• Journal of Life Science
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• v.19 no.7
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• pp.871-877
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• 2009

We investigated the effects of sodium butyrate, a histone deacetylase inhibitor, on the cell cycle progression in human monocytic leukemia U937 cells. Exposure of U937 cells to sodium butyrate resulted in growth inhibition, G1 arrest of the cell cycle and induction of apoptosis in a dose-dependent manner as measured by MTT assay and flow cytometry analysis. The increase in G1 arrest was associated with the down-regulation in cyclin D1, E, A, cyclin-dependent kinase (Cdk) 4 and 6 expression, and up-regulation of Cdk inhibitors such as p21 and p27. Sodium butyrate treatment also inhibited the phosphorylation of retinoblastoma protein (pRB) and p130, however, the levels of transcription factors E2F-1 and E2F-4 were not markedly modulated. Furthermore, the down-regulation of phosphorylation of pRB and p130 by this compound was associated with enhanced binding of pRB and E2F-1, as well as p130 and E2F-4, respectively. Overall, the present results demonstrate a combined mechanism involving the inhibition of pRBjp130 phosphorylation and induction of Cdk inhibitors as targets for sodium butyrate that may explain some of its anti-cancer effects in U937 cells.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.665-668
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• 2012

For a given graph G we consider a set S(G) of all symmetric matrices A = [$a_{ij}$] whose nonzero entries are placed according to the location of the edges of the graph, i.e., for $i{\neq}j$, $a_{ij}{\neq}0$ if and only if vertex $i$ is adjacent to vertex $j$. The minimum rank mr(G) of the graph G is defined to be the smallest rank of a matrix in S(G). In general the computation of mr(G) is complicated, and so is that of the maximum multiplicity MaxMult(G) of an eigenvalue of a matrix in S(G) which is equal to $n$ - mr(G) where n is the number of vertices in G. However, for trees T, there is a recursive formula to compute MaxMult(T). In this note we show that this recursive formula for MaxMult(T) also computes the path cover number $p$(T) of the tree T. This gives an alternative proof of the interesting result, MaxMult(T) = $p$(T).

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1529-1560
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• 2019

We are concerned with the following elliptic equations: $$(-{\Delta})^s_pu+V (x){\mid}u{\mid}^{p-2}u={\lambda}g(x,u){\text{ in }}{\mathbb{R}}^N$$, where $(-{\Delta})_p^s$ is the fractional p-Laplacian operator with 0 < s < 1 < p < $+{\infty}$, sp < N, the potential function $V:{\mathbb{R}}^N{\rightarrow}(0,{\infty})$ is a continuous potential function, and $g:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ satisfies a $Carath{\acute{e}}odory$ condition. We show the existence of at least one weak solution for the problem above without the Ambrosetti and Rabinowitz condition. Moreover, we give a positive interval of the parameter ${\lambda}$ for which the problem admits at least one nontrivial weak solution when the nonlinearity g has the subcritical growth condition.

• Analytical Science and Technology
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• v.15 no.1
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• pp.54-66
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• 2002

In order to study systematic survey of Kumho river pollution, water analysis for 24 items was conducted at 16 sites surrounding the Kumho river system for 3 times from May 2000 to February 2001. Analytical items for the study of water quality are as follows; water temperature, pH, BOD, COD, DO, SS, electrical conductivity, oil & grease, ABS, phenol, T-P, ${PO_4}^{3-}-P$, T-N, $NH_3-N$, ${NO_2}^--N$, ${NO_3}^--N$, Cu, Zn, Cr, Cd, Mn, Fe, Pb and As. The mean values obtained for water temperature, pH, BOD, COD, DO, SS, electrical conductivity, oil & grease, ABS, phenol T-P, T-N, Cu, Zn, Fe and Mn showed $17.84^{\circ}C$, 8.04, $2.54{\mu}g/mL$, $5.64{\mu}g/mL$, $7.07{\mu}g/mL$, $8.75{\mu}g/mL$, $600.4{\mu}S/cm$, $0.19{\mu}g/mL$, $0.015{\mu}g/mL$, $0.29{\mu}g/mL$, $0.21{\mu}g/mL$, $5.22{\mu}g/mL$, $0.005{\mu}g/mL$, $0.007{\mu}g/mL$, $0.044{\mu}g/mL$ and $0.001{\mu}g/mL$ respectively. As, Cd, Cr and Pb are not detected. The mean concentration of phenol, $NH_3-N$ and $NO_2-N$ were found to be increased compared to the prior study for 3 years from January 1997 to December 1999, that of BOD, COD, SS, oil & grease and ABS were found to be decreased and the others are nearly constant. The effect of Kumho river to the Nakdong river pollution are as follows. The mean concentration of BOD changed from $1.07{\mu}g/mL$ to $1.42{\mu}g/mL$ before and after of introducing of Kumho river water respectively. The mean concentration of COD, electrical conductivity, oil & grease, ABS, phenol, T-N and T-P changed from $1.99{\mu}g/mL$, $221{\mu}S/cm$, $0.15{\mu}g/mL$, $0.006{\mu}g/mL$, $0.06{\mu}g/mL$, $2.21{\mu}g/mL$ and $0.08{\mu}g/mL$ to $2.44{\mu}g/mL$, $392{\mu}S/cm$, $0.16{\mu}g/mL$, $0.015{\mu}g/mL$, $0.07{\mu}g/mL$, $2.81{\mu}g/mL$ and $0.19{\mu}g/mL$ respectively.

