• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1651-1670
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• 2016

In this paper, we investigate exponentially biharmonic maps u : (M, g) ${\rightarrow}$ (N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that if $\int_{M}e^{\frac{p{\mid}r(u){\mid}^2}{2}{\mid}{\tau}(u){\mid}^pdv_g$ < ${\infty}$ ($p{\geq}2$), $\int_{M}{\mid}{\tau}(u){\mid}^2dv_g$ < ${\infty}$ and $\int_{M}{\mid}d(u){\mid}^2dv_g$ < ${\infty}$, then u is harmonic. When u is an isometric immersion, we get that if $\int_{M}e^{\frac{pm^2{\mid}H{\mid}^2}{2}}{\mid}H{\mid}^qdv_g$ < ${\infty}$ for 2 ${\leq}$ p < ${\infty}$ and 0 < q ${\leq}$ p < ${\infty}$, then u is minimal. We also obtain that any weakly convex exponentially biharmonic hypersurface in space form N(c) with $c{\leq}0$ is minimal. These results give affirmative partial answer to conjecture 3 (generalized Chen's conjecture for exponentially biharmonic submanifolds).

• Analytical Science and Technology
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• v.6 no.5
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• pp.489-499
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• 1993

Some sorption behaviors of U(VI) ion on Arsenazo I-XAD-2 chelating resin were investigated. This chelating resin was synthesized by the diazonium coupling of Amberlite XAD-2 resin with Arsenzo I chelating reagent and characterized by elementary analysis method and IR spectrometry. The optimum conditions for the sorption of U(VI) ion were examined with respect to pH, U(VI) ion concentration and shaking time. Total sorption capacity of this chelating resin on U(VI) ion was 0.39mmol U(VI)/g resin in the pH range of 4.0~4.5. This chelating resin was showed increased sorption capacity on the increased pH value. It was confirmed that sorption mechanism of U(VI) ion on the Arsenazo I-XAD-2 chelating resin was competition reacting between U(VI) ion and $H^+$ ion. Breakthrough volume and overall capacity of U(VI) ion measured by column were was 600 ml and 0.38 mmol U(VI)/g resin, respectively. The desorption of U(VI) ion was showed recovery of 90~96% using 3M $HNO_3$ and 3M $Na_2CO_3$ as a desorption solution. The separation and concentration of U(VI) ion from natural water and sea water was performed successfully by Arsenazo I-XAD-2 chelating resin.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.911-926
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• 2022

Let u be a function on a locally finite graph G = (V, E) and Ω be a bounded subset of V. Let 𝜀 > 0, p > 2 and 0 ≤ λ < λ₁(Ω) be constants, where λ₁(Ω) is the first eigenvalue of the discrete Laplacian, and h : V → ℝ be a function satisfying h ≥ 0 and $h{\not\equiv}0$. We consider a perturbed Yamabe equation, say $$\{\begin{array}{lll}-{\Delta}u-{\lambda}u={\mid}u{\mid}^{p-2}u+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω and ∂Ω denote the interior and the boundary of Ω, respectively. Using variational methods, we prove that there exists some positive constant 𝜀₀ > 0 such that for all 𝜀 ∈ (0, 𝜀₀), the above equation has two distinct solutions. Moreover, we consider a more general nonlinear equation $$\{\begin{array}{lll}-{\Delta}u=f(u)+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ and prove similar result for certain nonlinear term f(u).

• Journal of the Mineralogical Society of Korea
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• v.18 no.3 s.45
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• pp.183-194
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• 2005

