• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.255-260
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• 2006

Let $m$ and $k$ be any positive integers, let $\mathbb{Z}_k$ the ring of integers of modulo $k$, let $G_m(\mathbb{Z}_k)$ the group of all $m$ by $m$ nonsingular matrices over $\mathbb{Z}_k$ and let ${\phi}_m(k)$ the order of $G_m(\mathbb{Z}_k)$. In this paper, ${\phi}_m(k)$ can be computed by the following investigation: First, for any relatively prime positive integers $s$ and $t$, $G_m(\mathbb{Z}_{st})$ is isomorphic to $G_m(\mathbb{Z}_s){\times}G_m(\mathbb{Z}_t)$. Secondly, for any positive integer $n$ and any prime $p$, ${\phi}_m(p^n)=p^{m^2}{\cdot}{\phi}_m(p^{n-1})=p{^{2m}}^2{\cdot}{\phi}_m(p^{n-2})={\cdots}=p^{{(n-1)m}^2}{\cdot}{\phi}_m(p)$, and so ${\phi}_m(k)={\phi}_m(p_1^n1){\cdot}{\phi}_m(p_2^{n2}){\cdots}{\phi}_m(p_s^{ns})$ for the prime factorization of $k$, $k=p_1^{n1}{\cdot}p_2^{n2}{\cdots}p_s^{ns}$.

• Journal of Soil and Groundwater Environment
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• v.7 no.2
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• pp.73-81
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• 2002

In normal Fenton's reagent, the reductive mechanism of carbon tetrachloride (CT) with superoxide radical (${O_2}^-$.) was observed and the rate of ${O_2}^-$. production was investigated as a function of $H_2O$$_2$ concentration and pH. As pH was increased, the rate of 1-hexanol degradation was rapidly decreased from 90% (at pH 3) to 5% (at pH 11). On the other hand, more degradation of carbon tetrachloride was observed at higher pH regimes indicating Fenton's reaction is an oxidant-reductant co-existing system at neutral pHs. The rate of $O_2^{-}$ . production was observed at different $H_2$$O_2$ concentrations and at different pHs. The rate increased from (45.3$\pm$7.8) x $10^{-6}$ M/s to (151.0$\pm$26.2) x $10^{-6}$ M/s ($294mM H_2$$O_2$) at pH 11: the rate 3150 increased from (22.1$\pm$3.8) x $10^{-6}$ M/s at pH 7 to (151.0$\pm$26.2) x $^10{-6}$ M/s at pH 11 with 294mM $H_2$$O_2$, These results showed that Fenton's reagent could be applied at wide pH regimes. Especially, carbon tetrachloride, which can not be easily adsorbed to soils and then can be dissolved into groundwater causing a cancer, could be efficiently treated by Fenton's reagent.reagent.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.131-150
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• 2019

In this paper, we consider the structure of ${\gamma}$-constacyclic codes of length $2p^s$ over the Galois ring $GR(p^a,m)$ for any unit ${\gamma}$ of the form ${\xi}_0+p{\xi}_1+p^2z$, where $z{\in}GR(p^a,m)$ and ${\xi}_0$, ${\xi}_1$ are nonzero elements of the set ${\mathcal{T}}(p,m)$. Here ${\mathcal{T}}(p,m)$ denotes a complete set of representatives of the cosets ${\frac{GR(p^a,m)}{pGR(p^a,m)}}={\mathbb{F}}p^m$ in $GR(p^a,m)$. When ${\gamma}$ is not a square, the rings ${\mathcal{R}}_p(a,m,{\gamma})=\frac{GR(p^a,m)[x]}{{\langle}x^2p^s-{\gamma}{\rangle}}$ is a chain ring with maximal ideal ${\langle}x^2-{\delta}{\rangle}$, where ${\delta}p^s={\xi}_0$, and the number of codewords of ${\gamma}$-constacyclic code are provided. Furthermore, the self-orthogonal and self-dual ${\gamma}$-constacyclic codes of length $2p^s$ over $GR(p^a,m)$ are also established. Finally, we determine the Rosenbloom-Tsfasman (RT) distances and weight distributions of all such codes.

