• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.977-986
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• 2010

Let $X_1$, $X_2$, $\cdots$ be identically distributed negatively associated random variables with $EX_1\;=\;0$ and $E|X_1|^3$ < $\infty$. In this paper we prove $lim_{{\epsilon\downarrow}0}\;\frac{1}{-\log\;\epsilon}\sum\limits_{n=1}^\infty\frac{1}{n^2}ES_n^2I\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;2$ and $lim_{\epsilon\downarrow0}\;\epsilon^{2-p}\sum\limits_{n=1}^\infty\frac{1}{n^p}$ $E|S_n|^pI\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;\frac{2}{2-p}$ for 0 < p < 2, where $S_n\;=\;\sum\limits_{i=1}^{n}X_i$ and 0 < $\sigma^2\;=\;EX_1^2\;+\;\sum\limits_{i=2}^{\infty}Cov(X_1,\;X_i)$ < $\infty$. We consider some results of i.i.d. random variables obtained by Liu and Lin(2006) under negative association assumption.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.751-763
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• 2015

Let ${\alpha}$ be a positive integer, and let $p_1$, $p_2$ be two distinct prime numbers with $p_1$ < $p_2$. By using elementary methods, we give two equivalent conditions of all even near-perfect numbers in the form $2^{\alpha}p_1p_2$ and $2^{\alpha}p_1^2p_2$, and obtain a lot of new near-perfect numbers which involve some special kinds of prime number pairs. One kind is exactly the new Mersenne conjecture's prime number pair. Another kind has the form $p_1=2^{{\alpha}+1}-1$ and $p_2={\frac{p^2_1+p_1+1}{3}}$, where the former is a Mersenne prime and the latter's behavior is very much like a Fermat number.

• Journal of the Korean Chemical Society
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• v.54 no.3
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• pp.287-290
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• 2010

In the present work we described oxidative cyclisation of peracetylated lactosyl carbamides with N-phenyl-S-chloro isothiocarbamoyl chloride and structural elucidation of novel peracetylated N-Lactosyl-1,2,4-Thiadiazolidin-3-one hydrochlorides. Antimicrobial activities of the title compounds were determined against bacteria S. aureus, E. coli, P. Vulgaris, P. Aeruginosa and fungi A. Niger, Penicillium.

• Honam Mathematical Journal
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• v.26 no.3
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• pp.281-286
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• 2004

We calculate the harmonic series $E_{2p}:=^P\;_{^{\infty}_{n=1}}{\frac{1}{n^{2p}}$ via Waring's formula.

• 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.

• The Pure and Applied Mathematics
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• v.25 no.1
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• pp.31-38
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• 2018

In [4], the authors show that if ${\mathbb{X}}$ is a ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type ($d_1$, ${\ldots}$, $d_s$) with $d_s$ > $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(md_s-1)$ is the number of lines containing exactly $d_s-points$ of ${\mathbb{X}}$ for $m{\geq}2$. They also show that if ${\mathbb{X}}$ is a ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type (1, 2, ${\ldots}$, s) with $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(m{\mathbb{X}}-1)$ is the number of lines containing exactly s-points in ${\mathbb{X}}$ for $m{\geq}s+1$. In this paper, we explore a standard ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ and find that if ${\mathbb{X}}$ is a standard ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type (1, 2, ${\ldots}$, s) with $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(m{\mathbb{X}}-1)=3$, which is the number of lines containing exactly s-points in ${\mathbb{X}}$ for $m{\geq}2$ instead of $m{\geq}s+1$.

• Journal of the Korean Chemical Society
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• v.47 no.1
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• pp.26-30
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• 2003

The dinuclear $Ag_2[Phen]_2[S_2P(OPr)_2]_2$(phen=1,10-phenanthroline; Pr=propyl), was prepared by the reaction of bis(dipropyldithiophosphato) silver(I) complex with 1,10-phenanthroline ligand, and its structure was determined by X-ray crystallography. The two dipropyldithiophosphato ligands each bridge two silver atoms to form an eight-membered $Ag_2S_4P_2$ ring, while the 1,10-phenanthroline molecule coordinates to a silver atom to complete the local tetrahedral geometry for the metal ion. The Ag-S bond distances are 2.559(1) and 2.567(1)${\AA}$, and the Ag-N bond distances are 2.366(3) and 2.471(3)${\AA}$.

• Journal of the Korean Chemical Society
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• v.45 no.3
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• pp.242-246
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• 2001

The quaternary thiophosphates, $A_2NiP_2S_6$ (A=Rb, Cs), have been synthesized with halide fluxes and structurally characterized by single-crystal X-ray diffraction technique. These compounds crystallize in the space group $C_{2h}^5-P2_1/n$ of the monoclinic system with two formula units in a cell of dimensions a=5.960(2), b=12.323(4), $c=7.491(3)\AA$, $\beta=97.05(3)^{\circ}$, and $V=546.0(3)\AA^3$ for Rb2NiP2S6 and a=5.957(4), b=12.696(7), $c=7.679(4)\AA$, $b=93.60(5)^{\circ}$, and $V=579.7(5)\AA^3$ for $Cs_2NiP_2S_6.$ These compounds are isostructural. The structure of $Cs_2NiP_2S_6$ is made up of one-dimensional $_\infty^1[NiP_2S_6^{2-}]$ chains along the a axis and these chains are isolated by $Cs^+$ ions. The Ni atom is octahedrally coordinated by six S atoms. These Ni$S_6$ octahedral units are linked by sharing three m-S atoms of the $[P_2S_6^{4-}]$ anions to form the infinite one-dimensional $_\infty^1[NiP_2S_6^{2-}]$ chain. For $Cs_2NiP_2S_6$, the magnetic susceptibility reveals an antiferromagnetic exchange interaction below 8K,which corresponds to the Neel temperature ($T_N$). Above $T_N$, this compound obeys Curie-Weiss law. The magnetic moment, C, and ${\theta}forCs_2NiP_2S_6$ are 2.77 B.M., 0.9593 K, and -19.02 K, respectively. The effective magnetic moment obtained from the magnetic data is agreed with the spin-only value of $Ni^{2+}d^8$(2.83 B.M.) system.

