• Journal of radiological science and technology
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• v.39 no.1
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• pp.1-11
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• 2016

The purpose of this study was to provide resources for medical exposure reduction through evaluation of organ dose and image resolution for lumbar spine around according to the size of the collimator in DR system. The size of the collimator were varied from $8^{\prime\prime}{\times}17^{\prime\prime}$ to $14^{\prime\prime}{\times}17^{\prime\prime}$ by 1" in AP and lateral projection for the lumbar spine radiography with RANDO phantom. The organ dose measured for liver, stomach, pancreas, kidney and gonad by the glass dosimeter. The image resolution was analyzed using the Image J program. The organ dose of around lumbar spine were reduced as the size of the collimator is decreased in AP projection. There were no significant changes decreasing rate whenever the size of the collimator were reduced 1" in the gonad. The organ dose showed higher on liver and kidney near the surface in lateral projection. There were decreasing rate of less than 5% in liver and kidney, but decreasing rate was 24.34% in the gonad whenever the size of the collimator were reduced 1". Organ dose difference for internal and external of collimator measured $549.8{\mu}Gy$ in the liver and $264.6{\mu}Gy$ in the stomach. There were no significant changes organ dose difference that measured $1,135.1{\mu}Gy$ in the gonad. Image Quality made no difference because SNR and PSNR were over than 30 dB when the collimator size is less than $9^{\prime\prime}{\times}17^{\prime\prime}$ on AP projection and $10^{\prime\prime}{\times}17^{\prime\prime}$ on lateral projection. Therefore, we are considered that the recommendations criterion for control of collimator were suggested in order to reduce unnecessary X-ray exposure and to obtain good image quality because lumbar spine radiography contains a lot of peripheral organs rather than other area radiography.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.395-404
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• 2005

Let α be a complex number with 𝕽α > 0. Let the functions f and g be analytic in the unit disc E = {z : |z| < 1} and normalized by the conditions f(0) = g(0) = 0, f'(0) = g'(0) = 1. In the present article, we study the differential subordinations of the forms $${\alpha}{\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}+{\frac{zf^{\prime}(z)}{f(z)}}{\prec}{\alpha}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}}+{\frac{zg^{\prime}(z)}{g(z)}},\;z{\in}E,$$ and $${\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}{\prec}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}},\;z{\in}E.$$ As consequences, we obtain a number of sufficient conditions for star likeness of analytic maps in the unit disc. Here, the symbol ' ${\prec}$ ' stands for subordination

• Communications of Mathematical Education
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• v.33 no.3
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• pp.255-273
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• 2019

In order to help students to understand the essence of prime concepts, this study looked at the history of prime concept development and analyzed how to introduce the concept of textbooks. In ancient Greece, primes were multiplicative atoms. At that time, the unit was not a number, but the development of decimal representations led to the integration of the unit into the number, which raised the issue of primality of 1. Based on the uniqueness of factorization into prime factor, 1 was excluded from the prime, and after that, the concept of prime of the atomic context and the irreducible concept of the divisor context are established. The history of the development of prime concepts clearly reveals that the fact that prime is the multiplicative atom is the essence of the concept. As a result of analyzing the textbooks, the textbook has problems of not introducing the concept essence by introducing the concept of prime into a shaped perspectives or using game, and the problem that the transition to analytic concept definition is radical after the introduction of the concept. Based on the results of the analysis, we have provided several pedagogical implications for helping to focus on a conceptual aspect of prime number.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.341-351
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• 2009

The notion of rough sets was introduced by Z. Pawlak in the year 1982. The notion of a $\Gamma$-semigroup was introduced by M. K. Sen in the year 1981. In 2003, Y. B. Jun studied the roughness of sub$\Gamma$-semigroups, ideals and bi-ideals in i-semigroups. In this paper, we study rough prime ideals and rough fuzzy prime ideals in $\Gamma$-semigroups.

• Korean Journal of Mathematics
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• v.19 no.3
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• pp.309-319
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• 2011

We give sufficient conditions that the homogeneous differential equations : for $t{\geq}t_0$(> 0), $$x^{{\prime}{\prime}}(t)+q(t)x^{\prime}(t)+p(t)x(t)=0,\\x^{{\prime}{\prime}}(t)+q(t)x^{\prime}(t)+F(t,x({\phi}(t)))=0$$, are oscillatory where $0{\leq}{\phi}(t)$, 0 < ${\phi}^{\prime}(t)$, $\lim_{t\to{\infty}}{\phi}(t)={\infty}$. and $F(t,u){\cdot}sgn$ $u{\leq}p(t)|u|$. We obtain comparison theorems.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1183-1198
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• 2013

We will introduce and study the notion of prime bases for weakly prime submodules and utilize them to derive some formulas on the weak radical of submodules of a module. In particular, we will show that every one dimensional integral domain weakly satisfies the radical formula and state some necessary conditions on local integral domains which are semi-compatible or satisfy the radical formula and also on Noetherian rings which weakly satisfy the radical formula.

