• Title, Summary, Keyword: G-domain

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ON SOME UNBOUNDED DOMAINS FOR A MAXIMUM PRINCIPLE

  • CHO, SUNGWON
    • The Pure and Applied Mathematics
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    • v.23 no.1
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    • pp.13-19
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    • 2016
  • In this paper, we study some characterizations of unbounded domains. Among these, so-called G-domain is introduced by Cabre for the Aleksandrov-Bakelman-Pucci maximum principle of second order linear elliptic operator in a non-divergence form. This domain is generalized to wG-domain by Vitolo for the maximum principle of an unbounded domain, which contains G-domain. We study the properties of these domains and compare some other characterizations. We prove that sA-domain is wG-domain, but using the Cantor set, we are able to construct a example which is wG-domain but not sA-domain.

*-NOETHERIAN DOMAINS AND THE RING D[X]N*, II

  • Chang, Gyu-Whan
    • Journal of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.49-61
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    • 2011
  • Let D be an integral domain with quotient field K, X be a nonempty set of indeterminates over D, * be a star operation on D, $N_*$={f $\in$ D[X]|c(f)$^*$= D}, $*_w$ be the star operation on D defined by $I^{*_w}$ = ID[X]${_N}_*$ $\cap$ K, and [*] be the star operation on D[X] canonically associated to * as in Theorem 2.1. Let $A^g$ (resp., $A^{[*]g}$, $A^{[*]g}$) be the global (resp.,*-global, [*]-global) transform of a ring A. We show that D is a $*_w$-Noetherian domain if and only if D[X] is a [*]-Noetherian domain. We prove that $D^{*g}$[X]${_N}_*$ = (D[X]${_N}_*$)$^g$ = (D[X])$^{[*]g}$; hence if D is a $*_w$-Noetherian domain, then each ring between D[X]${_N}_*$ and $D^{*g}$[X]${_N}_*$ is a Noetherian domain. Let $\tilde{D}$ = $\cap${$D_P$|P $\in$ $*_w$-Max(D) and htP $\geq$2}. We show that $D\;\subseteq\;\tilde{D}\;\subseteq\;D^{*g}$ and study some properties of $\tilde{D}$ and $D^{*g}$.

FLAT DIMENSIONS OF INJECTIVE MODULES OVER DOMAINS

  • Hu, Kui;Lim, Jung Wook;Zhou, De Chuan
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.4
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    • pp.1075-1081
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    • 2020
  • Let R be a domain. It is proved that R is coherent when IFD(R) ⩽ 1, and R is Noetherian when IPD(R) ⩽ 1. Consequently, R is a G-Prüfer domain if and only if IFD(R) ⩽ 1, if and only if wG-gldim(R) ⩽ 1; and R is a G-Dedekind domain if and only if IPD(R) ⩽ 1.

SEMISTAR G-GCD DOMAIN

  • Gmiza, Wafa;Hizem, Sana
    • Journal of the Korean Mathematical Society
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    • v.56 no.6
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    • pp.1689-1701
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    • 2019
  • Let ${\star}$ be a semistar operation on the integral domain D. In this paper, we prove that D is a $G-{\tilde{\star}}-GCD$ domain if and only if D[X] is a $G-{\star}_1-GCD$ domain if and only if the Nagata ring of D with respect to the semistar operation ${\tilde{\star}}$, $Na(D,{\star}_f)$ is a G-GCD domain if and only if $Na(D,{\star}_f)$ is a GCD domain, where ${\star}_1$ is the semistar operation on D[X] introduced by G. Picozza [12].

FACTORIZATION AND DIVISIBILITY IN GENERALIZED REES RINGS

  • Kim, Hwan-Koo;Kwon, Tae-In;Park, Young-Soo
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.3
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    • pp.473-482
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    • 2004
  • Let D be an integral domain, I a proper ideal of D, and R =D[It, $t^{-1}$] a generalized Rees ring, where t is an indeterminate. For suitable conditions, we show that R satisfies the ACCP (resp., is a BFD, an FFD, a (pre-) Schreier domain, a G-GCD domain, a PVMD, a v-domain) if and only if D satisfies the ACCP (resp., is a BFD, an FFD, a (pre-) Schreier domain, a G-GCD domain, a PVMD, a v-domain).

