• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1127-1133
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• 2014

Let S be a nonempty subset of a ring R. A map $f:R{\rightarrow}R$ is called strong commutativity preserving on S if [f(x), f(y)] = [x, y] for all $x,y{\in}S$, where the symbol [x, y] denotes xy - yx. Bell and Daif proved that if a derivation D of a semiprime ring R is strong commutativity preserving on a nonzero right ideal ${\rho}$ of R, then ${\rho}{\subseteq}Z$, the center of R. Also they proved that if an endomorphism T of a semiprime ring R is strong commutativity preserving on a nonzero two-sided ideal I of R and not identity on the ideal $I{\cup}T^{-1}(I)$, then R contains a nonzero central ideal. This short note shows that the conclusions of Bell and Daif are also true without the additivity of the derivation D and the endomorphism T.

• Korean Journal of Optics and Photonics
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• v.4 no.1
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• pp.1-8
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• 1993

A design of four-mirror optical system with reduction magnification 5X for deep UV ($\lambda$=248 nm of KrF excimer laser) submicron lithography is presented. Initially by using the paraxial quantities, the domain of solution for $t=d_1+d_2+d_3$<0 (d;: distance between the mirror $c_i$ and $c_{i+1}$ is found for the system which is free from the four off-axial Seidel first order aberrations that are coma, astigmatism, field curvature, and distortion. The solution with $d_5$=2.95 (normalized with respect to $c_i$= -1) is choosen and the aspherization is carried out to the spherical mirror surfaces ($c_3$ and $c_4$ in order to reduce the axial and residual off-axial higher order aberrations. The numerical aperture of the final system is as large as 0.4, which gives Rayleigh resolution of 0.38 $\mu\textrm{m}$.

• Journal of Korean society of Dental Hygiene
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• v.10 no.2
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• pp.311-322
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• 2010

Objectives : Since the program about sodium lauryl sulfate that might cause oral dryness and taste change including oral tissue allergy was on the air, the ingredients of D.I.Y dentifrices without sodium lauryl sulfate have been sold in online shopping mall and ordinary people can make the dentifrices easily. But there have not been any reports about the effect of dental plaque removal and preference about D.I.Y dentifrices. Therefore, this study was designed as a pilot study which aimed to investigate the effect of dental plaque removal and prefernece about D.I.Y dentifrices. Methods : 6 subjects were collected to test the effect of dental plaque removal with D.I.Y dentifrices with written consent. They didn't brushed the teeth during 12 hours until the check-up time on the next day. The O'leary index was calculated in baseline, 1 minute, 2 minute, 3 minute after brusing with D.I.Y dentifrices and market dentifrices. The preference about D.I.Y dentifrices through self-administered questionnaire was surveyed in 51 subjects after using D.I.Y dentifrices. Results : 1. The market dentifrices could remove larger amount of dental plaque than D.I.Y dentifrices, but, it wasn't significant. 2. In feeling refreshment, the market dentifrices had more positive answers significantly. 3. In feeling taste change, the market dentifries had more duration of taste change significantly. 4. In feeling oral dryness, the market dentifrices had more duration of oral dryness after toothbrushing. but, it wasn't significant. 5. As a result about reviewing the dental journals about ingredients of D.I.Y dentirices, green tea, sodium carbonate, bamboo salt, propolis had each evidence. But, We could not find out the evidences of calculus adhesion by corn starch, preservative by napri, disinfectant of peppermint. Conclusions : Although we cannot find the difference of the effect of dental plaque removal between D.I.Y dentifrices and market dentifrices, and D.I.Y dentifrices have the merits of decrease of oral dryness and taste change, it was suggested to have another test about stability and safety of D.I.Y dentifrices for safety of the user of D.I.Y dentifrices.

