• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.41-51
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• 2007

Let R be a ring with left identity e and suitably-restricted additive torsion, and Z(R) its center. Let H : $R{\times}R{\times}R{\rightarrow}R$ be a symmetric 3-additive mapping, and let h be the trace of H. In this paper we show that (i) if for each $x{\in}R$, $$n=<<\cdots,\;x>,\;\cdots,x>{\in}Z(R)$$ with $n\geq1$ fixed, then h is commuting on R. Moreover, h is of the form $$h(x)=\lambda_0x^3+\lambda_1(x)x^2+\lambda_2(x)x+\lambda_3(x)\;for\;all\;x{\in}R$$, where $\lambda_0\;{\in}\;Z(R)$, $\lambda_1\;:\;R{\rightarrow}R$ is an additive commuting mapping, $\lambda_2\;:\;R{\rightarrow}R$ is the commuting trace of a bi-additive mapping and the mapping $\lambda_3\;:\;R{\rightarrow}Z(R)$ is the trace of a symmetric 3-additive mapping; (ii) for each $x{\in}R$, either $n=0\;or\;<n,\;x^m>=0$ with $n\geq0,\;m\geq1$ fixed, then h = 0 on R, where denotes the product yx+xy and Z(R) is the center of R. We also present the conditions which implies commutativity in rings with identity as motivated by the above result.

• The Journal of the Petrological Society of Korea
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• v.25 no.4
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• pp.311-324
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• 2016

The characteristics of the rock cleavage in Jurassic granite from Geochang were analysed. The evaluation for three quarrying planes and three rock cleavages was performed using the parameters such as (1) reduction ratio between the value of spacing and the value of length, (2) microcrack spacing frequency(N), (3) total spacing($1mm{\geq}$), (4) exponential constant(a), (5) magnitude of exponent(${\lambda}$), (6) mean spacing($S_{mean}$), (7) difference value($S_{mean}-S_{median}$) between mean spacing and median spacing($S_{median}$) and (8) density of spacing. Especially the close dependence between the above spacing parameters and the parameters from the spacing-cumulative frequency diagrams was derived. The discrimination factors representing three quarrying planes and three rock cleavages were acquired through these mutual contrast. The analysis results of the research are summarized as follows. First, the reduction ratios of frequency(N), mean value, median value, the above difference value($S_{mean}-S_{median}$) and density for three rock cleavages are in orders of G(grain, (G1 + G2)/2) < H(hardway, (H1 + H2)/2) < R(rift, (R1 + R2)/2), H < G $\ll$ R, H < G $\ll$ R, H < G < R and H < G $\ll$ R. The values of the above five parameters for three planes show the various orders of R'(rift plane) $\ll$ H'(hardway plane) < G'(grain plane), R' $\ll$ G' < H', R' < H' < G', R' < G' < H' and R' $\ll$ H' < G', respectively. Second, the values of (I) parameters(2, 3, 4 and 5) and (II) parameters(6, 7 and 8) are in orders of (I) H < G < R and (II) R < G < H. On the contrary, the values of the above two groups(I~II) of parameters for three planes show reverse orders. Third, to review the overall characteristics of the arrangement among the six diagrams, these diagrams show an order of R2 < R1 < G2 < G1 < H2 < H1 from the related chart. In other words, above six diagrams can be summarized in order of rift(R1 + R2) < grain(G1 + G2) < hardway(H1 + H2). These results indicate a relative magnitude of rock cleavage related to microcrack spacing. Especially, two parameters for each diagram, the above difference value($S_{mean}-S_{median}$) and mean spacing, could provide advanced information for prediction the order of arrangement among the diagrams. Finally, the general chart for three planes and three rock cleavages were made. From the related chart, three exponential straight lines for three rock cleavages show an order of R(R1 + R2) < G(G1 + G2) < H(H1 + H2). On the contrary, three lines for three planes show an order of H'(R2 + G2) < G'(R1 + H2) < R'(G1 + H1). Consequently, correlation of the mutually reverse order between three planes and three rock cleavages can be drawn from the related chart.

