• Honam Mathematical Journal
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• v.31 no.4
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• pp.515-527
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• 2009

Let R be a commutative ring with identity. Then we prove $M_n(R)=GL_n(R)$ ${\cup}${$A{\in}M_n(R)\;{\mid}\;detA{\neq}0$ and det $A{\neq}U(R)$}${\cup}Z(M-n(R))$ where U(R) denotes the set of all units of R. In particular, it will be proved that the full matrix ring $M_n(F)$ over a field F is the disjoint union of the general linear group $GL_n(F)$ of degree n over the field F and the set $Z(M_n(F))$ of all zero-divisors of $M_n(F)$. Using the result and universal mapping property we prove that $M_n(F)$ is its total ring of fractions.

• Radiation Oncology Journal
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• v.16 no.2
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• pp.115-123
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• 1998

Purpose : This study was tried to evaluate the effect of the partial body fractionated irradiation on the frequency of chromosomal aberration. Materials and Methods : In three patients with uterine cervix carcinoma, chromosomal aberrations were analyzed during fractionated external beam radiotherapy Radiation field included whole pelvis and total dose was 5040 cGy in 28 fractions. Results : The values of the frequency of dicentrics and rings (Ydr) in pre-irradiated peripheral lymphocytes in three patients were 0.0060, 0.0000, and 0.0029, respectively. The frequency of dicentrics and rings, estimated during the course of radiotherapy, increased with radiation dose and best fitted to the linear equation, $Ydr=7.31{\times}10^{-5}D(cGy)+1.45{\times}10^{-2}$. The frequency of dicentrics and rings among the cells with dicentric and/or ring(Qdr) also showed increasing tendency and best fitted to the linear equation, $Qdr=1.01{\times}10^{-4}D(cGy)+1.04$. Conclusion : Ydr increased linearly with radiation dose in the dose range of our study, and Qdr showed increasing tendency with dose.

• Journal of Korean Society of Forest Science
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• v.89 no.1
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• pp.77-84
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• 2000

In order to understand the chemical binding forms of Cd in terms of its binding strength in wood, the radial distribution of it through dendroanalysis and its different chemical fractions in trunk wood of mature red pine(Pinus densiflora L.) trees grown in a relatively unpolluted area, in Kangwon-Province, were examined. Total Cd concentration in stem wood was determined by dry digestion and $H_2O$ and 0.01 M solutions of citric acid, malic acid, $CaCl_2$, $MgCl_2$, $Na_2EDTA$ were used as extracting solutions for Cd. Extracting efficiencies of applied solutions were expressed as % of Cd concentration extracted by $Na_2EDTA$ which extracted all Cd instead of Cd total concentration. Total concentration of Cd decreased from the innermost rings near pith towards the the outermost rings near cambium. Especially through the transition zone this tendency was observed clearly. $H_2O$ was the least effective extractant of Cd, then extracting efficiency increased in the order $MgCl_2$ < $CaCl_2$ $Na_2EDTA$ (extracted all Cd). According to the radial position, extracting efficiency of Cd was ranging from 7 to 30% by $H_2O$ and even from 60 to 95% by citric acid. The Cd extracting efficiencies of $H_2O$ and organic acids increased continuously from the stem center to outermost annual rings, whereas salts showed somewhat different tendency, suddenly decreasing near the outermost ring. The results are discussed with regard to the different chemical binding forms of Cd and the mobility of Cd in wood and comparable with ones in previous studies on Pinus sylvestris and Quercus patraea. According to the results, usefulness of radial distribution pattern of Cd in pine tree trunks for retrosective biomonitoring is questioned.