• 대한수학회보
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• 제36권3호
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• pp.543-564
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• 1999

Consider a symmetric bilinear form defined on $\prod\times\prod$ by $_{\lambda\mu}$ = $<\sigma,fg>\;+\;\lambdaL[f](a)L[g](a)\;+\;\muM[f](b)m[g](b)$ ,where $\sigma$ is a quasi-definite moment functional, L and M are linear operators on $\prod$, the space of all real polynomials and a,b,$\lambda$ , and $\mu$ are real constants. We find a necessary and sufficient condition for the above bilinear form to be quasi-definite and study various properties of corresponding orthogonal polynomials. This unifies many previous works which treated cases when both L and M are differential or difference operators. finally, infinite order operator equations having such orthogonal polynomials as eigenfunctions are given when $\mu$=0.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.583-587
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• 2008

Let $\mathfrak{L(H)}$ denote the algebra of bounded linear operators on a separable infinite dimensional complex Hilbert space $\mathfrak{H}$. We say that $T{\in}\mathfrak{L(H)}$ is a quasi-class A operator if $$T^*{\mid}T^2{\mid}T{{\geq}}T^*{\mid}T{\mid}^2T$$. In this paper we prove that if A and B are quasi-class A operators, and $B^*$ is invertible, then for a Hilbert-Schmidt operator X $$AX=XB\;implies\;A^*X=XB^*$$.

• 대한수학회보
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• 제57권2호
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• pp.371-381
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• 2020

A ring R is called right pure-injective if it is injective with respect to pure exact sequences. According to a well known result of L. Melkersson, every commutative Artinian ring is pure-injective, but the converse is not true, even if R is a commutative Noetherian local ring. In this paper, a series of conditions under which right pure-injective rings are either right Artinian rings or quasi-Frobenius rings are given. Also, some of our results extend previously known results for quasi-Frobenius rings.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1990년도 추계학술대회 논문집 학회본부
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• pp.267-271
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• 1990

This paper describes a 3-Phase Quasi-Resonant DC Link Inverter (3-phase QRI), which has two operating modes, ie. inverting mode and rectifying mode. First the 3-Phase QRI is simplified and the resonant circuit is analyzed in comparison with two resonant DC-to-DC converters. This analysis shows that the maximum voltage of resonant capacitor is limited to twice the input voltage irrespective of operating modes. A new simple control method in rectifying mode is suggested, which does not require any other element in power circuit. The characteristic of 3-Phase Quasi Resonant Inverter has been verified by simulation using the proposed control method.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권2호
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• pp.103-108
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• 2013

Observing that for any space X, there is a Wallman sublattice $\mathfrak{A}_X$ and that QFX is homeomorphic to a subspace $X_q$ of the Wallman cover $\mathfrak{L}(\mathfrak{A}_X)$ of $\mathfrak{A}_X$, we show that ${\beta}QFX$ and $\mathfrak{L}(\mathfrak{A}_X)$ are homeomorphic.

• 대한화장품학회지
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• 제43권4호
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• pp.349-355
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• 2017

