• 충청수학회지
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• 제21권4호
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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.

• 대한수학회보
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• 제46권2호
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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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• 제42권2호
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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.

• 충청수학회지
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• 제24권4호
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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 $n=0,1,2,{\cdots}$.

• 생명과학회지
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• 제26권11호
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• pp.1225-1231
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• 2016

본 연구에서 기존의 생리활성이 알려진 차가 버섯(Inonatus obliquus), 모링가(Moringa oleifera), 그라비올라(Anona muricata), 단풍마(Dioscorea quinquelaba), 가시오가피(Acanhopanax senticosus), 음양곽(Epimedii herba), 인진쑥(Artemisia capillaris), 그리고 오디(Morus alba) 추출물과 원두커피를 혼합하여 기능성 음료를 제조하였으며, 각각의 음료를 C1에서 C7으로 명명하였다. 각 음료의 항균, 항곰팡이, 항산화 활성 및 총 폴리페놀 함량을 조사하였다. 항균 및 항곰팡이에 대한 활성은 Gram positive bacteria인 Staphylococcus aureus에 대하여 C4, C5, C6 및 C7이 활성을 나타내었고, 특히 C7인 경우 항생제 내성균주인 MRSA에 대하여 강한 활성을 나타내었다. Gram negative bacteria에 대한 결과는 E. coli D31에 대하여 1.0 mg/ml의 농도에서 C1에서 C7 모든 음료가 활성을 나타내었고, 반면에 곰팡이인 Candida albicans에 대하여는 활성을 나타내지 않았다. 총 폴리페놀 함량은 C6의 경우가 7.37 mg/g으로 가장 높은 결과를 나타내었고, C5의 경우는 3.78 mg/g으로 가장 낮은 함량을 나타내었다. DPPH로 항산화 능력을 측정한 결과, C1에서 C7 모두 강한 활성을 나타내었고, 특히 C7인 경우 0.5 mg/ml의 농도에서 88%라는 높은 free radical 소거능력을 나타내었다. 이러한 결과를 바탕으로 각 기능성 음료의 생리활성의 기초자료를 제공하고 다양한 기능성 건강음료뿐 만 아니라 고부가가치 기능성 제품을 창출 할 수 있는 근거를 마련한 것으로 생각된다.

• Bulletin of the Korean Chemical Society
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• 제33권1호
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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.

• 호남수학학술지
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• 제46권1호
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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.

• 환경위생공학
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• 제21권4호
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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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• 제56권3호
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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.

• 충청수학회지
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• 제24권2호
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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.