• Journal of the Korean Chemical Society
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• v.26 no.5
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• pp.310-319
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• 1982

Cobalt(III) complexes with sexidentate ligands, N,N,N',N'-tetrakis(2-amino-ethyl)-1,2-ethanediamine (ten), -1,3-propanediamine (ttn), -1,4-butanediamine (ttmd), -(R,R)-and -(R,S)-2,4-pentanediamine (tptn) were prepared, and the characterization of d-d absorption band on the variation of chelate ring size and conformation of these complexes were studied by means of electronic spectra. The first d-d absorption bands of $[Co(L)]^{3+}$ complexes are shifted to smaller wave numbers in the order. ttn > (R,R)-tptn > ten > ttmd${\simeq}$(R,S)-tptn for (L). The UV, $^{13}C$ NMR, and Circular Dichroism studies indicate that the R,S-tptn ligand of $[Co(R,S-tptn)]^{3+}$ complex coodinates to cobalt(Ⅲ) ion as a sexidentate with one methyl group in axial position.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.243-257
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• 2016

If we let $L(2K;n):=\sum_{s=0}^{k-1}(^{2k}_{2s+1})\sum_{m=1}^{n-1}{\sigma}_{2k-2s-1,1}(m;2){\sigma}_{2s+1,1}(n-m;2)$ with $${\sigma}_{k,l}(n;2):=\sum\limits_{{d{\mid}n}\atop{d{\equiv}l(mod2)}}d^k$$, then we get the formula of L(2u; p)L(2v; p)L(2w; p).

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.641-644
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• 2005

Let L/F be a Galois quadratic extension such that F contains a primitive n-th root of 1. Let N = L(${\alpha}^{{\frac{1}{n}}$) where ${\alpha}{\in}L{\ast}$. We show that if $N_{L/F}({\alpha})\;{\in}L^n{\cap}F$, and [N : L] = m, then $G(N/ F) {\simeq}D_m$ or generalized quaternion group whether $N_{L/F}({\alpha})\;{\in}\;F^n\;or\;{\notin}F^n$, respectively.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.1-6
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• 2011

We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

• Korean Journal of Plant Resources
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• v.25 no.2
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• pp.176-183
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• 2012

This study was carried out to develop ferns as the natural antioxidant materials by graduating and extracting fronds of $Dryopteris$ $crassirhizoma$, $Dryopteris$ $nipponensis$, and $Polystichum$ $lepidocaulon$, which belong to Dryopteridaceae, using solvent, and analyzing the antioxidant effect of each fraction. The n-butanol fraction of $D.$ $crassirhizoma$ (550.0 $mg{\cdot}g^{-1}$), the ethyl acetate fraction of $D.$ $nipponensis$ (374.8 $mg{\cdot}g^{-1}$), and the n-butanol fraction of $P.$ $lepidocaulon$ (781.8 $mg{\cdot}g^{-1}$) showed relatively higher total contents of polyphenol. The chloroform fraction of $D.$ $crassirhizoma$ (72.9 $mg{\cdot}g^{-1}$), and the n-hexane fraction of $D.$ $nipponensis$ (72.9 $mg{\cdot}g^{-1}$) and $P.$ $lepidocaulon$ (154.5 $mg{\cdot}g^{-1}$) contained relatively higher total contents of flavonoids. DPPH radical scavenging activity was most excellent in the n-butanol fraction of $D.$ $crassirhizoma$ ($RC_{50}=0.02mg{\cdot}mL^{-1}$) and $P.$ $lepidocaulon$ ($RC_{50}=0.04mg{\cdot}mL^{-1}$), and the water fractions of $D.$ $nipponensis$ ($RC_{50}=0.01mg{\cdot}mL^{-1}$). ABTS radical scavenging activity was potent in the n-hexane and n-butanol fractions of $D.$ $crassirhizoma$ (each $RC_{50}=0.02mg{\cdot}mL^{-1}$), the ethyl acetate fraction of $D.$ $nipponensis$ ($RC_{50}=0.03mg{\cdot}mL^{-1}$), and the n-butanol fraction of $P.$ $lepidocaulon$ ($RC_{50}=0.06mg{\cdot}mL^{-1}$). There was the large amount of total polyphenol content in the n-butanol fraction of $D.$ $crassirhizoma$ and $P.$ $lepidocaulon$, and their radical scavenging activities were potent. Therefore, it was thought that biologically active substances of each fraction layer are required to be analyzed and used.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.959-970
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• 2017

In this paper, we investigate the transcendental meromorphic solutions with finite order of two different types of difference equations $${\sum\limits_{j=1}^{n}}a_jf(z+c_j)={\frac{P(z,f)}{Q(z,f)}}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ and $${\prod\limits_{j=1}^{n}}f(z+c_j)={\frac{P(z,f)}{Q(z,f)}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ that share three distinct values with another meromorphic function. Here $a_j$, $b_k$, $d_l$ are small functions of f and $a_j{\not{\equiv}}(j=1,2,{\ldots},n)$, $b_p{\not{\equiv}}0$, $d_q{\not{\equiv}}0$. $c_j{\neq}0$ are pairwise distinct constants. p, q, n are non-negative integers. P(z, f) and Q(z, f) are two mutually prime polynomials in f.