• Journal of the Ergonomics Society of Korea
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• v.17 no.3
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• pp.1-11
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• 1998

Focuses of this study are to investigate the usage status of head-restraint system(H/R) in usual driving and to simulate usage conditions of H/R at rear-end crashes. The usage of H/R was categorized into five classes according to the height and distance from occupant's head ; Large-$90^{\circ}$ H/R for enough height and short distance. Large-$70^{\circ}$ H/R for enough height and long distance. Small-$90^{\circ}$ H/R for low height and short distance. Small-$70^{\circ}$ H/R for low height and long distance. and No H/R. Then. these five conditions were tested to find out the degree of neck injuries by using a car-crash simulation package, DYNAMAN. Results from the investigation of H/R usage show that most of drivers(60%) have Small-$70^{\circ}$ H/R for low height and long distance. Results from the simulation performed at 15mph and 30mph show that: 1) at 15 mph, there is a possibility for neck injury in Small-$90^{\circ}$ H/R and Small-$70^{\circ}$ H/R. 2) at 30 mph. there is a high possibility of death in Small-$70^{\circ}$ H/R and Small-$90^{\circ}$ H/R.

• Food Science of Animal Resources
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• v.25 no.3
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• pp.310-315
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• 2005

The changes in pH, temperature, R-values and ${\mu}-calpain$ and its inhibitor activity of M. longissimus from Hanwoo steer were investigated at 1, 3, 9 and 24h postmortem. The pH and temperature of M. longissimus were significantly (p<0.05) decreased during 24h postmortem time, and were 6.50 and $31.99^{\circ}C$, respectively, at 3h postmortem. $R_{248}\;and\;R_{250}$ were increased, but $R_{258}$ was decreased after 9h postmortem time (p<0.05). Calpain I and calpastatin activity were decreased after 3h and 9h postmortem time, respectively (p<0.05). pH and temperature showed high positive correlations with $R_{258}$ (r=0.967 and r=0.970, respectively), calpain I (r =0.956 and r=0.954, respectively) and calpastatin (r=0.978 and r=0.986, respectively) but had high negative correlations with $R_{248}$ (r=-0.982 and r=-0.973, respectively) and $R_{248}$ (r=-0.983 and r=-0.976, respectively). from these results, the change of postmortem metabolism of M. longissimus from Hanwoo steer likely occurred after 9h postmortem time. However, the further study on the establishment of metabolism from Hanwoo between postmortem 3h and 9h are necessary to produce Hanwoo beef with high acceptance in meat quality.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1733-1757
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• 2017

Let $R={\oplus}_{{\alpha}{\in}{\Gamma}}R_{\alpha}$ be an integral domain graded by an arbitrary torsionless grading monoid ${\Gamma}$, ${\bar{R}}$ be the integral closure of R, H be the set of nonzero homogeneous elements of R, C(f) be the fractional ideal of R generated by the homogeneous components of $f{\in}R_H$, and $N(H)=\{f{\in}R{\mid}C(f)_v=R\}$. Let $R_H$ be a UFD. We say that a nonzero prime ideal Q of R is an upper to zero in R if $Q=fR_H{\cap}R$ for some $f{\in}R$ and that R is a graded UMT-domain if each upper to zero in R is a maximal t-ideal. In this paper, we study several ring-theoretic properties of graded UMT-domains. Among other things, we prove that if R has a unit of nonzero degree, then R is a graded UMT-domain if and only if every prime ideal of $R_{N(H)}$ is extended from a homogeneous ideal of R, if and only if ${\bar{R}}_{H{\backslash}Q}$ is a graded-$Pr{\ddot{u}}fer$ domain for all homogeneous maximal t-ideals Q of R, if and only if ${\bar{R}}_{N(H)}$ is a $Pr{\ddot{u}}fer$ domain, if and only if R is a UMT-domain.

• The Journal of the Petrological Society of Korea
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• v.25 no.2
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• pp.151-163
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• 2016

