• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• Journal of the Korean Society of Food Science and Nutrition
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• v.20 no.4
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• pp.320-328
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• 1991

The present study was designed to evaluate the effects of dietary vitamin E and coenzyme $Q_{10}$ supplementation on adriamycin (ADR) -induced lipid petoxidation in rats. After feeding the experimental diets for e weeks. Ann treatment significantly decreased growth performance of rats. But this decrement was not modified by supplementation of vitamin E or coenzyme $Q_{10}$ . Lipid peroxide values of plasma and heart mitochondria were elevated by Ann treatment. But these values were significantly decreased according to vitamin E or coenzyme $Q_{10}$ supplementation. Adriamycin treatment elevated glutathione peroxidase (GSH-Px) activity of rats, but this increment was modified by vitamin E supplementation. There was a tendency of higher superoxide dismutase (SOD) activity in ADR-treated rats. However, vitamin E or coenzyme $Q_{10}$ administration reduced this enzyme activity. With ADR treatment, arachidonic acid (20 : 4) was greatly increased, but docosahexaenoic acid (22 : 6) was not detected. Arachidonic acid was decreased and docosahexaenoic acid increased by supplementation of higher level of vitamin E or coenzyme $Q_{10}$ . Present data showed that dietary vitamin E and coenzyme $Q_{10}$ influenced on ADR-induced lipid peroxidation in rats, and also the degree of antioxidative effect was greater in vitamin E-supplemented rats.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.227-234
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• 2022

Let 𝔽_q be a finite field with odd q elements. In this article, we prove that if E ⊆ 𝔽^d_q, d ≥ 2, and |E| ≥ q, then there exists a set Y ⊆ 𝔽^d_q with |Y| ~ q^d such that for all y ∈ Y, the number of distances between the point y and the set E is ~ q. As a corollary, we obtain that for each set E ⊆ 𝔽^d_q with |E| ≥ q, there exists a set Y ⊆ 𝔽^d_q with |Y| ~ q^d so that any set E ∪ {y} with y ∈ Y determines a positive proportion of all possible distances. The averaging argument and the pigeonhole principle play a crucial role in proving our results.

• Journal of Photoscience
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• v.12 no.3
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• pp.175-183
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• 2005

Plants dissipate excess excitation energy from their photosynthetic apparatus by a process called non-photochemical quenching (NPQ). The major part of NPQ is energy dependent quenching (qE) which is dependent on the thylakoid pH and regulated by xanthophyll cycle carotenoids associated with photosystem (PS) II of higher plants. The acidification of the lumen leads to protonation and thus conformational change of light harvesting complex (LHC) proteins as well as PsbS protein of PSII, which results in the induction of qE. Although physiological importance of qE has been well established, the mechanistic understanding is rather insufficient. However, recent finding of crystal structure of LHCII trimer and identification of qE mutants in higher plants and algae enrich and sharpen our understanding of this process. This review summarizes our current knowledge on the qE mechanism. The nature of quenching sites and components involved in this process, and their contribution and interaction for the generation of qE appeared in the proposed models for the qE mechanism are discussed.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.237-244
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• 2018

Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let L be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in ${\mathcal{L}}$. Let p and q be natural numbers (p < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.93-100
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• 2017

Let $\mathcal{H}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let $\mathcal{L}$ be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in $\mathcal{L}$. Let p and q be natural numbers($p{\leqslant}q$). Let $\mathcal{B}_{p,q}=\{T{\in}Alg\mathcal{L}{\mid}T_{(p,q)}=0\}$. Let $\mathcal{A}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $\{0\}{\varsubsetneq}{\mathcal{A}}{\subset}{\mathcal{B}}_{p,q}$. If $\mathcal{A}$ is an ideal in $Alg{\mathcal{L}}$, then $T_{(i,j)}=0$, $p{\leqslant}i{\leqslant}q$ and $i{\leqslant}j{\leqslant}q$ for all T in $\mathcal{A}$.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1409-1418
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• 2023

The Hurwitz-type Euler zeta function ζ_E(z, q) is defined by the series ${\zeta}_E(z,\,q)\,=\,\sum\limits_{n=0}^{\infty}{\frac{(-1)^n}{(n\,+\,q)^z}},$ for Re(z) > 0 and q ≠ 0, -1, -2, . . . , and it can be analytic continued to the whole complex plane. An asymptotic expansion for ζ^'_E(-m, q) has been proved based on the calculation of Hermite's integral representation for ζ_E(z, q).

