• 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.

• Clean Technology
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• v.18 no.4
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• pp.404-409
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• 2012

In this study, the effects of mixing intensity and coagulant dosages on the characteristics of floc growth for phosphorus removal were investigated. The experiments were conducted under Al/P molar ratio of 1.0, 1.5 and 2.0; rapid mixing intensity with G value of 100, 300, and 500 $s^{-1}$. The characteristics of floc growth were measured by flocculation index (FSI) and the removal efficiencies of phosphorus by using different size filters. The removal efficiencies of soluble phosphorus increased as Al/P molar ratio and rapid mixing intensity increased. However, the highest removal efficiencies of T-P were observed at G value of 300 $s^{-1}$. When Al/P molar ratio was lower than 1.0, the value of FSI at G value of 500 $s^{-1}$ was the largest. However, when Al/P ratio was larger than 1.0, the value of FSI at G value 300 $s^{-1}$ was the largest. Effects of mixing intensity and Al/P molar ratio on coagulation for phosphorus removal of synthetic and real wastewater effluent were observed to be similar.

• Applied Biological Chemistry
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• v.31 no.1
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• pp.33-37
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• 1988

Three species of Pediococci, Pediococcus pentosaceus, Pediococcus acidilactici and Pediococcus halophilus were isolated from Kimchi. P. pentosaceus and P. acidilactici showed inhibitory activity against Streptococcus faecalis, Pseudomonas sp., P20 and Vibrio parahaemolyticus. However, the growth of all test organisms was not inhibited by P. halophilus. Ten strains contained one to seven plasmids, ranging in size from 1 to 60 megadaltons.

• The Korean Journal of Pesticide Science
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• v.5 no.1
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• pp.12-18
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• 2001

The effects of organophosphorus were examined with inhibition of the cholinesterase activity on tile chicken plasma in vivo and in vitro. The cholinesterase activity in chicken plasma determined by tile Ellman mettled was $23{\mu}mol$/min/g protein. After oral administration with 0.2 and 0.5 times of organophosphorus terbufos $LD_{50}$(1.81 mg/kg), cholinesterase activity were inhibited to 36% and 96% of control after 15min in vivo, respectively. After oral administration with 0.2 and 0.5 times of terbufos $LD_{50}$(1.81 mg/kg), then the recovery of cholinesterase activity followed to 99% and 56% of control after 11hr, respectively. Ki of phosphorodithioate and phosphorothioate with P=S was $74{\sim}322\;mole^{-1}min^{-1}$ in vitro. Ki of phosphate and phosphorothiolate with P=O was $13898{\sim}79610\;mole^{-1}min^{-1}$. Toxicology of organophosphorus with P=S was higher than that of organophosphorus with P=S by oxidation. $pI_{50}$ of phosphorodithioate and phosphorothioate with P=S was $21{\sim}102$ mg/L. $pI_{50}$ of phosphate and phosphorothiolate with P=O was $0.519{\sim}0.071$ mg/L. Enzyme-Inhibition method with cholinesterase was the rapid bioassay method to detect the organohpophorus pesticides in vitro.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.743-748
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• 2013

The purpose of this note is to introduce interesting and useful properties differential-basis and p-basis in theorem 3.3. The result gives a existence differential basis of $S^P$ [$[{\Lambda}_1]$](S) which has a p-basis over $S^p$ ($S^p[{\Lambda}_1]$).

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1133-1143
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• 1999

Chaterji strengthened version of a theorem for martin-gales which is a generalization of a theorem of Marcinkiewicz proving that if $X_n$ is a sequence of independent, identically distributed random variables with $E{\mid}X_n{\mid}^p\;<\;{\infty}$, 0 < P < 2 and $EX_1\;=\;1{\leq}\;p\;<\;2$ then $n^{-1/p}{\sum^n}_{i=1}X_i\;\rightarrow\;0$ a,s, and in $L^p$. In this paper, we probe a version of law of large numbers for double arrays. If ${X_{ij}}$ is a double sequence of random variables with $E{\mid}X_{11}\mid^log^+\mid X_{11}\mid^p\;<\infty$, 0 < P <2, then $lim_{m{\vee}n{\rightarrow}\infty}\frac{{\sum^m}_{i=1}{\sum^n}_{j=1}(X_{ij-a_{ij}}}{(mn)^\frac{1}{p}}\;=0$ a.s. and in $L^p$, where $a_{ij}$ = 0 if 0 < p < 1, and $a_{ij}\;=\;E[X_{ij}\midF_[ij}]$ if $1{\leq}p{\leq}2$, which is a generalization of Etemadi's marcinkiewicz-type SLLN for double arrays. this also generalize earlier results of Smythe, and Gut for double arrays of i.i.d. r.v's.

• Korean Journal of Microbiology
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• v.51 no.4
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• pp.319-328
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• 2015

The $sdu1^+$ gene encodes Sdu1, a PPPDE superfamily member of deubiquitinating enzymes (DUBs) in Schizosaccharomyces pombe. Sdu1 was previously shown to contain an actual ubiquitin C-terminal hydrolase (UCH) activity using the recombinant plasmid pYSTP which harbors the $sdu1^+$ gene. This work was designed to assess a thermotolerant role of Sdu1 against high incubation temperatures. In the temperature-shift experiments, the S. pombe cells harboring pYSTP grew much better after the shifts to $37^{\circ}C$ and $42^{\circ}C$, when compared with the vector control cells. After being shifted to $37^{\circ}C$ and $42^{\circ}C$ for 6 h, the S. pombe cells harboring pYSTP contained lower reactive oxygen species (ROS) levels, compared with the vector control cells. The nitric oxide (NO) levels of the S. pombe cells harboring pYSTP were slightly lower than those of the vector control cells in the absence or presence of the temperature shifting. The total glutathione (GSH) levels of the S. pombe cells harboring pYSTP were significantly higher than those of the vector control cells. Total superoxide dismutase (SOD) and GSH peroxidase activities were also higher in the S. pombe cells harboring pYSTP after the temperature shifts than in the vector control cells. In brief, the S. pombe Sdu1 plays a thermotolerant role against high incubation temperature through the down-regulation of ROS and NO and the up-regulation of total GSH content, total SOD and GSH peroxidase activities.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.9-20
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• 2008

Let ${X_i{\mid}i{\geq}1}$ be a strictly stationary sequence of associated random variables with mean zero and let ${\sigma}^2=EX_1^2+2\sum\limits_{j=2}^\infty{EX_1}{X_j}$ with 0 < ${\sigma}^2$ < ${\infty}$. Set $S_n={\sum\limits^n_{i=1}^\{X_i}$, the precise asymptotics for ${\varepsilon}^{{\frac{2(r-p)}{2-p}}-1}\sum\limits_{n{\geq}1}n^{{\frac{r}{p}}-{\frac{1}{p}}+{\frac{1}{2}}}P({\mid}S_n{\mid}{\geq}{\varepsilon}n^{{\frac{1}{p}}})$,${\varepsilon}^2\sum\limits_{n{\geq}3}{\frac{1}{nlogn}}p({\mid}Sn{\mid}{\geq}{\varepsilon\sqrt{nloglogn}})$ and ${\varepsilon}^{2{\delta}+2}\sum\limits_{n{\geq}1}{\frac{(loglogn)^{\delta}}{nlogn}}p({\mid}S_n{\mid}{\geq}{\varepsilon\sqrt{nloglogn}})$ as ${\varepsilon}{\searrow}0$ are established under the suitable conditions.

• 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.