• Biomolecules & Therapeutics
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• v.27 no.6
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• pp.522-529
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• 2019

M1/M2 polarization of immune cells including microglia has been well characterized. It mediates detrimental or beneficial roles in neuroinflammatory disorders including cerebral ischemia. We have previously found that sphingosine 1-phospate receptor subtype 1 ($S1P_1$) in post-ischemic brain following transient middle cerebral artery occlusion (tMCAO) can trigger microglial activation, leading to brain damage. Although the link between $S1P_1$ and microglial activation as a pathogenesis in cerebral ischemia had been clearly demonstrated, whether the pathogenic role of $S1P_1$ is associated with its regulation of M1/M2 polarization remains unclear. Thus, this study aimed to determine whether $S1P_1$ was associated with regulation of M1/M2 polarization in post-ischemic brain. Suppressing $S1P_1$ activity with its functional antagonist, AUY954 (5 mg/kg, p.o.), attenuated mRNA upregulation of M1 polarization markers in post-ischemic brain at 1 day and 3 days after tMCAO challenge. Similarly, suppressing $S1P_1$ activity with AUY954 administration inhibited M1-polarizatioin-relevant $NF-{\kappa}B$ activation in post-ischemic brain. Particularly, $NF-{\kappa}B$ activation was observed in activated microglia of post-ischemic brain and markedly attenuated by AUY954, indicating that M1 polarization through $S1P_1$ in post-ischemic brain mainly occurred in activated microglia. Suppressing $S1P_1$ activity with AUY954 also increased mRNA expression levels of M2 polarization markers in post-ischemic brain, further indicating that $S1P_1$ could also influence M2 polarization in post-ischemic brain. Finally, suppressing $S1P_1$ activity decreased phosphorylation of M1-relevant ERK1/2, p38, and JNK MAPKs, but increased phosphorylation of M2-relevant Akt, all of which were downstream pathways following $S1P_1$ activation. Overall, these results revealed $S1P_1$-regulated M1/M2 polarization toward brain damage as a pathogenesis of cerebral ischemia.

• Applied Chemistry for Engineering
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• v.3 no.2
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• pp.189-193
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• 1992

The success of 3M's worldwide Pollution Prevention Pays (3P) Program convinced 3M's top management that the program should be expanded into a comprehensive environmental management system called 3P Plus. The emphasize of the 3P Plus program is to continually minimize the environmental impact of 3M processes, products, and operations to include energy management, resource recovery, and other initiatives. 3M's experience with the 3P and 3P Plus programs will be described. 3M's experience can serve as a model for other multi-national companies interested in sustainable development and economic growth with environmental protection.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1385-1422
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• 2019

Let p be an odd prime. The algebraic structure of all negacyclic codes of length $8_{p^s}$ over the finite commutative chain ring ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$ where $u^2=0$ is studied in this paper. Moreover, we classify all negacyclic codes of length $8_{p^s}$ over ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$ into 5 cases, i.e., $p^m{\equiv}1$ (mod 16), $p^m{\equiv}3$, 11 (mod 16), $p^m{\equiv}5$, 13 (mod 16), $p^m{\equiv}7$, 15 (mod 16) and $p^m{\equiv}9$ (mod 16). From that, the structures of dual and some self-dual negacyclic codes and number of codewords of negacyclic codes are obtained.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.429-441
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• 2020

