• Honam Mathematical Journal
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• v.34 no.1
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• pp.45-54
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• 2012

In this paper, we prove stabilities of multiplicative functional equations in three variables such as $r(\frac{x+y+z}{3})-r(x+y+z)$=$\frac{2r(\frac{x+y}{2})r(\frac{y+z}{2})r(\frac{z+x}{2})}{r(\frac{x+y}{2})r(\frac{y+z}{2})+r(\frac{y+z}{2})r(\frac{z+x}{2})+r(\frac{z+x}{2})r(\frac{x+y}{2})}$ and $r(\frac{x+y+z}{3})+r(x+y+z)$=$\frac{4r(\frac{x+y}{2})r(\frac{y+z}{2})r(\frac{z+x}{2})}{r(\frac{x+y}{2})r(\frac{y+z}{2})+r(\frac{y+z}{2})r(\frac{z+x}{2})+r(\frac{z+x}{2})r(\frac{x+y}{2})}$.

• Asian-Australasian Journal of Animal Sciences
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• v.24 no.1
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• pp.125-129
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• 2011

The aim was to determine the relationship between muscle structure and meat quality traits in neuromuscular compartments (NMCs: R1, R2, R3, R4) of pig semitendinosus muscle. Barrows from the INTA-MGC genetic line (Argentina) were slaughtered at 100 kg body weight. In each NMC the following parameters were determined: the fibre types I, IIA, IIX and IIB by immunohistochemistry, the fibre cross sectional area (FCSA), the pH of meat after 24 h post-mortem ($pH_{24}$), instrumental meat tenderness (WB) and colour ($L^*$, $a^*$, $b^*$). There were significant differences in the following: $L^*$ (R1 = R4$a^*$ (R1>R4>R2 = R3), $b^*$ (R1 = R4R1 = R3 = R4), $pH_{24}$ (R1 = R4>R2 = R3). The relative percentages of FCSA were as follows: I (R4>R1>R3>R2), IIA (R1>R4>R3>R2), IIX (R1 = R2 = R3 = R4) and IIB (R2>R3>R1>R4). The correlation values were statistically significant between IIB and WB (R1 and R4, $r_s$ = 0.66), (R2 and R3 $r_s$ = 0.74), IIB and $L^*$ (R1 and R4 $r_s$ = 0.84), IIX and $L^*$ without discriminating NMCs. Our data suggest that the NMC where the sampling takes place is important for determining meat quality traits because of the heterogeneity of the whole muscle.

• Bulletin of the Korean Chemical Society
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• v.26 no.2
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• pp.233-237
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• 2005

Cyclopentadiene compounds, 2-[CR'R(OMe)]-1,3-Me$_2C_5H_3$ (R, R' = 2,2'-biphenyl, 2) and 2-[CR'R(OSiMe$_3$)]-1,3-Me$_2C_5H_3$ (R, R' = 2,2'-biphenyl, 3; R = ph, R' = ph, 4; R = 2-naphthyl, R' = H, 5) are readily synthesized from 2-bromo-3-methoxy-1,3-dimethylcyclopentene (1). Reaction of the cyclopentadienes with Ti(NMe$_2$)$_4$ in toluene results in clean formation of the cyclopentadienyl tris(dimethylamido)titanium complexes, which are transformed to the trichloride complexes, 2-[CR'R(OMe)]-1,3-Me$_2C_5H_2$}TiCl$_3$ (R, R' = 2,2'-biphenyl, 6) and {2-[CR'R(OSiMe$_3$)]-1,3-Me$_2C_5H_2$}TiCl$_3$ (R, R' = 2,2'-biphenyl, 7; R = ph, R' = ph, 8; R = 2-naphthyl, R' = H, 9). Attempts to form C1-bridged Cp/oxido complexes by elimination of MeCl or Me$_3$SiCl were not successful. X-ray structures of 6, 7 and an intermediate complex {2-[Ph$_2$C(OSiMe$_3$)]-1,3-Me$_2C_5H_2$}TiCl$_2$(NMe$_2$) (10) were determined.

• 한국정보디스플레이학회:학술대회논문집
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• 2008.10a
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• pp.247-249
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• 2008

Low Temperature a-Si:H TFT on stainless steel substrate has been developed for the flexible electrophoretic display. Stability of low temperature a-Si:H TFT is more important point than its initial device characteristics. Thus, we have studied device characteristics of low temperature a-Si:H TFT in terms of stability for driving electrophoretic display.

• Bulletin of the Korean Chemical Society
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• v.20 no.4
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• pp.427-430
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• 1999

The Grignard coupling reaction of bis(chloromethyl)diorganosilanes [(ClCH2)2SiR1R2: R1 = R2 = Me, la; R1 = Me, R2 = Ph, lb; R1 = R2 = Ph, lc] with diorganodichlorosilanes [(Cl2SiR3R4: R3 = R4 = Me, 2a; R3 = Me, R4 = Ph, 2b; R3 = R4 = Ph, 2c] at THE reflux temperature gave the intermolecular C-Si coupling product of 1,1,3,3-tetraorgano-1,3-disilacyclobutanes 3a-f in poor to moderate yields ranging from 7% to 50% along with polydiorganosilapropanes. The cyclization reaction of la-c with methyl-substituted dichlorosilanes 2a, b gave 1,3-disilacyclobutanes 3a-c, e, d in moderate yields (42-50%), while the same reaction with dichlorodiphenylsilane (2c) to 1,3-disilacyclobutanes 3d, f resulted in low yield (7-18%) probably due to the steric hindrance of two-phenyl groups on the silicon of 2c.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.603-613
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• 2006

