• 호남수학학술지
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• 제34권1호
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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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• 제24권1호
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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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• 제26권2호
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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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• 한국정보디스플레이학회 2008년도 International Meeting on Information Display
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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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• 제20권4호
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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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• 제46권4호
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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 $J_2^r(S)=S{\cap}J_2^r(R)$.

• 대한수학회보
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• 제58권6호
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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.

• 대한화학회지
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• 제35권5호
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• pp.493-499
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• 1991

여러 가지 유기용매에서 서로 다른 대이온을 가진 trans-$[Co(R,R-chxn)_2Cl_2]^+$착물의 원편광이색성(CD) 스펙트럼을 측정하였다. 여기서 R,R-chxn은 (1R,2R)-1,2-diaminocyclohexane 이다. 착물의 CD 스펙트럼에서 관찰된 변화는 현저한 용매의존성을 나타내었다. 그리고 첫 흡수띠 영역$(^1A_{2g})$에서 CD 스펙트럼의 변화 정도는 용매의 donor number(DN)에 의존하였다. trans-[Co(R,R-chxn)$_2Cl_2]^+$ 착물의 CD 스펙트럼 변화는 $^1H$ NMR 스펙트럼으로부터 R,R-chxn 리간드 중의 수평방향의 N-H 수소와 용매분자와의 우선적인 상호작용에 기인되는 것으로 해석되었다.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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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 $n{\geq}7r^2+9r-26$.

• 대한수학회지
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• 제45권2호
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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.