• 대한수학회보
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• 제30권1호
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• pp.71-77
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• 1993

Every ring considered in the paper will be assumed to be commutative and have a unit element. An ideal A of a ring R will be called primal if the elements of R which are zero divisors modulo A, form an ideal of R, say pp. If A is a primal ideal of R, P is called the adjoint ideal of A. The adjoint ideal of a primal ideal is prime [2]. The definition of primal ideals may also be formulated as follows: An ideal A of a ring R is primal if in the residue class ring R/A the zero divisors form an ideal of R/A. If Q is a primary idel of a ring R then every zero divisor of R/Q is nilpotent; therefore, Q is a primal ideal of R. That a primal ideal need not be primary, is shown by an example in [2]. Let R[X], and R[[X]] denote the polynomial ring and formal power series ring in an indeterminate X over a ring R, respectively. Let S be a multiplicative system in a ring R and S$^{-1}$ R the quotient ring of R. Let Q be a P-primary ideal of a ring R. Then Q[X] is a P[X]-primary ideal of R[X], and S$^{-1}$ Q is a S$^{-1}$ P-primary ideal of a ring S$^{-1}$ R if S.cap.P=.phi., and Q[[X]] is a P[[X]]-primary ideal of R[[X]] if R is Noetherian [1]. We search for analogous results when primary ideals are replaced with primal ideals. To show an ideal A of a ring R to be primal, it sufficies to show that a-b is a zero divisor modulo A whenever a and b are zero divisors modulo A.

• Tuberculosis and Respiratory Diseases
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• 제58권5호
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• pp.490-497
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• 2005

연구배경 : Paraoxonase는 산소유리기 제거효소의 하나로서, 유기인제 화합물의 독소제거에 있어서 중요한 역할을 한다. 본 연구에서는 한국인 남성에서 PON1 Q192R 유전자 다형성이 흡연과 관련하여 폐암발생에 미치는 영향을 조사하였다. 대상 및 방법 : 연구대상자는 조직 병리학적으로 폐암으로 새롭게 진단받은 남성 환자 335명과, 이들과 3세 이내에서 연령을 짝지은 동수의 대조군으로 하였다. 직접면접조사를 통하여 인적사항과 직업력 그리고 흡연력, 음주력 등을 조사하였다. TaqMan 실시간 중합 효소 연쇄반응을 이용하여 PON1 유전자 다형성을 확인하고, 폐암과 흡연 그리고 PON1 유전자 다형성 유형 사이의 상호 관련성을 통계적으로 분석하였다. 결 과 : 흡연과 PON1 유전자 Q/Q형이 폐암 발생 위험도를 유의하게 증가시켰다. 흡연자에서 PON1 Q/Q형인 사람이 Q/R 혹은 R/R형인 사람에 비하여 폐암에 대한 교차비(95% 신뢰구간)가 2.56(1.52 - 4.31)으로 폐암발생 위험도가 통계적으로 유의하게 증가하였다. 비흡연자이며 PON1 Q/R 혹은 R/R형인 사람을 비교군으로 하였을 때, 비흡연자이며 PON1 Q/Q형인 군, 흡연자이며 Q/R 혹은 R/R형인 군, 흡연자이며 Q/Q형군으로 이행할수록 대응비는 모든 세포유형에서 유의하게 증가하였다. 특히 흡연자이며 Q/Q형인 사람은 비흡연자이며 PON1 Q/R 혹은 R/R형인 사람에 비하여, 편평세포암종은 53.77(6.55 - 441.14)배, 선암종은 6.25(1.38 - 28.32)배, 소세포암종은 59.94(4.66 - 770.39) 배 더 잘 생기는 것으로 나타났다. 결 론 : 흡연과 PON1 Q/Q형은 폐암의 위험인자이며, 흡연과 PON1 Q/Q형은 조직학적 유형에 관계없이 폐암발생 위험도를 서로 상승적으로 증가시키는 것으로 판단된다.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.331-345
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• 2021