피부색은 건강상태나 연령을 인식하는데 중요한 역할을 할 뿐만 아니라 선호하는 피부색에 따라 매력을 느끼는 기준이 되기도 한다. 다수의 소비자들은 자신의 피부색을 개선시키기 위해 화장품을 선택하기도 하며 이러한 수요에 따라 화장품의 종류는 다양해졌다. 최근에는 '하얗고 밝은 피부'에서 '건강하고 생기있어 보이는 피부' 등 안색의 선호가 다양해지고 관련 표현의 효능을 표방하는 화장품이 증가하고 있지만 '피부색(안색) 개선'에 대한 객관적인 평가 기준이 없어 본 연구에서는 피부색을 표현하는 형용사(complexion -describing adjectives, CDAs)를 선정하고 quasi $L^*a^*b^*$ 값을 이용한 통계분석 방법으로 피부색을 표현하는 형용사를 정량화하였다. CDA 7개['창백한(pale)', '깨끗한(clear)', '화사한(radiant)', '생기있는(lively)', '건강한(healthy)', '불그스름한(rosy)', '칙칙한(dull)']를 선별하였고 피부색을 평가한 경험이 있는 30명의 패널이 각각의 형용사를 밝은 피부 사진과 어두운 피부 사진의 색감에 적용하고 이를 다시 수치화하여 단어간에 통계적 유의성 여부를 확인하였다. 그 결과, 어두운 피부의 기준 이미지와 각각의 CDA를 반영한 조정 이미지, 밝은 피부의 기준 이미지와 각각의 CDA를 반영한 조정 이미지간의 quasi $L^*$, $a^*$, $b^*$ 값이 통계적 유의차를 보였다(p< 0.05). 그러나 같은 CDA를 반영한 밝은 피부와 어두운 피부간에는 통계적 유의차가 없었고, 비슷한 계열의 형용사 간에 그룹화되는 경향[(i)창백한-깨끗한-화사한 (ii)생기있는-건강한-불그스름한 (iii)칙칙한]을 확인하였다. 본 연구에서는 주관적인 느낌을 표현하는 형용사를 객관적 지표로 수치화하고 이를 통해 피부색을 평가하는 기준으로 활용할 수 있음을 제시하고자 한다.

• 대한수학회논문집
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• 제27권1호
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• pp.117-128
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• 2012

Using the concept of a g-monotone mapping we prove some common fixed point theorems for g-non-decreasing mappings which satisfy some generalized nonlinear contractions in partially ordered complete quasi b-metric spaces. The new theorems are generalizations of very recent fixed point theorems due to L. Ciric, N. Cakic, M. Rojovic, and J. S. Ume, [Monotone generalized nonlinear contractions in partailly ordered metric spaces, Fixed Point Theory Appl. (2008), article, ID-131294] and R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan [Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8].

• 대한수학회보
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• 제40권3호
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• pp.457-464
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• 2003

Given a Riemannian manifold (M, $\alpha$) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric $L\;=\;{\alpha}+{\beta}$, where $\beta$ is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor ($g_{ij}$) of an (a, b, f)-metric. Then we determine the maximal domain D of $TM{\backslash}O$ for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.

• 대한수학회지
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• 제51권5호
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• pp.1089-1104
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• 2014

An operator $T{\in}L(H)$, is said to belong to k-quasi class $A_n^*$ operator if $$T^{*k}({\mid}T^{n+1}{\mid}^{\frac{2}{n+1}}-{\mid}T^*{\mid}^2)T^k{\geq}O$$ for some positive integer n and some positive integer k. First, we will see some properties of this class of operators and prove Weyl's theorem for algebraically k-quasi class $A_n^*$. Second, we consider the tensor product for k-quasi class $A_n^*$, giving a necessary and sufficient condition for $T{\otimes}S$ to be a k-quasi class $A_n^*$, when T and S are both non-zero operators. Then, the existence of a nontrivial hyperinvariant subspace of k-quasi class $A_n^*$ operator will be shown, and it will also be shown that if X is a Hilbert-Schmidt operator, A and $(B^*)^{-1}$ are k-quasi class $A_n^*$ operators such that AX = XB, then $A^*X=XB^*$. Finally, we will prove the spectrum continuity of this class of operators.

• 대한수학회보
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• 제50권5호
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• pp.1433-1439
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• 2013

A ring R is called left morphic if $$R/Ra{\simeq_-}l(a)$$ for every $a{\in}R$. Equivalently, for every $a{\in}R$ there exists $b{\in}R$ such that $Ra=l(b)$ and $l(a)=Rb$. A ring R is called left quasi-morphic if there exist $b$ and $c$ in R such that $Ra=l(b)$ and $l(a)=Rc$ for every $a{\in}R$. A result of T.-K. Lee and Y. Zhou says that R is unit regular if and only if $$R[x]/(x^2){\simeq_-}R{\propto}R$$ is morphic. Motivated by this result, we investigate the morphic property of the ring $$S_n=^{def}R[x_1,x_2,{\cdots},x_n]/(\{x_ix_j\})$$, where $i,j{\in}\{1,2,{\cdots},n\}$. The morphic elements of $S_n$ are completely determined when R is strongly regular.