Let M(X, Y) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlet-type spaces 𝓓_α^p, M(𝓓_p-1^p, 𝓓_q-1^q) = {0}, if p ≠ q, 0 < p, q < ∞. If 0 < p, q < ∞, p ≠ q, 0 < s < 1 such that p + s, q + s > 1, then M(𝓓_p-2+s^p, 𝓓_q-2+s^q) = {0}. However, X ∩ 𝓓_p-1^p ⊆ X ∩ 𝓓_q-1^q and X ∩ 𝓓_p-2+s^p ⊆ X ∩ 𝓓_q-2+s^p whenever X is a subspace of the Bloch space 𝓑 and 0 < p ≤ q < ∞. This says that the set of multipliers M(X ∩ 𝓓 _p-2+s^p, X∩𝓓_q-2+s^q) is nontrivial. In this paper, we study the multipliers M(X ∩ 𝓓_p-2+s^p, X ∩ 𝓓_q-2+s^q) for distinct classical subspaces X of the Bloch space 𝓑, where X = 𝓑, BMOA or 𝓗^∞.

• Geophysics and Geophysical Exploration
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• v.16 no.3
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• pp.109-118
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• 2013

On and near the 23-m high earthen Cheongcheon dam in Boryeong City, Korea, short seismic refraction and surface-wave profiles were conducted using a 5-kg sledgehammer. From vertical and horizontal components of the seismic waves, near-surface P-wave velocities (${\nu}_p$) and S-wave velocities (${\nu}_s$) were derived by inverting first-arrival refraction times and dispersion curves of Rayleigh waves. Average ${\nu}_p$ and ${\nu}_s$ for the Jurassic sedimentary basement were determined to be 1650 and 950 m/s at a depth of 30 m directly beneath the dam and 1650 m/s and 940 m/s at a depth of 10 m at the toe of the dam, respectively. The dynamic Poisson's ratio for these strata were therefore in the range of 0.24 to 0.25, which is consistent with ratios for consolidated sedimentary strata. Near a 45-m borehole 152 m downstream from the dam crest, an SH tomogram indicates a refraction boundary with an average ${\nu}_s$ of 870 m/s at depths of 10 ~ 12 m. At this site, the overburden comprises the upper layer with relatively constant ${\nu}_p$ and ${\nu}_s$ around 500 and 200 m/s, respectively, and the lower layer in which both ${\nu}_p$ and ${\nu}_s$ increase with depth almost linearly. The dynamic Poisson's ratios for the overburden were in the range of 0.30 to 0.43.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.9C
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• pp.669-675
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• 2008

For an odd prime p, n=4k and $d=((p^2k+1)/2)^2$, there are $(p^{2k}+1)/2$ distinct decimated sequences, s(dt+1), $0{\leq}l<(p^{2k}+1)/2$, of a p-ary m-sequence, s(t) of period $p^n-1$. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+l) takes the values in $\{-1,-1{\pm}\sqrt{p^n},-1+2\sqrt{p^n}\}$ and their, cross-correlation distribution is also derived.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.8
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• pp.5393-5399
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• 2014

To examine the effects of a mycosporine-like amino acids (MAAs) mixture from microalgae, Chlamydomonas sp, on the anti-wrinkle activities, the expression levels of genes that are associated with skin aging, including type I procollagen, elastin and involucrin, were analyzed. Asterina 330+palythine (A+P) and shinorine+palythine (S+P) mixtures were purified from Chlamydomonas sp using the following steps: 80% methanolic extraction, column purification, and HPLC analysis. As a result of the MTT assay, A+P and S+P did not induce cellular cytotoxicity with up to 0.1 mg/mL of both MAAs. In addition, the treatment of UV-exposed fibroblasts with A+P (0.05 mg/mL) and S+P (0.01 mg/mL) increased the levels of the PCOLCE mRNAs by 2.7 and 3.6 fold compared to the control group, respectively, The levels of elastin gene expression were elevated 5.59 and 3.1 fold in the A+P and S+P treated (0.01 mg/mL) cells, respectively. In particular, at a concentration of 0.01 mg /mL, the A+P and S+P expression levels of Involucrin mRNAs were increased 3.5 and 2.5 fold in the UV-exposed cells compared to the control, respectively. In conclusion, the MAAs derived from Chlamydomonas sp can be utilized as functional cosmetic materials with anti-wrinkle effects on the skin.