• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.11
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• pp.2103-2108
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• 2017

For n points $p_i$ on the m-dimensional plane $R^m$ and a fixed range r, consider a set $T_i$ containing points the distances from $p_i$ of which are less than or equal to r. In case m=1, $T_i$ is an interval on a line, it is a circle on a plane when m=2. For the vertices corresponding to the sets $T_i$, there is an edge between the vertices if the two sets intersect. Then this graph is called an intersection graph G. For m=1 G is called a proper interval graph and for m=2, it is called an unit disk graph. In this paper, we are concerned in the intersection graph G(r) when r changes. In particular, we consider the problem to find the minimum r such that G(r)is connected. For this problem, we propose an O(n) algorithm for the proper interval graph and an $O(n^2{\log}\;n)$ algorithm for the unit disk graph. For the dynamic environment in which the points on a line are added or deleted, we give an O(log n) algorithm for the problem.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.611-622
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• 2010

A ring R is called left max-coherent provided that every maximal left ideal is finitely presented. $\mathfrak{M}\mathfrak{I}$ (resp. $\mathfrak{M}\mathfrak{F}$) denotes the class of all max-injective left R-modules (resp. all max-flat right R-modules). We prove, in this article, that over a left max-coherent ring every right R-module has an $\mathfrak{M}\mathfrak{F}$-preenvelope, and every left R-module has an $\mathfrak{M}\mathfrak{I}$-cover. Furthermore, it is shown that a ring R is left max-injective if and only if any left R-module has an epic $\mathfrak{M}\mathfrak{I}$-cover if and only if any right R-module has a monic $\mathfrak{M}\mathfrak{F}$-preenvelope. We also give several equivalent characterizations of MI-injectivity and MI-flatness. Finally, $\mathfrak{M}\mathfrak{I}$-dimensions of modules and rings are studied in terms of max-injective modules with the left derived functors of Hom.

• Korean Journal of Microbiology
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• v.47 no.4
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• pp.289-294
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• 2011

We investigated the cold shock sensitivity of DEAD-box RNA helicase gene deleted strains of in Bacillus subtilis CU1065. To understand cold shock effects, cells were cultivated at $37^{\circ}C$ to log phase ($O.D_{600}$=0.5-0.6) and then temperature was shifted to $15^{\circ}C$. Cold shock slow down the growth rate of wild type and deleted strains of DEAD-box RNA helicase gene (ydbR, yfmL, yqfR, deaD). The growth rate of ydbR deleted strain is 5 times severely reduced compared to that of wild type strain (CU1065). But the growth rate of other three (yfmL, yqfR, deaD) deleted strains is nearly equal to the growth rate of wild type. Compared to $37^{\circ}C$, the amount of ydbR and yqfR mRNA transcripts are increased at the growth temperature of $15^{\circ}C$. On the other hands the mRNA transcripts of yfmL and deaD are not changed at both conditions of $37^{\circ}C$ and $15^{\circ}C$. Upon cold shock treatment ydbR mRNA transcript is clearly increased. After treatment of rifampicin (bacteria transcription inhibitor) the amount of ydbR mRNA was measured. Temperature shift from $37^{\circ}C$ to $15^{\circ}C$ and rifampicin treatment showed slowly decay of ydbR mRNA. But at $37^{\circ}C$ and rifampicin treatment ydbR mRNA is rapidly reduced. These results showed that cold shock induction of ydbR mRNA resulted from the stability of ydbR mRNA and not from the transcription induction of ydbR. In relation to these results, we found the cold box element of csp (cold shock protein gene) in 5' untranslated region of ydbR gene. Cold shock induction of ydbR is caused by the stability of ydbR mRNA like the stability of csp mRNA.