Let p(z)be a polynomial of degree n. Then Bernstein's inequality [12,18] is $${\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;n\;{\max_{{\mid}z{\mid}=1}{\mid}(z){\mid}}$$. For q > 0, we denote $${\parallel}p{\parallel}_q=\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}$$, and a well-known fact from analysis [17] gives $${{\lim_{q{\rightarrow}{{\infty}}}}\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}={\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p(z){\mid}$$. Above Bernstein's inequality was extended by Zygmund [19] into L^q norm by proving ║p'║_q ≤ n║p║_q, q ≥ 1. Let p(z) = a₀ + ∑ⁿ_𝜈=𝜇 a_𝜈z^𝜈, 1 ≤ 𝜇 ≤ n, be a polynomial of degree n having no zero in |z| < k, k ≥ 1. Then for 0 < r ≤ R ≤ k, Aziz and Zargar [4] proved $${\max\limits_{{\mid}z{\mid}=R}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;{\frac{nR^{{\mu}-1}(R^{\mu}+k^{\mu})^{{\frac{n}{\mu}}-1}}{(r^{\mu}+k^{\mu})^{\frac{n}{\mu}}}\;{\max\limits_{{\mid}z{\mid}=r}}\;{\mid}p(z){\mid}}$$. In this paper, we obtain the L^q version of the above inequality for q > 0. Further, we extend a result of Aziz and Shah [3] into L^q analogue for q > 0. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.

• 대한수학회보
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• 제56권3호
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• pp.729-743
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• 2019

In this paper, we introduce strongly quasi primary ideals which is an intermediate class of primary ideals and quasi primary ideals. Let R be a commutative ring with nonzero identity and Q a proper ideal of R. Then Q is called strongly quasi primary if $ab{\in}Q$ for $a,b{\in}R$ implies either $a^2{\in}Q$ or $b^n{\in}Q$ ($a^n{\in}Q$ or $b^2{\in}Q$) for some $n{\in}{\mathbb{N}}$. We give many properties of strongly quasi primary ideals and investigate the relations between strongly quasi primary ideals and other classical ideals such as primary, 2-prime and quasi primary ideals. Among other results, we give a characterization of divided rings in terms of strongly quasi primary ideals. Also, we construct a subgraph of ideal based zero divisor graph ${\Gamma}_I(R)$ and denote it by ${\Gamma}^*_I(R)$, where I is an ideal of R. We investigate the relations between ${\Gamma}^*_I(R)$ and ${\Gamma}_I(R)$. Further, we use strongly quasi primary ideals and ${\Gamma}^*_I(R)$ to characterize von Neumann regular rings.

• 아동학회지
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• 제36권3호
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• pp.175-194
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• 2015

The purpose of this preliminary study was to investigate the validity of the 'Attachment Q-set' as a measuring tool for 5 years attachment stability. The subjects comprised 18 boys and 15 girls aged 5 in a daycare center in G city, in Kyongnam. The instruments used in this study were 'Attachment Q-set', ASCT, and IPPA-R. Based on experts' rating, the Q-set was modified, reducing it from 90 to 75 items, and used a Likert 5-points scale. ASCT scores as well as types were compared with the scores of the Q-set and IPPA-R. The attachment type was classified into either secure or insecure. The IPPA-R score of the secure infants was significantly higher than the insecure, and correlated with the ASCT score. However, there was no significant correlation between the Q-set score with the attachment types or the ASCT scores. The Q-set scores were partially correlated with the IPPA-R. This results were discussed in terms of the Q-set's invalidity for rating attachment levels of 5 years as well as the limitations imposed by the subjects' restrictive numbers.

• 대한수학회지
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• 제38권1호
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• pp.101-123
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• 2001

For a linear operator Q from R(sup)d into R(sup)d and 0$\alpha$ and parameter b on the other. characterization of strictly (Q,b)-semi-stable distributions among (Q,b)-semi-stable distributions is made. Existence of (Q,b)-semi-stable distributions which are not translation of strictly (Q,b)-semi-stable distribution is discussed.