The mineralogical, physicochemical and thermal properties of the Myogi bentonite occurring in Japan were measured. A adsorption properties of U, Th, Ce and Eu ions on the Myogi bentonite were also investigated in different solution concentrations and pH conditions. The Myogi bentonite showed a strong alkaline character (pH 10.4), very high swelling, viscosity property and CEC, and a slow flocculation behavior due to the strong hydrophilic property. By the thermal analysis, the dehydroxylation of crystal water in bulk and clay fractions of the Myogi bentonite occur at $591^{\circ}C$ and $658^{\circ}C$, respectively, The adsorption experiments of ions such as U, Th, Ce and Eu were conducted for 0.2 g bentonites with 20mL solutions of various concentrations and different pH conditions with pH 3, 5, 7, 9, and 11. As a result, the Myogi bentonite showed excellent adsorption capacities for Ce, Th and Eu ions, whereas U ion showed very low adsorption capacity. Generally, Ce, Th and Eu ions showed the similar adsorption properties for the different concentrated solutions and pH conditions. These adsorption properties seem to be affected by the formation of various forms of chemical species and precipitation as well as ionic exchange reaction and surface adsorptions on smectite. Some associated zeolite minerals perhaps have some effects on the adsorption of U, Th, Ce and Eu on Myogi bentonite.

• Fisheries and Aquatic Sciences
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• v.15 no.3
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• pp.197-202
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• 2012

This study examined and compared the exopeptidase and endoprotease activities of the hepatopancreas (HP) of cuttlefish, squid, and octopus species. The protein concentration in crude extract (CE) from octopus HP was 3,940 mg/100 g, lower than those in CEs from squid HP (4,157 mg/100 g) and cuttlefish HP (5,940 mg/100 g). With azocasein of pH 6 as a substrate, the total activity in HP CE of octopus was 31,000 U, lower than the values for cuttlefish (57,000 U) and squid (69,000 U). Regardless of sample type, the total activities of the CEs with azocasein as the substrate were higher at pH 6 (31,000-69,000 U) than at pH 9 (19,000-34,000 U). With L-leucine-p-nitroanilide (LeuPNA) of pH 6 as the substrate, the total activity of the HP CE from octopus was 138,000 U, higher than values from both cuttlefish HP (72,000 U) and squid HP (63,000 U). Regardless of sample type, the total activities of the CEs with LeuPNA as the substrate were higher at pH 6 (63,000-138,000 U) than at pH 9 (41,000-122,000 U). With LeuPNA as the substrate, the total activities of the CEs from octopus HP and cuttlefish HP were higher at pH 6 than at pH 9. However, there was no difference in total activity between pH 6 and 9 for squid HP CE with LeuPNA as the substrate. These results suggest that the octopus HP is superior to the cuttlefish HP and squid HP as a potential resource for extracting exopeptidases. Exopeptidases from octopus HP have potential industrial applications and their use might aid in reducing pollution related to the octopus industry.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.173-179
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• 2018

In this paper, we investigate the stability of positive weak solution for the singular p-Laplacian nonlinear system $-div[{\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^{p-2}{\nabla}u]+m(x){\mid}u{\mid}^{p-2}u={\lambda}{\mid}x{\mid}^{-(a+1)p+c}b(x)f(u)$ in ${\Omega}$, Bu = 0 on ${\partial}{\Omega}$, where ${\Omega}{\subset}R^n$ is a bounded domain with smooth boundary $Bu={\delta}h(x)u+(1-{\delta})\frac{{\partial}u}{{\partial}n}$ where ${\delta}{\in}[0,1]$, $h:{\partial}{\Omega}{\rightarrow}R^+$ with h = 1 when ${\delta}=1$, $0{\in}{\Omega}$, 1 < p < n, 0 ${\leq}$ a < ${\frac{n-p}{p}}$, m(x) is a weight function, the continuous function $b(x):{\Omega}{\rightarrow}R$ satisfies either b(x) > 0 or b(x) < 0 for all $x{\in}{\Omega}$, ${\lambda}$ is a positive parameter and $f:[0,{\infty}){\rightarrow}R$ is a continuous function. We provide a simple proof to establish that every positive solution is unstable under certain conditions.