• Journal of the Korean Statistical Society
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• v.3 no.1
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• pp.13-16
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• 1974

In my former paper [3] I defined an almost periodicity of weakly sationary random processes (a.p.w.s.p.) and presented some basic results of it. In this paper I shall present some notes on the Fourier series of an a.p.w.s.p., resulting from [3]. All the conditions at the introduction of [3] are assumed to hold without repreating them here. The essential facts are as follows : The weakly stationary process $X(t,\omega), t\in(-\infty,\infty), \omega\in\Omega$, defined on a probability space $(\Omega,a,P)$, has a spectral representation $$X(t,\omega)=\int_{-\infty}^{infty}{e^{it\lambda\xi}(d\lambda,\omega)},$$ where $\xi(\lambda)$ is a random measure. Then, the continuous covariance $\rho(\mu) = E(X(t+u) X(t))$ has the form $$\rho(u)=\int_{-\infty}^{infty}{e^{iu\lambda}F(d\lambda)},$$ $E$\mid$\xi(\lambda+0)-\xi(\lambda-0)$\mid$^2 = F(\lambda+0) - F(\lambda-0) \lambda\in(-\infty,\infty)$, assumimg that $\rho(u)$ is a uniformly almost periodic function.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• Current Research on Agriculture and Life Sciences
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• v.4
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• pp.77-86
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• 1986

The purpose of this study is to estimate an optimum formula of rainfall intensity on basis of the characteristics for short period of rainfall duration in Kyungpook province for the design of urban sewerage and small basin drain system. Results studied are as follows; 1. The optimum method for Taegu and Pohang, Iwai's and Gumbel-Chow's method are recommended respectively. 2. The opotimum type of rainfall intensity for these area, $I=\frac{a}{\sqrt{t}+b}$ (Japanese type), is confirmed with 2.52~4.17 and 1.86~4.54 as a standard deviation for Taegu and Pohang respectively. The optimum formula of rainfall intensity are as follows. Taegu : T : 200 year - $I=\frac{824}{\sqrt{t}+1.5414}$ T : 100 year - $I=\frac{751}{\sqrt{t}+1.4902}$ T : 50 year - $I=\frac{678}{\sqrt{t}+1.4437}$ T : 30 year - $I=\frac{623}{\sqrt{t}+1.4017}$ T : 20 year - $I=\frac{580}{\sqrt{t}+1.3721}$ T : 10 year - $I=\frac{502}{\sqrt{t}+1.3145}$ T : 5 year - $I=\frac{418}{\sqrt{t}+1.2515}$ Pohang : T : 200 year - $I=\frac{468}{\sqrt{t}+1.1468}$ T : 100 year - $I=\frac{429}{\sqrt{t}+1.1605}$ T : 50 year - $I=\frac{391}{\sqrt{t}+1.1852}$ T : 30 year - $I=\frac{362}{\sqrt{t}+1.2033}$ T : 20 year - $I=\frac{339}{\sqrt{t}+1.2229}$ T : 10 year - $I=\frac{299}{\sqrt{t}+1.2578}$ T : 5 year - $I=\frac{257}{\sqrt{t}+1.3026}$ 3. Significant I.D.F. curves derived should be applied to estimate a suitable rainfall intensity and rainfall duration.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.139-144
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• 2000

The generalized noncommutative torus $T_{\rho}^d$ of rank m was defined in [2]. Assume that for the completely irrational noncommutative subtorus $A_{\rho}$ of rank m of $T_{\rho}^d$ there is no integer q > 1 such that $tr(K_0(A_{\rho}))=\frac{1}{q}{\cdot}tr(K_0(A_{\rho^{\prime}}))$ for $A_{\rho^{\prime}}$ a completely irrational noncommutative torus of rank m. All $C^*$-algebras ${\Gamma}({\eta})$ of sections of locally trivial $C^*$-algebra bundles ${\eta}$ over $M=\prod_{i=1}^{e}S^{2k_i}{\times}\prod_{i=1}^{s}S^{2n_i+1}$, $\prod_{i=1}^{s}\mathbb{PR}_{2n_i}$, or $\prod_{i=1}^{s}L_{k_i}(n_i)$ with fibres $T_{\rho}^d{\otimes}M_c(\mathbb{C})$ were constructed in [6, 7, 8]. We prove that ${\Gamma}({\eta}){\otimes}M_{p^{\infty}}$ is isomorphic to $C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C}){\otimes}M_{p^{\infty}}$ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, that $\mathcal{O}_{2u}{\otimes}{\Gamma}({\eta})$ is isomorphic to $\mathcal{O}_{2u}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if and only if cd and 2u - 1 are relatively prime, and that $\mathcal{O}_{\infty}{\otimes}{\Gamma}({\eta})$ is not isomorphic to $\mathcal{O}_{\infty}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if cd > 1 when no non-trivial matrix algebra can be ${\Gamma}({\eta})$.