• Asian Pacific Journal of Cancer Prevention
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• v.16 no.12
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• pp.4937-4944
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• 2015

MicroRNAs (miRNAs) are emerging as critical regulators in carcinogenesis and tumor progression. Recently, miR-99a has been reported as a tumor suppressor gene in various human cancers, but its functions in the context of anaplastic thyroid cancer (ATC) remain unknown. In this study, we reported that miR-99a was commonly downregulated in ATC tissue specimens and cell lines with important functional consequences. Overexpression of miR-99a not only dramatically reduced ATC cell viability by inducing cell apoptosis and accumulation of cells at G1 phase, but also inhibited tumorigenicity in vivo. We then screened and identified a novel miR-99a target, mammalian target of rapamycin (mTOR), and it was further confirmed by luciferase assay. Up-regulation of miR-99a would markedly reduce the expression of mTOR and its downstream phosphorylated proteins (p-4E-BP1 and p-S6K1). Similar to restoring miR-99a expression, mTOR down-regulation suppressed cell viability and increased cell apoptosis, whereas restoration of mTOR expression significantly reversed the miR-99a antitumor activity and the inhibition of mTOR/p-4E-BP1/p-S6K1 signal pathway profile. In clinical specimens and cell lines, mTOR was commonly overexpressed and its protein levels were statistically inversely correlated with miR-99a expression. Taken together, our results demonstrated for the first time that miR-99a functions as a tumor suppressor and plays an important role in inhibiting the tumorigenesis through targeting the mTOR/p-4E-BP1/p-S6K1 pathway in ATC cells. Given these, miR-99a may serve as a novel prognostic/diagnostic and therapeutic target for treating ATC.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.1-16
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• 2019

Let a, b, P, and Q be real numbers with $PQ{\neq}0$ and $(a,b){\neq}(0,0)$. The Horadam sequence $\{W_n\}$ is defined by $W_0=a$, $W_1=b$ and $W_n=PW_{n-1}+QW_{n-2}$ for $n{\geq}2$. Let the sequence $\{X_n\}$ be defined by $X_n=W_{n+1}+QW_{n-1}$. In this study, we obtain some new identities between the Horadam sequence $\{W_n\}$ and the sequence $\{X_n\}$. By the help of these identities, we show that Diophantine equations such as $$x^2-Pxy-y^2={\pm}(b^2-Pab-a^2)(P^2+4),\\x^2-Pxy+y^2=-(b^2-Pab+a^2)(P^2-4),\\x^2-(P^2+4)y^2={\pm}4(b^2-Pab-a^2),$$ and $$x^2-(P^2-4)y^2=4(b^2-Pab+a^2)$$ have infinitely many integer solutions x and y, where a, b, and P are integers. Lastly, we make an application of the sequences $\{W_n\}$ and $\{X_n\}$ to trigonometric functions and get some new angle addition formulas such as $${\sin}\;r{\theta}\;{\sin}(m+n+r){\theta}={\sin}(m+r){\theta}\;{\sin}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},\\{\cos}\;r{\theta}\;{\cos}(m+n+r){\theta}={\cos}(m+r){\theta}\;{\cos}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},$$ and $${\cos}\;r{\theta}\;{\sin}(m+n){\theta}={\cos}(n+r){\theta}\;{\sin}\;m{\theta}+{\cos}(m-r){\theta}\;{\sin}\;n{\theta}$$.

• Archives of Pharmacal Research
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• v.27 no.7
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• pp.769-775
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• 2004

Hepatic ischemia and reperfusion (l/R) predisposes the liver to secondary stresses such as endotoxemia, possibly via dysregulation of the hepatic microcirculation secondary to an imbalanced regulation of the vascular stress genes. In this study, the effect of hepatic I/R on the hepatic vasoregulatory gene expression in response to endotoxin was determined. Rats were subjected to 90 min of hepatic ischemia and 6 h of reperfusion. Lipopolysaccharide (LPS, 1 mg/kg) was injected intraperitoneally after reperfusion. Plasma and liver samples were obtained 6 h after reperfusion for serum aminotransferase assays and RT-PCR analysis of the mRNA for the genes of interest： endothelin-1 (ET-1), its receptors $ET_A$ and $ET_B$, endothelial nitric oxide synthase (eNOS), inducible nitric oxide synthase (iNOS), heme oxygenase-1 (HO-1), cyciooxygenase-2 (COX-2), and tumor necrosis factor-a (TNF-${\alpha}$). The activities of serum aminotransferases were significantly increased in the I/R group. This increase was markedly potentiated by LPS treatment. The ET-1 mRNA was increased by LPS alone, and this increase was significantly greater in both the I/R alone and I/R ＋ LPS groups compared to the sham. There were no significant differences in ETA receptor mRNA levels among any of the experimental groups. $ET_B$ mRNA was increased by both LPS alone and I/R alone, with no significant difference between the I/R alone and I/R ＋ LPS groups. The eN OS and HO-1 transcripts were increased by I/R alone and further increased by I/R ＋ LPS. The iNOS mRNA levels were increased by I/R alone, but increased significantly more by both LPS alone and I/R ＋ LPS compared to I/R alone. The TNF-${\alpha}$ mRNA levels showed no change with I/R alone, but were increased by both LPS alone and I/R ＋ LPS. The COX-2 expression was increased significantly by I/R alone and significantly more by I/R ＋ LPS. Taken collectively, significantly greater induction of the vasodilator genes over the constriction forces was observed with I/R ＋ LPS. These results may partly explain the increased susceptibility of ischemic livers to injury as a result of endotoxemia.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.207-222
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• 2011

