence $$ \cdots \to G_n(A) \longrightarrow^{i_*} G_n(X, A) \longrightarrow^{j_*} G_n^{Rel}(X, A) \longrightarrow^\partial $$ $$ \cdots \to G_1^{Rel}(X, A) \to G_0(A) \ to G_0(X, A) $$ where $i_*, j_*$ and \partial$ are restrictions of the usual homomorphisms of the homotopy sequence $$ \cdot \to^\partial \pi_n(A) \longrightarrow^{i_*} \pi_n(X) \longrightarrow^{j_*} \pi_n(X, A) \to \cdot \to \pi_0(A) \to \pi_0(X) $$.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.479-486
• /
• 2016

The norm N(G) of a group G is the intersection of the normalizers of all the subgroups of G. In this paper, the structure of finite groups with a cyclic norm quotient is determined. As an application of the result, an interesting characteristic of cyclic groups is given, which asserts that a finite group G is cyclic if and only if Aut(G)/P(G) is cyclic, where P(G) is the power automorphism group of G.

• Korean Journal of Mathematics
• /
• v.14 no.2
• /
• pp.241-248
• /
• 2006

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, and characterize the G-fuzzy congruence generated by a left and right compatible fuzzy relation on a semigroup.

• Pediatric Gastroenterology, Hepatology & Nutrition
• /
• v.23 no.1
• /
• pp.26-34
• /
• 2020

Purpose: To compare the clinical features, diagnostic findings, and medications of children with infrequent bowel movements or fecal soiling. Methods: This study enrolled 333 children (189 male; age range, 1 month to 18 years) diagnosed with functional constipation by Rome III or IV criteria. We classified them into 3 groups (infrequent bowel movement without fecal soiling [G3-a], infrequent bowel movement with fecal soiling [G3-b], and fecal soiling only [G3-c]) and into 2 subgroups of fecal soiling (G2-b) or not (G2-a). Retrospective data on clinical characteristics, colon transit time (CTT) test results, and medications were collected. The Wilcoxon rank-sum test, Kruskal-Wallis test, Chi-square test, and Fisher's exact test were used for the statistical analysis. Results: The median age (months) and interquartile range (IQR) was 33 (45) in G3-a, 54 (40) in G3-b, and 73 (48) in G3-c (p<0.0001). G3-c had the latest onset (median, 18; IQR, 18; p=0.0219) and longest symptom duration (24 [24], p=0.0148). PEG 4000 was used in 60.6% (G3-a), 96.8% (G3-b), and 83.2% (G3-c) of patients (p<0.0001). The median age (months) and IQR were 33.0 (45.0) in G2-a and 63.5 (52.5) in G2-b (p<0.0001). G2-b had later onset (median, 12; IQR, 19.5; p=0.0062) and longer symptom duration than G2-a (24 [12], p=0.0070). PEG 4000 was used in 60.6% (G2-a) and 88.3% (G2-b) of children (p<0.0001). No statistically significant intergroup differences were seen in maintenance laxative dose, CTT, or CTT type. Conclusion: Infrequent bowel movement and fecal soiling represent the advanced stage of chronic functional constipation.