• Korean Journal of Mathematics
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• v.24 no.2
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• pp.297-305
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• 2016

In this paper, by using fixed point theorem, we obtain the stability of the following functional equations $$f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)f(p,q)h(r,s)\\f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)g(p,q)h(r,s)$$, where G is a commutative semigroup, ${\theta}:G^4{\rightarrow}{\mathbb{R}}_k$ a function and f, g, h are functionals on $G^2$.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.435-447
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• 2012

Let G be a group. Let R be a G-graded commutative ring with identity and M be a G-graded multiplication module over R. A proper graded submodule Q of M is semiprime if whenever $I^nK{\subseteq}Q$, where $I{\subseteq}h(R)$, n is a positive integer, and $K{\subseteq}h(M)$, then $IK{\subseteq}Q$. We characterize semiprime submodules of M. For example, we show that a proper graded submodule Q of M is semiprime if and only if grad$(Q){\cap}h(M)=Q+{\cap}h(M)$. Furthermore if M is finitely generated then we prove that every proper graded submodule of M is contained in a graded semiprime submodule of M. A proper graded submodule Q of M is said to be almost semiprime if (grad(Q)$\cap$h(M))n(grad$(0_M){\cap}h(M)$) = (Q$\cap$h(M))n(grad$(0_M){\cap}Q{\cap}h(M)$). Let K, Q be graded submodules of M. If K and Q are almost semiprime in M such that Q + K $\neq$ M and $Q{\cap}K{\subseteq}M_g$ for all $g{\in}G$, then we prove that Q + K is almost semiprime in M.

• BMB Reports
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• v.40 no.6
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• pp.899-910
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• 2007

Extracellular Regulated Kinases (ERK) and Protein Kinase B (Akt) are intermediaries in relaying extracellular growth signals to intracellular targets. Each pathway can become activated upon stimulation of G protein-coupled receptors mediated by $G_q$ and $G_{i/o}$ proteins subjected to regulation by RGS proteins. The goal of the study was to delineate the specificity in which cardiac RGS proteins modulate $G_{q^-}$ and $G_{i/o}$-induced ERK and Akt phosphorylation. To isolate $G_{q^-}$ and $G_{i/o}$-mediated effects, we exclusively expressed muscarinic $M_2$ or $M_3$ receptors in COS-7 cells. Western blot analyses demonstrated increase of phosphorylation of ERK 1.7-/3.3-fold and Akt 2.4-/6-fold in $M_{2^-}/M_{3^-}$ expressing cells through carbachol stimulation. In co-expressions, $M_3/G_q$-induced activation of Akt was exclusively blunted through RGS3s/RGS3, whereas activation of ERK was inhibited additionally through RGS2/RGS5. $M_2/G_{i/o}$ induced Akt activation was inhibited by all RGS proteins tested. RGS2 had no effect on $M_2/G_{i/o}$-induced ERK activation. The high degree of specificity in RGS proteins-depending modulation of $G_{q^-}$ and $G_{i/o}$-mediated ERK and Akt activation in the muscarinic network cannot merely be attributed exclusively to RGS protein selectivity towards $G_q$ or $G_{i/o}$ proteins. Counter-regulatory mechanisms and inter-signaling cross-talk may alter the sensitivity of GPCR-induced ERK and Akt activation to RGS protein regulation.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.579-591
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• 2002

Let G be a finite group and $\omega$(G) the set of elements orders of G. Denote by h($\omega$(G)) the number of isomorphism classes of finite groups H satisfying $\omega$(G)=$\omega$(H). In this paper, we show that for G=PSL(3, q), h($\omega$(G))=1 where q=11, 12, 19, 23, 25 and 27 and h($\omega$(G)=2 where q = 17 and 29.