• Asian Pacific Journal of Cancer Prevention
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• v.14 no.7
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• pp.4095-4099
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• 2013

Oxidative stress induces apoptosis in many cellular systems including glioblastoma cells, with caspase-8 activation was regarded as a major contribution to $H_2O_2$-induced cell death. This study focused on the role of the autophagic protein p62 in $H_2O_2$-induced apoptosis in U87MG cells. Oxidative stress was applied with $H_2O_2$, and cell apoptosis and viability were measured with use of caspase inhibitors or autophagic mediators or siRNA p62, GFP-p62 and GFP-p62-UBA (del) transfection. We found that $H_2O_2$-induced U87MG cell death was correlated with caspase-8. To understand the role of p62 in MG132-induced cell death, the levels of p62/SQSTM1 or autophagy in U87MG cells were modulated with biochemical or genetic methods. The results showed that the over-expression of wild type p62/SQSTM1 significantly reduced $H_2O_2$ induced cell death, but knockdown of p62 aggravated the process. In addition, inhibition of autophagy promoted p62 and active caspase-8 increasing $H_2O_2$-induced apoptosis while induction of autophagy manifested the opposite effect. We further demonstrated that the function of p62/SQSTM1 required its C-terminus UBA domain to attenuate $H_2O_2$ cytotoxity by inhibition of caspase-8 activity. Our results indicated that p62/SQSTM1 was a potential contributor to mediate caspase-8 activation by autophagy in oxidative stress process.

• Journal of Information Science Theory and Practice
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• v.4 no.4
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• pp.64-74
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• 2016

In this paper we define a two parametric new generalized useful average code-word length $L_{\alpha}^{\beta}$(P;U) and its relationship with two parametric new generalized useful information measure $H_{\alpha}^{\beta}$(P;U) has been discussed. The lower and upper bound of $L_{\alpha}^{\beta}$(P;U), in terms of $H_{\alpha}^{\beta}$(P;U) are derived for a discrete noiseless channel. The measures defined in this communication are not only new but some well known measures are the particular cases of our proposed measures that already exist in the literature of useful information theory. The noiseless coding theorems for discrete channel proved in this paper are verified by considering Huffman and Shannon-Fano coding schemes on taking empirical data. Also we study the monotonic behavior of $H_{\alpha}^{\beta}$(P;U) with respect to parameters ${\alpha}$ and ${\beta}$. The important properties of $H_{{\alpha}}^{{\beta}}$(P;U) have also been studied.

• East Asian mathematical journal
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• v.14 no.1
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• pp.63-76
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• 1998

we consider the hp-version to solve non-constant coefficients elliptic equations $-div(a{\nabla}u)=f$ with Dirichlet boundary conditions on a bounded polygonal domain $\Omega$ in $R^2$. In [6], M. Suri obtained an optimal error-estimate for the hp-version: ${\parallel}u-u^h_p{\parallel}_{1,\Omega}{\leq}Cp^{(\sigma-1)}h^{min(p,\sigma-1)}{\parallel}u{\parallel}_{\sigma,\Omega}$. This optimal result follows under the assumption that all integrations are performed exactly. In practice, the integrals are seldom computed exactly. The numerical quadrature rule scheme is needed to compute the integrals in the variational formulation of the discrete problem. In this paper we consider a family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties, which can be used for calculating the integrals. Under the numerical quadrature rules we will give the variational form of our non-constant coefficients elliptic problem and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_{1,\Omega}$.

• Journal of the Korean Chemical Society
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• v.38 no.10
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• pp.769-773
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• 1994

Higher order structure of 5S rRNA isolated from Xanthomonas celebensis was examined using angiogenic extracted from milk. Angiogenin cleaved exclusively 3' P-O bonds on the far sides of pyrimidines in the single-stranded sequences of 5S rRNA. Whereas angiogenin acted only on the loop d of 5S rRNA at pH 7.0 in the presence of 10 mM $Mg^{2+}$, it acted on all the loops (a, b, c and d) except loop e in the absence of $Mg^{2+}$. In the absence of $Mg^{2+}$, bonds $U_{74}$-$G_{75}$, $U_{77}$-$A_{78}$ and $U_{103}$-$A_{104}$ were highly susceptible to the action of angiogenin both at pH 7.0 and at pH 3.5. On the other hand, at pH 3.5 in the absence of $Mg^{2+}$ angiogenin strongly cleaved the bond $C_{17}$-$G_{18}$ of loop a and the bond $U_{55}$-$G_{56}$ of loop b. The results lead us to the following conclusion. First, angiogenin can be used as one of the probes for the tertiary structure analysis of 5S rRNA. Second, the structure of loop d of 5S rRNA is variable depending on the concentrations of $Mg^{2+}$ and $H^{1+}$.