• 품질경영학회지
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• 제47권4호
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• pp.713-723
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• 2019

Purpose: The purpose of this study is to develop a statistical program for capability analysis of measuring system and measurement process based upon KS Q ISO 22514-7. Methods: R is a powerful open source functional programming language that provides high level graphics and interfaces to other languages. Therefore, in this study, we will develop the statistical program using R language. Results: The R program developed in this study consists of the following five modules. ① Measuring system capability analysis with Type 1 study data: MSCA_Type1.R ② Measuring system capability analysis with Linearity study(Type 4 study) data: MSCA_Type4.R ③ Measurement process capability analysis with Type 1 study & Gage R&R study data: MPCA_T1GRR.R ④ Measurement process capability analysis with Type 4 study & Gage R&R study data: MPCA_T4GRR.R ⑤ Attribute measurement processes capability analysis : AttributeMP.R Conclusion: KS Q ISO 22514-7 evaluates measuring systems and measurement processes on the basis of the measurement uncertainty that was determined according to the GUM(KS Q ISO/IEC Guide 98-3). KS Q ISO 22514-7 offers precise procedures, however, computations are more intensive. The R program of this study will help to evaluate the measurement process.

• 대한수학회논문집
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• 제10권4호
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• pp.823-829
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• 1995

In this paper, we prove that $x^{1+\frac{q-1}{5}} + ax (a \neq 0)$ is not a permutation polynomial over $F_{q^r} (r \geq 2)$ and we show some properties of $x^{1+\frac{q-1}{m}} + ax (a \neq 0)$ over $F_{q^r} (r \geq 2)$.

• 대한수학회보
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• 제42권3호
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• pp.477-484
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• 2005

Let R be a ring with an automorphism 17. An ideal [ of R is ($\sigma$-ideal of R if $\sigma$(I).= I. A proper ideal P of R is ($\sigma$-prime ideal of R if P is a $\sigma$-ideal of R and for $\sigma$-ideals I and J of R, IJ $\subseteq$ P implies that I $\subseteq$ P or J $\subseteq$ P. A proper ideal Q of R is $\sigma$-semiprime ideal of Q if Q is a $\sigma$-ideal and for a $\sigma$-ideal I of R, I$^{2}$ $\subseteq$ Q implies that I $\subseteq$ Q. The $\sigma$-prime radical is defined by the intersection of all $\sigma$-prime ideals of R and is denoted by P$_{(R). In this paper, the following results are obtained: (1) For a principal ideal domain R, P$_{(R) is the smallest $\sigma$-semiprime ideal of R; (2) For any ring R with an automorphism $\sigma$ and for a skew Laurent polynomial ring R[x, x$^{-1}$; $\sigma$], the prime radical of R[x, x$^{-1}$; $\sigma$] is equal to P$_{(R)[x, x$^{-1}$; $\sigma$ ].

• 대한수학회보
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• 제61권4호
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• pp.959-968
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• 2024

Suppose f belongs to the Bloch space with f(0) = 0. For 0 < r < 1 and 0 < p < ∞, we show that $$M_p(r,\,f)\,=\,({\frac{1}{2\pi}}{\int_{0}^{2\pi}}\,{\mid}f(re^{it}){\mid}^pdt)^{1/p}\,{\leq}\,({\frac{{\Gamma}(\frac{p}{2}+1)}{{\Gamma}(\frac{p}{2}+1-k)}})^{1/p}\,{\rho}{\mathcal{B}}(log\frac{1}{1-r^2})^{1/2},$$ where ρʙ(f) = sup_z∈ⅅ(1 - |z|²)|f'(z)| and k is the integer satisfying 0 < p - 2k ≤ 2. Moreover, we prove that for 0 < r < 1 and p > 1, $${\parallel}f_r{\parallel}_{B_q}\,{\leq}\,r\,{\rho}{\mathcal{B}}(f)(\frac{1}{(1-r^2)(q-1)})^{1/q},$$ where f_r(z) = f(rz) and ||·||ʙ_q is the Besov seminorm given by ║f║ʙ_q = (∫_𝔻 |f'(z)|^q(1-|z|²)^q-2dA(z)). These results improve previous results of Clunie and MacGregor.