• East Asian mathematical journal
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• v.18 no.1
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• pp.15-20
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• 2002

We study the relationships between strongly prime ideals and completely prime ideals, concentrating on the connections among various radicals(prime radical, upper nilradical and generalized nilradical). Given a ring R, consider the condition: (*) nilpotent elements of R form an ideal in R. We show that a ring R satisfies (*) if and only if every minimal strongly prime ideal of R is completely prime if and only if the upper nilradical coincides with the generalized nilradical in R.

• Journal of The Korean Astronomical Society
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• v.47 no.2
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• pp.77-86
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• 2014

Using a cosmological ${\Lambda}CDM$ simulation, we analyze the differences between the widely-used spin parameters suggested by Peebles and Bullock. The dimensionless spin parameter ${\lambda}$ proposed by Peebles is theoretically well-justified but includes an annoying term, the potential energy, which cannot be directly obtained from observations and is computationally expensive to calculate in numerical simulations. The Bullock's spin parameter ${\lambda}^{\prime}$ avoids this problem assuming the isothermal density profile of a virialized halo in the Newtonian potential model. However, we find that there exists a substantial discrepancy between ${\lambda}$ and ${\lambda}^{\prime}$ depending on the adopted potential model (Newtonian or Plummer) to calculate the halo total energy and that their redshift evolutions differ to each other significantly. Therefore, we introduce a new spin parameter, ${\lambda}^{\prime\prime}$, which is simply designed to roughly recover the value of ${\lambda}$ but to use the same halo quantities as used in ${\lambda}^{\prime}$. If the Plummer potential is adopted, the ${\lambda}^{\prime\prime}$ is related to the Bullock's definition as ${\lambda}^{\prime\prime}=0.80{\times}(1+z)^{-1/12}{\lambda}^{\prime}$. Hence, the new spin parameter ${\lambda}^{\prime\prime}$ distribution becomes consistent with a log-normal distribution frequently seen for the ${\lambda}^{\prime}$ while its mean value is much closer to that of ${\lambda}$. On the other hand, in case of the Newtonian potential model, we obtain the relation of ${\lambda}^{\prime\prime}=(1+z)^{-1/8}{\lambda}^{\prime}$; there is no significant difference at z = 0 as found by others but ${\lambda}^{\prime}$ becomes more overestimated than ${\lambda}$ or ${\lambda}^{\prime\prime}$ at higher redshifts. We also investigate the dependence of halo spin parameters on halo mass and redshift. We clearly show that although the ${\lambda}^{\prime}$ for small-mass halos with $M_h$ < $2{\times}10^{12}M_{\odot}$ seems redshift independent after z = 1, all the spin parameters explored, on the whole, show a stronger correlation with the increasing halo mass at higher redshifts.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.603-612
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• 2012

In this paper, we introduce and study the intuitionistic fuzzy prime (semi-prime) ${\Gamma}$-ideals of ${\Gamma}$-LA-semigroups and some interesting properties are investigated. The main result of the paper is: if $A={\langle}{\mu}_A,{\gamma}_A{\rangle}$ is an IFS in ${\Gamma}$-LA-semigroup S, then $A={\langle}{\mu}_A,{\gamma}_A{\rangle}$ is an intuitionistic fuzzy prime (semi-prime) ${\Gamma}$-ideal of S if and only if for any $s,t{\in}[0,1]$, the sets $U({\mu}_A,s)=\{x{\in}S:{\mu}_A(x){\geq}s\}$ and $L({\gamma}_A,t)=\{x{\in}S:{\gamma}_A(x){\leq}t\}$ are prime (semi-prime) ${\Gamma}$-ideals of S.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.809-813
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• 2012

We introduce the notion of R($g$, $g^{\prime}$)-continuity on generalized topological spaces, which is a strong form of ($g$, $g^{\prime}$)-continuity. We investigate some properties and relationships among R($g$, $g^{\prime}$)-continuity, ($g$, $g^{\prime}$)-continuity and some strong forms of ($g$, $g^{\prime}$)-continuity.