• Progress in Medical Physics
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• v.26 no.3
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• pp.178-184
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• 2015

The Markus ionization chamber(R) is a small plane parallel ionization chamber widely used in clinical electron beam dosimetry. Plane parallel chambers were recommended for low energy electron dosimetry with the beam quality at $R_{50}<4.0g/cm^2$ (${\bar{E}}{\approx}10MeV$) according to TRS-398 protocol. However, the quality correction factors ($k_{Q,Q_0}$) of the Markus chamber was not presented in TRS-398 protocol for electron beam quality at $R_{50}<2.0g/cm^2$ (${\bar{E}}{\approx}4MeV$). In this study, the $k_{Q,Q_0}$ factors of the Markus chambers (PTW-34045) for beam qualities at $R_{50}=1.0$, 1.4, 2.0, 2.5, 3.0, and $5.0g/cm^2$ were determined by Monte Carlo calculations (DOSRZnrc/EGSnrc) and the dosimetric formalism of quality correction factor. The derived $k_{Q,Q_0}$ values were evaluated using the produced data based on TRS-398 and TG-51 protocols and known values for the Markus chamber.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.433-446
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• 1999

Let G denote either of the groups $GL_2(q)$ or $SL_2(q)$. The mapping $theta$ sending a matrix to its transpose-inverse is an auto-mophism of G and therefore we can form the group $G^+$ = G.<$theta$>. In this paper conjugacy classes of elements in $G^+$ -G are found. These classes are closely related to the congruence classes of invert-ible matrices in G.

• The Korean Journal of Ecology
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• v.14 no.2
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• pp.171-179
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• 1991

In this study, the balnce of the litter production and decompsition on the forest floors in the green belt nearby seoul, which had been established in 1972, and turnover cycles of minerral nutrients were inverstigated. litter production and decomposition in the forests of quercus accutissima, q, serrata, q. mongolica, salix koreensis and alnus hirsuta were reached at the equilibium stated from 1972 to 1988 but this balance in the pine forest of pinus densiflore and p. rigida was not. Under the forests in the blance of the litter production and decomposition, the maximum amounts of n, p, k, ca and na retured to soil annually were 4.9g/㎡ in the alnus hirsuta forest, 0.35g/㎡ in the salix koreensis forest, 2.70g/㎡ in the quercus accutissima forest, 8.85g/㎡ in the s. koreensis forest and 3.93g/㎡ in the s. koreensis forest, respectively, and the minimum were 2.8g/㎡ in the s. koreensis forest, 0.108g/㎡ in the q. mongolica forest, 0.06g/㎡ in the s. koreensis forest, 2.12g/㎡ q. mongolica forest and 0.15g/㎡ in the q.accutissima forest.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.59 no.3
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• pp.385-389
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• 2014

Flavonols as a major kind of plant secondary metabolites are known for health-promoting compounds in onions (Allium cepa L.). The objectives of this study are to determine profiles of flavonol glycosides in different 75 onion accessions. A total of five flavonols (quercetin 3,4'-diglucoside, Q34'diG; quercetin 3-glucoside, Q3G; quercetin 4'-glucoside, Q4'G; isorhamnetin 4'-glucoside, I4'G; quercetin, Q) were identified from onion accessions. In positive ion mode using LC-ESI-MS, individual flavonols were confirmed from one and two glycosylation binding with aglycone such as quercetin and isorhamnetin. Total flavonol contents were distributed in white onion (range of 0.18-6.47 mg/g DW) and purple onion accessions (range of 2.39-6.47 mg/g), respectively. The mean of flavonol contents in purple onion (4.41 mg/g) showed 1.4-fold higher than white onion (3.23 mg/g). The Q34'diG and Q4'G were considered as the major compounds of flavonol glycosides in onion accessions.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.775-783
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• 2023

Van Hamme's (G.2) supercongruence modulo p⁴ for primes p ≡ 3 (mod 4) and p > 3 was first established by Swisher. A q-analogue of this supercognruence was implicitly given by the first author and Schlosser. In this paper, we present a new q-analogue of Van Hamme's (G.2) supercongruence for p ≡ 3 (mod 4).

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.941-947
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• 2009

Let q be a power of 16. Every polynomial $P\in\mathbb{F}_q$[t] is a strict sum $P=A^2+A+B^3+C^3+D^3+E^3$. The values of A,B,C,D,E are effectively obtained from the coefficients of P. The proof uses the new result that every polynomial $Q\in\mathbb{F}_q$[t], satisfying the necessary condition that the constant term Q(0) has zero trace, has a strict and effective representation as: $Q=F^2+F+tG^2$. This improves for such q's and such Q's a result of Gallardo, Rahavandrainy, and Vaserstein that requires three polynomials F,G,H for the strict representation $Q=F^2$+F+GH. Observe that the latter representation may be considered as an analogue in characteristic 2 of the strict representation of a polynomial Q by three squares in odd characteristic.