• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.985-994
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• 1994

Boundary value problems are common in nature. Here we restrict our attention to the second order differential equations of the form $$ (1.1) \frac{d^2 y}{dx^2} = P(x)y(x) + Q(x), 0 \leq x \leq 1, $$ $$ y(0) = \alpha, $$ $$ y(1) = \beta, $$ where P(x) and Q(x) are continuous functions with $P(x) \geq 0, x \in [0, 1]$.

• Asian-Australasian Journal of Animal Sciences
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• v.20 no.8
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• pp.1236-1242
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• 2007

Sixty healthy growing pigs ($Duroc{\times}Landrace{\times}Yorkshire$ with an average BW of 21.4 kg) were used to determine the true digestible phosphorus (TDP) requirement of growing pigs on the basis of growth performance and serum biochemical indices. Pigs were assigned randomly to one of five dietary treatments (12 pigs/diet), representing five levels of TDP (0.16%, 0.20%, 0.23%, 0.26% and 0.39%). There were three replications per treatment, with four pigs (2 barrows and 2 gilts) in each replication (2 pigs/pen) A randomized-block design was used, with pen as the experimental unit. Experimental diets were formulated to provide the 5 TDP levels with a total calcium (Ca) to TDP ratio of 2:1, and offered to pigs at 5% BW for 28 d. The total Ca contents of the five diets were 0.33, 0.38, 0.45, 0.51 and 0.79%, respectively. During the 28-d experimental period, the ADG of pigs was affected by dietary TDP levels as described by Equation 1: y = $-809,532x^4+788,079x^3-276,250x^2+42,114x-1$,759; ($R^2$ = 0.99; p<0.01; y = ADG, g/d; x = dietary TDP, %). The feed:gain ratio for pigs was affected by dietary TDP levels as described by Equation 2: y = $3,651.1x^4-3,480.4x^3+1,183.8x^2-172.5x+10.9$ ($R^2$ = 0.99; p<0.01; y = feed:gain ratio; x = dietary TDP, %). Total P concentrations in serum were affected by dietary TDP levels as described by Equation 3: y = $-3,311.7x^4+3,342.7x^3-1,224.6x^2+195.6x-8.7$ ($R^2$ = 0.99; p<0.01; y = total serum P concentration and x = dietary TDP, %). The highest ADG (782 g/d), the lowest feed:gain ratio (1.07), and the highest total serum P concentration (3.1 mmol/L) were obtained when dietary TDP level was 0.34%. Collectively, these results indicate that the optimal TDP requirement of growing pigs is 0.34% of the diet (e.g., 5.1 g/day for a 30-kg pig that consumed 1.5 kg feed daily) at a total Ca to TDP ratio of 2:1.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.15-21
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• 2019

Let X be a reduced closed subscheme in ${\mathbb{P}}^n$ and $${\pi}_q:X{\rightarrow}Y={\pi}_q(X){\subset}{\mathbb{P}}^{n-1}$$ be an isomorphic projection from the center $q{\in}{\mathbb{P}}^n{\backslash}X$. Suppose that the minimal free presentation of $I_X$ is of the following form $$R(-3)^{{\beta}2,1}{\oplus}R(-4){\rightarrow}R(-2)^{{\beta}1,1}{\rightarrow}I_X{\rightarrow}0$$. In this paper, we prove that $H^1(I_X(k))=H^1(I_Y(k))$ for all $k{\geq}3$. This implies that Y is k-normal if and only if X is k-normal for $k{\geq}3$. Moreover, we also prove that reg(Y) ${\leq}$ max{reg(X), 4} and that $I_Y$ is generated by homogeneous polynomials of degree ${\leq}4$.

• Korean Journal of Microbiology
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• v.52 no.2
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• pp.230-235
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• 2016

This study was carried out to analyze the differences in enzyme activity and stability between the native Fe superoxide dismutase (FeSOD) and the 6xHis-tagged superoxide dismutase (6xHis-FeSOD) of Streptomyces subrutilus P5. The optimum pHs for both native FeSOD and 6xHis-FeSOD were 7, while the pH range of the activity was narrower for the 6xHis-FeSOD. The native FeSOD was stable at pH 4-9, but the 6xHis-FeSOD lost its stability at pH > 9. The temperatures of the optimum activities were same for both types of enzymes. However, the heat stability of the 6xHis-FeSOD was clearly decreased; even at $20^{\circ}C$ the enzyme lost the activity after 360 min. In contrast, the native FeSOD was stable after 720 min at below $40^{\circ}C$. $H_2O_2$ inhibition was occurred already at 0.5 mM for the 6xHis-tagged enzyme. Therefore, from the results that the 6xHis-FeSOD retained the enzyme activity at pH 6-7 and $20-40^{\circ}C$, it can be assumed that the protein structure became destabilized under different storage conditions and sensitive to the enzyme inhibitor.