• Proceedings of the Botanical Society of Korea Conference
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• 1999.07a
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• pp.11-15
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• 1999

In order to evlauate feasibility of the gene tagging by the maize transposable element Ac in heterologous plant systems, we have investigated physical distances and directions of transposition of the element in Arabidopsis thaliana and tobacco cultured cell line BY-2. We prepared a T-DNA construct that carried a non-autonomous derivative of Ac with a site for cleavage by endonuclease I-Scel (designated dAc-I-RS element). Another cleavage site was also introduced into the T-DNA region outside dAc-I-RS. A number of transgenic Arabidopsis plants were generated, each of which had a single copy of the T-DNA at a different chromosomal location. To examine the pattern of transposition, three out of these transgenic plants were crossed with the Arabidopsis plant that carried the gene for Ac transposase and progeny in which dAc-I-RS had been transposed were isolated. After digestion of the genomic DNA of these progeny with I-SceI, sizes of segment of DNA were determined byd pulse-field gel electrophoresis. We also performed linkage analysis for the transposed elements and sites of mutations near the elements. Our results with three transgenic lines showed that 50% of all transposition events had occurred within 1,700 kilo-base pairs (kb) on the same chromosome, with 35% within 200 kb, and that the elements transposed in both directions on the chromosome with roughly equal probability. The data thus indicate that the Ac-Ds system is most useful for tagging of genes that are present within 200 kb of the chromosomal site of Ac in Arabidopsis. In addition, determination of the precise localization of the transposed dAc-I-RS element should definitely assist in map-based cloning of genes around insertion sites. In the present paper, we report typical examples of such gene isolation studies.

• Proceedings of the Botanical Society of Korea Conference
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• 1985.08b
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• pp.51-57
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• 1985

In order to evlauate feasibility of the gene tagging by the maize transposable element Ac in heterologous plant systems, we have investigated physical distances and directions of transposition of the element in Arabidopsis thaliana and tobacco cultured cell line BY-2. We prepared a T-DNA construct that carried a non-autonomous derivative of Ac with a site for cleavage by endonuclease I-Scel (designated dAc-I-RS element). Another cleavage site was also introduced into the T-DNA region outside dAc-I-RS. A number of transgenic Arabidopsis plants were generated, each of which had a single copy of the T-DNA at a different chromosomal location. To examine the pattern of transposition, three out of these transgenic plants were crossed with the Arabidopsis plant that carried the gene for Ac transposase and progeny in which dAc-I-RS had been transposed were isolated. After digestion of the genomic DNA of these progeny with I-SceI, sizes of segment of DNA were determined byd pulse-field gel electrophoresis. We also performed linkage analysis for the transposed elements and sites of mutations near the elements. Our results with three transgenic lines showed that 50% of all transposition events had occurred within 1, 700 kilo-base pairs (kb) on the same chromosome, with 35% within 200 kb, and that the elements transposed in both directions on the chromosome with roughly equal probability. The data thus indicate that the Ac-Ds system is most useful for tagging of genes that are present within 200 kb of the chromosomal site of Ac in Arabidopsis. In addition, determination of the precise localization of the transposed dAc-I-RS element should definitely assist in map-based cloning of genes around insertion sites. In the present paper, we report typical examples of such gene isolation studies.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.6
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• pp.88-97
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• 1994

We describe the design, fabrication, and performance of the optical fiber-photodiode 1$\times$12 arry module using mesa-type InS10.53T GaS10.47TAS/INP 1$\times$12 PIN photodiode array. We fabricated the PIN PD array for high-speed optical fiber parallel data link optimizing quantum efficiency, operating speed sensitivity from the PIN-FET structure, and electrical AC crosstalk. For each element of the array, the diameter of the photodetective area is 80 $\mu$m, the diameter of the p-metal pad is 90 $\mu$m, and the photodiode seperation is 250 $\mu$m to use Si v-groove. Ground conductor line is placed around diodes and p-metal pads are formed in zigzag to reduce Ac capacitance coupling between array elements. The dark current (IS1dT) is I nA and the capacitance(CS1pDT) is 0.9 pF at -5 V. No signifcant variations of IS1dT and CPD from element to element in the array were observed. We calulated the coupling efficiency for 10/125 SMF and 50/125 GI MMF, and measured the responsivity of the PD array at the wavelength is 1.55 $\mu$ m. Responsivities are 0.93 A/W for SMF and 0.96 A/W for MMF. The optical fiber-PD array module is useful in numerous high speed digital and analog photonic system applications.