The characteristics of the rock cleavage in Jurassic granite from Geochang were analysed. The evaluation for the three directions of rock cleavages was performed using the parameters such as (1) frequency of microcrack spacing(N), (2) total spacing(${\leq}1mm$), (3) mean spacing($S_{mean}$), (4) difference value($S_{mean}-S_{median}$) between mean spacing($S_{mean}$) and median spacing($S_{median}$), (5) density of spacing(${\rho}$), (6) difference value between two exponents for the whole range of the diagrams(${\lambda}_H-{\lambda}_L$), (7) mean value of exponent(${\lambda}_M$), (8) mean value of exponential constant($a_M$), (9) difference value between two exponents for the section under the initial points of intersection(${\lambda}t_H-{\lambda}t_L$), (10) mean value of exponent(${\lambda}t_M$) and (11) mean value of exponential constant($at_M$). The results of correlation analysis between the values of parameters for three rock cleavages and those for three planes are as follows. The values of (I) parameters(1, 2, 7 and 8) and (II) parameters(3, 4 and 5) are in orders of (I) H(hardway, (H1 + H2)/2) < G(grain, (G1 + G2)/2) < R(rift, (R1 + R2)/2) and (II) R < G < H. On the contrary, the values of the above two groups(I~II) of parameters for three planes show reverse orders. Besides, the values of parameter $6({\lambda}_H-{\lambda}_L)$, parameter $9({\lambda}t_H-{\lambda}t_L)$, parameter $10({\lambda}t_M)$ and parameter $11(at_M)$ for three planes are in orders of R(rift plane, (G1 + H2)/2) < H(hardway plane, (R2 + G2)/2) < G(grain plane, (R1 + H2)/2), H < G < R, H < R < G and R < H < G, respectively. The values of the above four parameters for three rock cleavages show the various orders of R < H < G, R < H < G, H < G < R and H < G < R, respectively. Meanwhile, the spacing values equivalent to the initial points of contact and intersection between the two directions of diagrams were derived. The above spacing values for three rock cleavages are in order of rift(R1 and R2) < grain(G1 and G2) < hardway(H1 and H2). The spacing values for three planes are in order of rift plane(G1 and H1) < hardway plane(R2 and G2) < grain plane(R1 and H2). In particular, the intersection angles for three rock cleavages and three planes are in order of rift and rift plane < hardway and hardway plane < grain and grain plane. Consequently, the two diagrams of rift(R1 and R2) and rift plane(G1 and H1) show higher frequency of the point of contact and intersection. These characteristics of change were derived through the general chart for three planes and three rock cleavages. Lastly, the correlation analysis through the values of parameters along with the distribution pattern is useful for discriminating three quarrying planes.

• The Korean Journal of Zoology
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• v.19 no.3
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• pp.113-122
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• 1976

The rate of $^{3}H$-thymidine uptake induced by MMS in asynchronous HeLa $S_3$ suspension cells was decreased in direct proprotion to dose increase. The combined treatment of BUdR or IUdR with MMS was more effective in reducing the rate of $^{3}H$-thymidine uptake. MMS-stimulated $^{3}H$-thymidine uptake was detected in synchronized $G_2$ stage cells of HeLa $S_3$ suspension cultures following treatment with thymidine double shock. BUdR and IUdR greatly enhanced MMS-stimulated $^{3}H$-thymidine uptake. IUdR was found to be a more effective sensitizer than BUdR in this respect.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1523-1528
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• 2018

For $r{\geq}2$, let ${\mathcal{H}}$ be an r-uniform hypergraph with n vertices and m hyperedges. Let R be a random vertex set obtained by choosing each vertex of ${\mathcal{H}}$ independently with probability p. Let ${\mathcal{H}}[R]$ be the subhypergraph of ${\mathcal{H}}$ induced on R. We obtain an upper bound on the matching number ${\nu}({\mathcal{H}}[R])$ and a lower bound on the independence number ${\alpha}({\mathcal{H}}[R])$ of ${\mathcal{H}}[R]$. First, we show that if $mp^r{\geq}{\log}\;n$, then ${\nu}(H[R]){\leq}2e^{\ell}mp^r$ with probability at least $1-1/n^{\ell}$ for each positive integer ${\ell}$. It is best possible up to a constant factor depending only on ${\ell}$ if $m{\leq}n/r$. Next, we show that if $mp^r{\geq}{\log}\;n$, then ${\alpha}({\mathcal{H}}[R]){\geq}np-{\sqrt{3{\ell}np\;{\log}\;n}-2re^{\ell}mp^r$ with probability at least $1-3/n^{\ell}$.

• Electrical & Electronic Materials
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• v.4 no.2
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• pp.123-131
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• 1991

SiH$_{4}$환원에 의한 selective CVD-W 공정에서 SiH$_{4}$ 유속의 W막 특성에 대한 효과를 조사하였다. 0.7$_{4}$/SW$_{2}$(=R)<0.9에서 .betha.-W이 나타나기 시작하여 SiH$_{4}$ 유속의 증가에 따라 .betha.-W의 함량은 게속 증가한다. W막의 표면 형태도 SiH$_{4}$유속의 증가에 따라 나뭇잎 모양(R<0.5), 흐릿하고 불안정한 모양(0.70.9에서는 주상의 결정립을 나타낸다. R.leq.0.7에서는 .alpha.-W만 존재하다가 0.7$_{4}$유속의 증가에 따라 증착속도와 W막의 정기저항이 증가한다. 특히, R.geq.0.9에서 전기저항이 급증한다. SiH$_{4}$유속의 증가에 따라 선택성이 악화되며 특히 1.1

• 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.