• Journal of Korean Society of Environmental Engineers
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• v.34 no.5
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• pp.326-334
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• 2012

To determine the concentrations and the mass flow of selected 10 perfluorinated compounds (PFCs), a field study was conducted in a wastewater treatment plant. Raw influent, primary influent, primary effluent, aeration tank effluent, secondary effluent, final effluent, dehydration liquor, primary sludge, thickened sludge, final sludge were collected over 3 days in the summer and the winter respectively. Collected samples were equally mixed and then served as an analytical sample. Total 10 compounds were analyzed. In terms of treated water, the concentration of perfluorooctanesulfonate (PFOS) and perfluorooctanoate (PFOA) were in range of N.D.~26.29 ng/L and N.D.~38.15 ng/L respectively. Perfluorononanoate (PFNA) and perfluorohexanesulfonate (PFHxS) were ranged from N.D. to 36.79 ng/L and from N.D. to 24.36 ng/L. In terms of sludges, a concentration of PFOS, PFOA, and perfluorodecanesulfonate (PFDS) were detected from 6.82 to 59.37 ng/g, from 0.13 to 0.37 ng/g, from N.D. to 0.83 ng/g respectively. Mass loading for PFCs increased during wastewater treatment except for PFNA. The observed increase in mass flow of PFCs may have resulted from biodegradation of precursor compounds.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.269-278
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• 2008

Let ${\partial}D$ be the boundary of the open unit disk D in the complex plane and $L^p({\partial}D)$ the class of all complex, Lebesgue measurable function f for which $\{\frac{1}{2\pi}{\int}_{-\pi}^{\pi}{\mid}f(\theta){\mid}^pd\theta\}^{1/p}<{\infty}$. Let P be the orthogonal projection from $L^p({\partial}D)$ onto ${\cap}_{n<0}$ ker $a_n$. For $f{\in}L^1({\partial}D)$, ${\hat{f}}(z)=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}P_r(t-\theta)f(\theta)d{\theta}$ is the harmonic extension of f. Let ${\hat{P}}$ be the composition of P with the harmonic extension. In this paper, we will show that if $1, then ${\hat{P}}:L^p({\partial}D){\rightarrow}H^p(D)$ is bounded. In particular, we will show that ${\hat{P}}$ is unbounded on $L^{\infty}({\partial}D)$.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.813-830
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• 2022

The generating functions of the divisor function σ_s(n) = Σ_0<d|n d^s are quasimodular forms. In this paper, we find the basis of the space of quasimodular forms of weight 6 on Γ₀(10) consisting of Eisenstein series and η-quotients. Then we evaluate the convolution sum Σ_ak+bl+cm=n σ(k)σ(l)σ(m) with lcm(a, b, c) = 10 and Σ_al+bm=n lσ(l)σ(m) and Σ_al+bm=n σ₃(l)σ(m) with lcm(a, b) = 10.

• Journal of Chest Surgery
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• v.37 no.9
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• pp.781-786
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• 2004

None of the currently available strategies for diagnosis and management of the pleural effusion are ideal. We tried to evaluate the validity of VEGF in differential diagnosis of the pleural effusion and find out if VEGF were correlated with the established markers. Material and Method: 35 patients with pleural effusion were divided into malignant effusion (n=10), benign effusion (n=5), infectious effusion (n=10), and pneumothorax (n=10), respectively. The pleural fluids from each group were examined for differential cell count, chemistry (glucose, protein, LDH, and ADA), and VEGF. Result: Glucose level was lower in infectious effusion compared with benign effusion (60.5$\pm$36.09 mg/dL vs. 162.0$\pm$19.80 mg/dL, p=0.011). ADA level in infectious effusion was higher compared with malignant effusion (87.9$\pm$42.62 IU/L vs. 27.7$\pm$31.04 IU/L, p=0.024). Malignant effusion (p=0.026) and infectious effusion (p=0.048) showed significantly higher level of VEGF than that of pneumothorax. VEGF level was substantially higher in malignant effusion compared with benign effusion (364.38$\pm$433.83 pg/dL vs. 53.3$\pm$22.20 pg/dL, p=NS). The pleural VEGF level did not correlate with the other markers. Conclusion: The measuring pleural VEGF may be helpful in diagnosing malignant and infectious pleural effusion that increase angiogenesis and vascular permeability, but it can not discriminate between the two. The pleural VEGF may not be correlated with the established markers. The measurement of pleural VEGF might discriminate between malignant and benign effusion.