• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.437-445
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• 2008

We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.311-319
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• 2009

Let H be a Hilbert space which is the direct sum of five closed subspaces $X_0,\;X_1,\;X_2,\;X_3$ and $X_4$ with $X_1,\;X_2,\;X_3$ of finite dimension. Let J be a $C^{1,1}$ functional defined on H with J(0) = 0. We show the existence of at least four nontrivial critical points when the sublevels of J (the torus with three holes and sphere) link and the functional J satisfies sup-inf variational inequality on the linking subspaces, and the functional J satisfies $(P.S.)^*_c$ condition and $f|X_0{\otimes}X_4$ has no critical point with level c. For the proof of main theorem we use the nonsmooth version of the classical deformation lemma and the limit relative category theory.

• Journal of Ginseng Research
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• v.42 no.2
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• pp.133-143
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• 2018

Background: AD-2 (20(R)-dammarane-3b, 12b, 20, 25-tetrol; 25-OH-PPD) is a ginsenoside and isolated from Panax ginseng, showing anticancer activity against extensive human cancer cell lines. In this study, effects and mechanisms of 1C ((20R)-3b-O-(L-alanyl)-dammarane-12b, 20, 25-triol), a modified version of AD-2, were evaluated for its development as a novel anticancer drug. Methods: MTT assay was performed to evaluate cell cytotoxic activity. Cell cycle and levels of reactive oxygen species (ROS) were determined using flow cytometry analysis. Western blotting was employed to analyze signaling pathways. Results: 1C concentration-dependently reduces prostate cancer cell viability without affecting normal human gastric epithelial cell line-1 viability. In LNCaP prostate cancer cells, 1C triggered apoptosis via Bcl-2 family-mediated mitochondria pathway, downregulated expression of mouse double minute 2, upregulated expression of p53 and stimulated ROS production. ROS scavenger, N-acetylcysteine, can attenuate 1C-induced apoptosis. 1C also inhibited the proliferation of LNCaP cells through inhibition on $Wnt/{\beta}-catenin$ signaling pathway. Conclusion: 1C shows obvious anticancer activity based on inducing cell apoptosis by Bcl-2 family-mediated mitochondria pathway and ROS production, inhibiting $Wnt/{\beta}-catenin$ signaling pathway. These findings demonstrate that 1C may provide leads as a potential agent for cancer therapy.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.617-630
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• 2011

Let X, Y be vector spaces, and let r be 2 or 4. It is shown that if an odd mapping $f:X{\rightarrow}Y$ satisfies the functional equation $${\hspace{50}}rf(\frac{\sum_{j=1}^{d}\;x_j} {r})+\;{\sum\limits_{\iota(j)=0,1 \atop {\sum_{j=1}^{d}}\;{\iota}(j)=l}}\;rf(\frac{\sum_{j=1}^{d}{(-1)^{\iota(j)}x_j}}{r}) \\({\ddag}){\hspace{160}}=(_{d-1}C_l-_{d-1}C_{l-1}+1)\;{\sum\limits_{j=1}^{d}\;f(x_j)}$$ then the odd mapping $f:X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation in Banach modules over a unital $C^*$-algebra. As an application, we show that every almost linear bijection $h:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ of a unital $C^*$-algebra ${\mathcal{A}}$ onto a unital $C^*$-algebra ${\mathcal{B}}$ is a $C^*$-algebra isomorphism when $h(2^nuy)=h(2^nu)h(y)$ for all unitaries $u{\in}{\mathcal{A}}$, all $y{\in}{\mathcal{A}}$, and $n=0,1,2,{\cdots}$.

• Journal of Life Science
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• v.26 no.11
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• pp.1225-1231
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• 2016

In this study, our investigated the antioxidant activities and compared other bioassay including anti-microbial, antifungal activities and total polyphenol contents of functional healthy drinks from some medicinal herbs and coffee mixture. The kind of medicinal herbs, chaga mushroom (Inonatus obliqurs), moringa (Moringa Oleifera), gravila (Anona muricata), mulberry (Morus alba), Dioscoreaceae (Dioscorea quinquelaba), Berberidaceae (Epimedii Herba), Asteraceae (Artemisia capillaries) and siberian ginseng (Acanthopanax senticous,). The functional healthy drinks, named C1, C2, C3, C4, C5, C6 and C7 were summered in Table 1. The in vitro antimicrobial activity was examined against Gram positive bacteria, Gram negative bacteria and a fungus. The functional healthy drinks were broad spectrum of anti-microbial activity without antifungal activity against Candida albicans KCTC7965. In particularly, the C7 showed strong activity against Methicillin Resistant Staphylococcus aureus CCARM3089, CCARM 3115 and CCARM3561. And, the C7 showed 88% of free radical scavenging effect on 0.5 mg/ml using 1,1-diphenyl-2-picrylhydrazyl (DPPH) method. Functional healthy drink C7 was mulberry extracts from Morus alba, chaga mushroom from Inonatus obliqurs and moringa from Moringa olifera in additionally coffee extracts. Its results confirm that the potential use of mulberry extracts as a good source of antibacterial compounds or as a health promoting food and health drinks.