Let R be a commutative ring and let M be a GV -torsionfree R-module. Then M is said to be a $\omega$-module if $Ext_R^1$(R/J, M) = 0 for any J $\in$ GV (R), and the w-envelope of M is defined by $M_{\omega}$ = {x $\in$ E(M) | Jx $\subseteq$ M for some J $\in$ GV (R)}. In this paper, $\omega$-modules over commutative rings are considered, and the theory of $\omega$-operations is developed for arbitrary commutative rings. As applications, we give some characterizations of $\omega$-Noetherian rings and Krull rings.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.445-456
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• 2008

Let M be a right R-module, G an ordered group and ${\sigma}$ a map from G into the group of automorphisms of R. The conditions under which the Malcev-Neumann module M* ((G)) is a PS module and a p.q.Baer module are investigated in this paper. It is shown that: (1) If $M_R$ is a reduced ${\sigma}$-compatible module, then the Malcev-Neumann module M* ((G)) over a PS-module is also a PS-module; (2) If $M_R$ is a faithful ${\sigma}$-compatible module, then the Malcev-Neumann module M* ((G)) is a p.q.Baer module if and only if the right annihilator of any G-indexed family of cyclic submodules of M in R is generated by an idempotent of R.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.263-271
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• 2012

We introduce the concept of fuzzy $r$-minimal ${\beta}$-open set on a fuzzy minimal space and basic some properties. We also introduce the concept of fuzzy $r-M$ ${\beta}$-continuous mapping which is a generalization of fuzzy $r-M$ continuous mapping and fuzzy $r-M$ semicontinuous mapping, and investigate characterization for the continuity.

• East Asian mathematical journal
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• v.28 no.2
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• pp.159-172
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• 2012

In all Mathematics I Textbooks(Kim, S. H., 2010; Kim, H. K., 2010; Yang, S. K., 2010; Woo, M. H., 2010; Woo, J. H., 2010; You, H. C., 2010; Youn, J. H., 2010; Lee, K. S., 2010; Lee, D. W., 2010; Lee, M. K., 2010; Lee, J. Y., 2010; Jung, S. K., 2010; Choi, Y. J., 2010; Huang, S. K., 2010; Huang, S. W., 2010) in high schools in Korea these days, it is written and taught that for a positive real number $a$, $a^{\frac{m}{n}}$ is defined as $a^{\frac{m}{n}}={^n}\sqrt{a^m}$, where $m{\in}\mathbb{Z}$ and $n{\in}\mathbb{N}$ have common prime factors. For that situation, the author shows his opinion that the definition is not well-defined and $a^{\frac{m}{n}}$ must be defined as $a^{\frac{m}{n}}=({^n}\sqrt{a})^m$, whenever $^n\sqrt{a}$ is defined, based on the field axiom of the real number system including rational number system and natural number system. And he shows that the following laws of exponents for reals: $$\{a^{r+s}=a^r{\cdot}a^s\\(a^r)^s=a^{rs}\\(ab)^r=a^rb^r$$ for $a$, $b$>0 and $s{\in}\mathbb{R}$ hold by the completeness axiom of the real number system and the laws of exponents for natural numbers, integers, rational numbers and real numbers are logically equivalent.