Near-rings considered are right near-rings and R is a near-ring. $J_0^r(R)$, the right Jacobson radical of R of type-0, was introduced and studied by the present authors. In this paper $J_1^r(R)$ and $J_2^r(R)$, the right Jacobson radicals of R of type-1 and type-2 are introduced. It is proved that both $J_1^r$ and $J_2^r$ are radicals for near-rings and $J_0^r(R){\subseteq}J_1^r(R){\subseteq}J_2^r(R)$. Unlike the left Jacobson radical classes, the right Jacobson radical class of type-2 contains $M_0(G)$ for many of the finite groups G. Depending on the structure of G, $M_0(G)$ belongs to different right Jacobson radical classes of near-rings. Also unlike left Jacobson-type radicals, the constant part of R is contained in every right 1-modular (2-modular) right ideal of R. For any family of near-rings $R_i$, $i{\in}I$, $J_{\nu}^r({\oplus}_{i{\in}I}R_i)={\oplus}_{i{\in}I}J_{\nu}^r(R_i)$, ${\nu}{\in}\{1,2\}$. Moreover, under certain conditions, for an invariant subnear-ring S of a d.g. near-ring R it is shown that $J_2^r(S)=S{\cap}J_2^r(R)$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1341-1354
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• 2021

Let r ≥ 2, and let k_i ≥ 2 for 1 ≤ i ≤ r. Mixed van der Waerden's theorem states that there exists a least positive integer w = w(k₁, k₂, k₃, …, k_r; r) such that for any n ≥ w, every r-colouring of [1, n] admits a k_i-term arithmetic progression with colour i for some i ∈ [1, r]. For k ≥ 3 and r ≥ 2, the mixed van der Waerden number w(k, 2, 2, …, 2; r) is denoted by w₂(k; r). B. Landman and A. Robertson [9] showed that for k < r < $\frac{3}{2}$(k - 1) and r ≥ 2k + 2, the inequality w₂(k; r) ≤ r(k - 1) holds. In this note, we establish some results on w₂(k; r) for 2 ≤ r ≤ k.

• Journal of the Korean Chemical Society
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• v.35 no.5
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• pp.493-499
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• 1991

The circular dichroism (CD) spectrum of trans-[Co(R,R-chxn)$_2Cl_2]^+$ complex with different counter-ions have been measured in several organic solvents, where R,R-chxn is (1R,2R)-1,2-diaminocyclohexane. The observed variations in the CD spectrum of the complex exhibited remarkable solvent dependences. And it has been observed that the degree of the change of CD spectrum in the first absorption band region $(^1A_{2g})$ depends on the donor number (DN) of the solvents. From $^1H$ NMR spectrum, it is interpreted that these variations in the CD spectrum of trans-[Co(R,R-chxn)$_2Cl_2]^+$ complex are due to the favorable interaction between solvent molecules and the equatorial N-H protons of R,R-chxn ligands.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.49-58
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• 2009

For $1{\leq}k{\leq}r$, let ${\sigma}$($K_{r,r}$ - ke, n) be the smallest even integer such that every n-term graphic sequence ${\pi}$ = ($d_1$, $d_2$, ..., $d_n$) with term sum ${\sigma}({\pi})$ = $d_1$ + $d_2$ + ${\cdots}$ + $d_n\;{\geq}\;{\sigma}$($K_{r,r}$ - ke, n) has a realization G containing $K_{r,r}$ - ke as a subgraph, where $K_{r,r}$ - ke is the graph obtained from the $r\;{\times}\;r$ complete bipartite graph $K_{r,r}$ by deleting k edges which form a matching. In this paper, we determine ${\sigma}$($K_{r,r}$ - ke, n) for even $r\;({\geq}4)$ and $n{\geq}7r^2+{\frac{1}{2}}r-22$ and for odd r (${\geq}5$) and $n{\geq}7r^2+9r-26$.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.425-433
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• 2008

Let R be a ring with identity $1_R$ and let U(R) denote the group of all units of R. A ring R is called locally finite if every finite subset in it generates a finite semi group multiplicatively. In this paper, some results are obtained as follows: (1) for any semilocal (hence semiperfect) ring R, U(R) is a finite (resp. locally finite) group if and only if R is a finite (resp. locally finite) ring; U(R) is a locally finite group if and only if U$(M_n(R))$ is a locally finite group where $M_n(R)$ is the full matrix ring of $n{\times}n$ matrices over R for any positive integer n; in addition, if $2=1_R+1_R$ is a unit in R, then U(R) is an abelian group if and only if R is a commutative ring; (2) for any semiperfect ring R, if E(R), the set of all idempotents in R, is commuting, then $R/J\cong\oplus_{i=1}^mD_i$ where each $D_i$ is a division ring for some positive integer m and |E(R)|=$2^m$; in addition, if 2=$1_R+1_R$ is a unit in R, then every idempotent is central.