• Applied Microscopy
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• v.38 no.3
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• pp.151-157
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• 2008

Trigeminal primary afferents expressing $P2X_3$ or transient receptor potential vanilloid 1 (TRPV1) are involved in the transmission of nociceptive information. In order to characterize $P2X_3$- and TRPV1-immunopositive neurons in the trigeminal ganglion (TG) and trigeminal caudal nucleus (Vc), we performed immunofluorescence experiments using anti-$P2X_3$ and anti-TRPV1 antisera and a morphometric analysis. 77.4% (1,401/1.801) of all the $P2X_3$-postive neurons coexpressed TRPV1 and 51.9% (1,401/2,698) of all the THFV1-immunopositive neurons also costained for $P2X_3$ in the TG. Immunoreactivity for both $P2X_3$ and TRPV1 were present in medium-sized neurons but not in small- and large-sized neurons. $P2X_3$ and/or TRPV1-immunopositive fibers were observed in the primary afferents and their associated axons in the Vc. These fibers and terminals were distributed in the superficial lamina of Vc: $P2X_3$-immunopositive fibers and terminals were distributed in the lamina I and II, expecially in the inner part of lamina II (lamina IIi), whereas TRPV1-immunopositive ones were densely detected in the lamina I and outer part of lamina II (lamina IIo). Immunopositive fibers and terminals for both $P2X_3$ and TRPV1 were observed on the border between lamina IIi and IIo. These results suggest that terminals coexpressing $P2X_3$ and TRPV1 are involved in specific roles in the transmission and processing of orofacial nociceptive information.

• Journal of the Korean Ceramic Society
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• v.45 no.3
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• pp.179-184
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• 2008

(40-x)BaO${\cdot}xFe_2O_3{\cdot}60P_2O_5$ glasses with $5{\leq}x{\leq}35mol%$ were investigated by ESR spectroscopy. Two resonances observed near g=2.0 and g=4.3. The line at g=4.3 disappeared with the increase of the $Fe_2O_3$ content. The resonance at $g{\approx}2.0$ displayed characteristic signal consisting of superposed extremely broad and narrow components. The broader one indicates the presence of the association of two or more $Fe^{3+}$ ions, antiferromagnetically and the narrow one is related to the microclusters involving iron ions. Temperature dependence of the ESR integrated intensity revealed short-range antiferromagnetic character for $x{\geq}15mol%$.

• The Mathematical Education
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• v.12 no.2
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• pp.5-12
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• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.921-936
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• 2011

In this paper, our main purpose is to establish the existence of weak solutions of a weak solutions of a class of p-q-Laplacian system involving concave-convex nonlinearities: $$\{\array{-{\Delta}_pu-{\Delta}_qu={\lambda}V(x)|u|^{r-2}u+\frac{2{\alpha}}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\;x{\in}{\Omega}\\-{\Delta}p^v-{\Delta}q^v={\theta}V(x)|v|^{r-2}v+\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,\;x{\in}{\Omega}\\u=v=0,\;x{\in}{\partial}{\Omega}}$$ where ${\Omega}$ is a bounded domain in $R^N$, ${\lambda}$, ${\theta}$ > 0, and 1 < ${\alpha}$, ${\beta}$, ${\alpha}+{\beta}=p^*=\frac{N_p}{N_{-p}}$ is the critical Sobolev exponent, ${\Delta}_su=div(|{\nabla}u|^{s-2}{\nabla}u)$ is the s-Laplacian of u. when 1 < r < q < p < N, we prove that there exist infinitely many weak solutions. We also obtain some results for the case 1 < q < p < r < $p^*$. The existence results of solutions are obtained by variational methods.

• Korean Journal of Materials Research
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• v.15 no.2
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• pp.112-114
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• 2005

Dispersion stability of the $Sm_xCe_{1-x}O_{2-2/x}$ nanoparticles, which was produced by hydrothermal process, was studied in aqueous suspension using ESA (Eletrokinetic Sonic Amplitude). The average particle size of the synthesized $Sm_xCe_{1-x}O_{2-2/x}$ at nanoparticles was about $5{\pm}2nm$. The dispersion and rheological behavior of the $Sm_xCe_{1-x}O_{2-2/x}$ nanoparticles aqueous suspension was investigated using $NH_4OH\;and\;HNO_3$ as a disperse agent. The colloidal stability of aqueous suspensions with $Sm_xCe_{1-x}O_{2-2/x}$ nanoparticles at different pH values has been investigated by means of zeta potential, average particle size, and the distribution of synthesized $Sm_xCe_{1-x}O_{2-2/x}$ nanoparticles. The isoelectric point of the $Sm_xCe_{1-x}O_{2-2/x}$ nanoparticles was at pH around 11 and the value of zeta potential was at its maximum near pH 6.5.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.977-986
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• 2010

Let $X_1$, $X_2$, $\cdots$ be identically distributed negatively associated random variables with $EX_1\;=\;0$ and $E|X_1|^3$ < $\infty$. In this paper we prove $lim_{{\epsilon\downarrow}0}\;\frac{1}{-\log\;\epsilon}\sum\limits_{n=1}^\infty\frac{1}{n^2}ES_n^2I\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;2$ and $lim_{\epsilon\downarrow0}\;\epsilon^{2-p}\sum\limits_{n=1}^\infty\frac{1}{n^p}$ $E|S_n|^pI\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;\frac{2}{2-p}$ for 0 < p < 2, where $S_n\;=\;\sum\limits_{i=1}^{n}X_i$ and 0 < $\sigma^2\;=\;EX_1^2\;+\;\sum\limits_{i=2}^{\infty}Cov(X_1,\;X_i)$ < $\infty$. We consider some results of i.i.d. random variables obtained by Liu and Lin(2006) under negative association assumption.