• Bulletin of the Korean Chemical Society
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• v.33 no.1
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• pp.143-148
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• 2012

The photodissociation dynamics of cyclopropyl bromide ($C_3H_5Br$) and cyclobutyl bromide ($C_4H_7Br$) at 234 nm was investigated. A two-dimensional photofragment ion-imaging technique coupled with a [2+1] resonanceenhanced multiphoton ionization scheme was utilized to obtain speed and angular distributions of the nascent $Br(^2P_{3/2})$ and $Br^*(^2P_{1/2})$ atoms. The recoil anisotropies for the Br and $Br^*$ channels were measured to be ${\beta}_{Br}=0.92{\pm}0.03$ and ${\beta}_{Br^*}=1.52{\pm}0.04$ for $C_3H_5Br$ and ${\beta}_{Br}=1.10{\pm}0.03$ and ${\beta}_{Br^*}=1.49{\pm}0.05$ for $C_4H_7Br$. The relative quantum yield for Br was found to be ${\Phi}_{Br}=0.13{\pm}0.03$ and for $C_3H_5Br$ and $C_4H_7Br$, respectively. The soft radical limit of the impulsive model adequately modeled the related energy partitioning. The nonadiabatic transition probability from the 3A' and 4A' potential energy surfaces was estimated and discussed.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.146-167
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• 2024

In this paper, we investigate the stability of the general decic functional equation $$\sum_{i=0}^{11}_{11}C_i(-1)^{11-i}f(x+iy)=0$$ in the sense of Rassias.

• Journal of environmental and Sanitary engineering
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• v.21 no.4 s.62
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• pp.49-60
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• 2006

The ion exchange resins have been synthesized from chlormethyl styrene - 1,4 - divinylbenzene(DVB) with 1%, 2%, 4% and 8%-crosslinking and 1-aza-18-crown-6 macrocyclic ligand by copolymerization method. Content of chlorine in styrene-DVB copolymer was decreased as crosslink increased and it is because as crosslink increased 1%, 2%, 4% and 8% DVB content increased and crosslink density increased and cavity was reduced. Functional group of resin almost disappeared as C-C1 peak around $700cm^{-1}$ was substituted with 1-aza-18-C-6 macrocyclic ligand and new peak of C-N around $1020cm^{-1}$ appeared, so it was confirmed that styrene-DVB copolymer and ligand were compounded. As crosslink increased in the analysis of element contents, it resulted in the reduction of nitrogen content and it is because as crosslink increased, it led to the reduction of chlorine content in the process of substitution reaction and it affected macrocyclic ligand substituted. Thermo analysis curve of functional synthetic resin decomposed three part of 1-aza-18-C-6, styrene, and DVB. Form of functional synthetic resin showed distortion of its particles as macrocyclic ligand was introduced to styrene-DVB copolymer and hydrogen of ligand caused substitution with chlorine element of styrene molecule.

• BMB Reports
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• v.56 no.3
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• pp.172-177
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• 2023

BEST family is a class of Ca²⁺-activated Cl- channels evolutionary well conserved from bacteria to human. The human BEST paralogs (BEST1-BEST4) share significant amino acid sequence homology in the N-terminal region, which forms the transmembrane helicases and contains the direct calcium-binding site, Ca²⁺-clasp. But the cytosolic C-terminal region is less conserved in the paralogs. Interestingly, this domain-specific sequence conservation is also found in the BEST1 orthologs. However, the functional role of the C-terminal region in the BEST channels is still poorly understood. Thus, we aimed to understand the functional role of the C-terminal region in the human and mouse BEST1 channels by using electrophysiological recordings. We found that the calcium-dependent activation of BEST1 channels can be modulated by the C-terminal region. The C-terminal deletion hBEST1 reduced the Ca²⁺-dependent current activation and the hBEST1-mBEST1 chimera showed a significantly reduced calcium sensitivity to hBEST1 in the HEK293 cells. And the C-terminal domain could regulate cellular expression and plasma membrane targeting of BEST1 channels. Our results can provide a basis for understanding the C-terminal roles in the structure-function of BEST family proteins.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.147-162
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• 2011

In this paper, we investigate the Ulam-Hyers stability of $C^{\star}$-ternary algebra 3-homomorphisms for the functional equation $$f(x_1+x_2,y_1+y_2,z_1+z_2)=\;\displaystyle\sum_{1{\leq}i,j,k{\leq}2}\;f(x_i,y_j,z_k)$$ in $C^{\star}$-ternary algebras.