KAPLANSKY-TYPE THEOREMS IN GRADED INTEGRAL DOMAINS

  • CHANG, GYU WHAN;KIM, HWANKOO;OH, DONG YEOL
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.4
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    • pp.1253-1268
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    • 2015
  • It is well known that an integral domain D is a UFD if and only if every nonzero prime ideal of D contains a nonzero principal prime. This is the so-called Kaplansky's theorem. In this paper, we give this type of characterizations of a graded PvMD (resp., G-GCD domain, GCD domain, $B{\acute{e}}zout$ domain, valuation domain, Krull domain, ${\pi}$-domain).

ON OVERRINGS OF GORENSTEIN DEDEKIND DOMAINS

  • Hu, Kui;Wang, Fanggui;Xu, Longyu;Zhao, Songquan
    • Journal of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.991-1008
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    • 2013
  • In this paper, we mainly discuss Gorenstein Dedekind do-mains (G-Dedekind domains for short) and their overrings. Let R be a one-dimensional Noetherian domain with quotient field K and integral closure T. Then it is proved that R is a G-Dedekind domain if and only if for any prime ideal P of R which contains ($R\;:_K\;T$), P is Gorenstein projective. We also give not only an example to show that G-Dedekind domains are not necessarily Noetherian Warfield domains, but also a definition for a special kind of domain: a 2-DVR. As an application, we prove that a Noetherian domain R is a Warfield domain if and only if for any maximal ideal M of R, $R_M$ is a 2-DVR.

A Study on the Pitch Search Time Reduction of G.723.1 Vocoder by Improved Hybrid Domain Cross-correlation (개선된 혼성영역 교차상관법에 의한 G.723.1의 피치검색시간 단축에 관한 연구)

  • Jo, Wang-Rae;Choi, Seong-Young;Bae, Myung-Jin
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.59 no.12
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    • pp.2324-2328
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    • 2010
  • In this paper we proposed a new algorithm that can reduce the open-loop pitch estimation time of G.723.1. The time domain cross-correlation method is simple but has long processing time by recursive multiplication. For reduction of processing time, we use the method that compute the cross-correlation by multiplying the Fourier value of speech by it's complex conjugate. Also, we can reduce the processing time by omitting the bit-reversing of FFT and IFFT for time-frequency domain transform. As a result, the processing time of improved hybrid domain cross-correlation algorithm is reduced by 67.37% of conventional time domain cross-correlation.

A REMARK ON HALF-FACTORIAL DOMAINS

  • Oh, Heung-Joon
    • The Pure and Applied Mathematics
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    • v.4 no.1
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    • pp.93-96
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    • 1997
  • An atomic integral domain R is a half-factorial domain (HFD) if whenever $\chi_1$$\chi_{m}=y_1$$y_n$ with each $\chi_{i},y_j \in R$ irreducible, then m = n. In this paper, we show that if R[X] is an HFD, then $Cl_{t}(R)$ $\cong$ $Cl_{t}$(R[X]), and if $G_1$ and $G_2$ are torsion abelian groups, then there exists a Dedekind HFD R such that Cl(R) = $G_1\bigoplus\; G_2$.

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The effects of a vocabulary instructional method on vocabulary learning strategy use and the affective domain: Focus on an analysis of students' survey responses (어휘 지도 방법이 어휘 학습전략 사용과 정의적 측면에 미치는 효과: 학생 설문 조사 분석을 중심으로)

  • Kim, Nahk-Bohk
    • English Language & Literature Teaching
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    • v.11 no.3
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    • pp.89-112
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    • 2005
  • This study investigated the effects of collocation-based vocabulary instruction for the experimental group (G2). It was compared to the traditional wordlist-based vocabulary instruction for the control group (G1). This results reflect the development of low level high school EFL learners' vocabulary learning strategy use and the positive change in the affective domain. In the analysis of the survey responses, G1 and G2 did not differ significantly on the first questionnaire. They did, however, differ significantly on the second questionnaire. G2 used more strategies to discover and to consolidate the meaning of the words by means of combining words. In terms of the affective domain, G2 participated more actively in the learning activities, which had a significant effect on vocabulary growth, memory, self-confidence, motivation, and cooperative learning. This is attributable to the fact that G2 was more inquisitive, interested, challenged, participatory, cooperative, and attentive than G1 in performing the vocabulary task activities. Moreover, the data collected from the questionnaire showed that G2 performed more interactive and dynamic activities in solving the given tasks.

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