• Journal of Korean Society of Environmental Engineers
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• v.32 no.11
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• pp.1063-1068
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• 2010

This study compared UV and UV/$H_2O_2$ inactivation of E.coli, a possible indicator microorganism for fecal contamination of water, and $Q{\ss}$ phage, an indicator for pathogenic viruses. UV inactivation of $Q{\ss}$, T4 and lambda phages in actual secondary effluent was investigated, too. As a result, similar inactivation efficiency between $Q{\ss}$ phage and E.coli was observed during UV treatment, while $Q{\ss}$ phage showed higher resistance to UV/$H_2O_2$ than E.coli. $Q{\ss}$ phage resistance to UV or UV/$H_2O_2$ does not reflect those of all pathogenic viruses. However, the result tells that the use of E.coli inactivation efficiency in evaluating microbiological safety of water could not always ensure the sufficient safety from pathogenic viruses. Meanwhile, $Q{\ss}$ phage showed less resistance to UV than T4 and lambda phages, indicating that the use of $Q{\ss}$ phage as an indicator virus may bring insufficient disinfection effectiveness by causing the introduction of lower UV dose than required. Consequently, it can be thought that T4 or lambda phages would be more desirable indicators in ensuring the sufficient disinfection effectiveness for various pathogenic viruses.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.465-479
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• 2012

For $0<p{\leq}{\infty}$ and a convex body $K$ in $\mathbb{R}^n$, Lutwak, Yang and Zhang defined the concept of dual $L_p$-centroid body ${\Gamma}_{-p}K$ and $L_p$-John ellipsoid $E_pK$. In this paper, we prove the following two results: (i) For any origin-symmetric convex body $K$, there exist an ellipsoid $E$ and a parallelotope $P$ such that for $1{\leq}p{\leq}2$ and $0<q{\leq}{\infty}$, $E_qE{\supseteq}{\Gamma}_{-p}K{\supseteq}(nc_{n-2,p})^{-\frac{1}{p}}E_qP$ and $V(E)=V(K)=V(P)$; For $2{\leq}p{\leq}{\infty}$ and $0<q{\leq}{\infty}$, $2^{-1}{\omega_n}^{\frac{1}{n}}E_qE{\subseteq}{\Gamma}_{-p}K{\subseteq}{2\omega_n}^{-\frac{1}{n}}(nc_{n-2,p})^{-\frac{1}{p}}E_qP$ and $V(E)=V(K)=V(P)$. (ii) For any convex body $K$ whose John point is at the origin, there exists a simplex $T$ such that for $1{\leq}p{\leq}{\infty}$ and $0<q{\leq}{\infty}$, ${\alpha}n(nc_{n-2,p})^{-\frac{1}{p}}E_qT{\supseteq}{\Gamma}_{-p}K{\supseteq}(nc_{n-2,p})^{-\frac{1}{p}}E_qT$ and $V(K)=V(T)$.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.413-421
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• 2017

In this paper, we study the generalizations of Euler numbers and polynomials by using the q-extension with p-adic integral on $\mathbb{Z}_p$. We call these: the generalized q-${\omega}$-Euler numbers $E^{({\alpha})}_{n,q,{{\omega}}(a)$ and polynomials $E^{({\alpha})}_{n,q,{\omega}}(x;a)$. We investigate some elementary properties and relations for $E^{({\alpha})}_{n,q,{{\omega}}(a)$ and $E^{({\alpha})}_{n,q,{\omega}}(x;a)$.