• KOREAN POULTRY JOURNAL
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• v.5 no.7 s.45
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• pp.43-43
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• 1973

• Journal of Korean Society for Atmospheric Environment
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• v.9 no.3
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• pp.255-256
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• 1993

Recently, Ghim and Son (1993) compared the air quality impacts of two point sources P1 and P3 in Seoul in the first quarter of 1988, whose emission rates were 99.9g/s and 49.4g/s, and whose stack heights were 75m and 21m. They said that higher concentrations from P3 in the nearby area were responsible for shorter stack height of P3. But concentrations were not raised so high only because the stack height was reduced from 75m to 21m. Volume of exit gas from P3 was also much smaller than that from P1.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.85-97
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• 2022

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}\;=\;\{\array{{\frac{p}{2}}&p\text{ is even}\\{\frac{p-1}{2}}\;&p\text{ is odd,}}$$ and M = {±1, ±2, ⋯ ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{S}}_{{\lambda}_1}-\bar{\mathbb{S}}_{{\lambda}^c_1}{\mid}{\leq}1$ where $\bar{\mathbb{S}}_{{\lambda}_1}$ and $\bar{\mathbb{S}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling of graphs which are obtained from path and cycle.

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.237-253
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• 2023

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} & \;\;p\text{ is even} \\ {\frac{p-1}{2}} & \;\;p\text{ is odd,}$$ and M = {±1, ±2, … ± ρ} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling ${\frac{{\lambda}(u)+{\lambda}(v)}{2}}$ if λ(u) + λ(v) is even and ${\frac{{\lambda}(u)+{\lambda}(v)+1}{2}}$ if λ(u) + λ(v) is odd such that ${\mid}{\bar{{\mathbb{S}}}}_{\lambda}{_1}-{\bar{{\mathbb{S}}}}_{{\lambda}^c_1}{\mid}{\leq}1$ where ${\bar{{\mathbb{S}}}}_{\lambda}{_1}$ and ${\bar{{\mathbb{S}}}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of few graphs including the closed helm graph, web graph, jewel graph, sunflower graph, flower graph, tadpole graph, dumbbell graph, umbrella graph, butterfly graph, jelly fish, triangular book graph, quadrilateral book graph.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.55-69
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• 2024

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} && p\;\text{is even} \\ {\frac{p-1}{2}} && p\;\text{is odd,}}$$ and M = {±1, ±2, … ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{s}}_{{\lambda}_1}-\bar{\mathbb{s}}_{{\lambda}^c_1}{\mid}\,{\leq}\,1$ where $\bar{\mathbb{s}}_{{\lambda}_1}$ and $\bar{\mathbb{s}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G with a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of some union of graphs.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.235-250
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• 2023

Let 1 ≤ p, q < ∞ be fixed, and let R = [r_jk] be an infinite scalar matrix such that 1 ≤ r_jk < ∞ and sup_j,k r_jk < ∞. Let 𝓑(𝑙_p, 𝑙_q) be the set of all bounded linear operator from 𝑙_p into 𝑙_q. For a fixed Banach algebra 𝐁 with identity, we define a new vector space S^R_p,q(𝐁) of infinite matrices over 𝐁 and a paranorm G on S^R_p,q(𝐁) as follows: let $$S^R_{p,q}({\mathbf{B}})=\{A:A^{[R]}{\in}{\mathcal{B}}(l_p,l_q)\}$$ and $G(A)={\parallel}A^{[R]}{\parallel}^{\frac{1}{M}}_{p,q}$, where $A^{[R]}=[{\parallel}a_{jk}{\parallel}^{r_{jk}}]$ and M = max{1, sup_j,k r_jk}. The existance of S^R_p,q(𝐁) equipped with the paranorm G(·) including its completeness are studied. We also provide characterizations of β -dual of the paranormed space.