• YAKHAK HOEJI
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• v.38 no.2
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• pp.140-148
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• 1994

${\beta}-Lactamase$ stability, chemotherapeutic activity, and pharmacokinetics of 7-[(Z)-2-(2-aminothiazole-4-yl)-2-methoxyiminoacetamido]-3-[4-(2-pyridyl)piperazinyl]thiocarbonylthiomethyl-3-cephem-4-carboxylic acid(CEN1), 7-[(Z)-2-(2-aminothiazole-4-yl)-2-methoxyiminoacetamido]-3-[4-(2-pyrimidyl)piperazinyl]thiocarbonylthiomethyl-3-cephem-4-carboxylic acid(CEN2), pivaloyloxymethyl-7-[(Z)-2-(2-aminothizaole-4-yl)-2-methoxyiminoacetamido]-3-[4-(2-pyridyl)piperazinyl]thiocarbonyl-thiomethyl-3-cephem-4-carboxylate(CEN1P), and pivaloyloxymethyl-7-{(Z)--2-(2-aminothizaole-4-yl)-2-methoxyiminoacetamido]-3-[4-(2-pyridyl)piperazinyl]thiocarbonyl-thiomethyl-3-cephem-4-carboxylate(CEN2P) were examined. CEN1, CEN2, CEN1P, and CEN2P were very stable to the ${\beta}-lactamase$ obtained from three strains(Enterobacter cloacae P99, Escherichia coli TEM, and Citrobacter freundii). Chemotherapeutic activities$(ED_{50})$ of CEN2 and CEN2P against experimental systemic infections due to Streptococcus pyogenes 77A and Escherichia coli 078 were superior to those of CEN1 and CEN1P, respectively. The $ED_{50}$ values of CEN1, CEN2 were 5.82 mg/kg, 0.89 mg/kg(s.c., S. pyogenes 77A) while those of CEN1P, CEN2P were 14.56mg/kg, 6.40mg/kg(p.o., S. pyogenes 77A), respectively. The pharmacokinetics of CEN1, CEN2, CEN1P, and CEN2P were investigated in mice and rats. In mice, peak blood levels of $1.25\;{\mu}g/ml$ were recorded within 20 min after oral administration of a single dose equivalent to 40 mg/kg CEN1P. Cmax of CEN1P was much higher than that of CEN1 in mice and rats. Oral absorption of CEN2P was much higher than that of CEN2.

• Reproductive and Developmental Biology
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• v.36 no.3
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• pp.173-181
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• 2012

Sphingosine-1-phosphate (S1P) has a many function involved proliferation, differentiation and survival of many cells. In this study, to investigate whether S1P improve the developmental competence of porcine embryos, 50 nM of S1P were supplemented during in vitro maturation (with EGF or without EGF) medium and/or in vitro culture (IVC) medium. Addition of S1P was significantly increased the rate of oocytes reaching metaphase II (MII) compared to the control (83.5 vs. 64.1%) in without EGF medium, but not with EGF medium (89.5 vs. 84.6%). When treated with $1{\mu}M$ of N1N-dimethylsphingosine (DMS), a sphingosine kinase inhibitor which is blocked endogenous generation of S1P, the meiotic progression rates to MII stage (without EGF: 45.2 and with EGF: 66.7%) were significantly decreased and degeneration rates (without EGF: 51.2 and with EGF: 30.1%) were increased in both medium compared to control group during IVM periods. Also, the rates of blastocyst formation was significantly increased in the S1P treated group compared to control group (29.0 vs. 19.2%) of EGF supplemented medium, whereas there were no effect in the EGF free medium (9.0 vs. 10.5%). After 12 h IVM, the phosphorylation of ERK1 and ERK2, which is major signaling pathway of MAP kinase, were increased in the S1P group than that of control or DMS group. When supplemented of S1P during IVC, the rates of blastocyst formation and total cell number (30.2% and 40.6) were significantly increased in S1P-treated group compared with control (20.1% and 32.5), DMS (12.3% and 25.1), and S1P plus DMS group (24.7% and 33.6). The percentage of apoptosis nuclei in the S1P group was significantly decreased than other groups. Also, the rates of blastocyst formation (26.7 vs. 14%) and total cell number (42.8 vs. 32.5) were significantly increased in the S1P group than those of control group when S1P added during the entire IVM and IVC periods. Taken together, our results indicate that S1P supplementation in IVM and/or IVC medium affects beneficial effect of meiotic maturation and subsequent developmental competence of porcine embryos.