• Kyungpook Mathematical Journal
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• 제58권1호
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• pp.9-17
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• 2018

Let $R ={\oplus}_{n{\in}Z}R_n$ be a graded commutative Noetherian ring and let I be a graded ideal of R and J be an arbitrary ideal. It is shown that the i-th generalized local cohomology module of graded module M with respect to the (I, J), is graded. Also, the asymptotic behaviour of the homogeneous components of $H^i_{I,J}(M)$ is investigated for some i's with a specified property.

• 대한수학회보
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• 제55권1호
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• pp.187-204
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• 2018

Let $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}\;R_{\alpha}$ be a graded integral domain, H be the set of nonzero homogeneous elements of R, and ${\star}$ be a semistar operation on R. The purpose of this paper is to study the properties of $quasi-Pr{\ddot{u}}fer$ and UMt-domains of graded integral domains. For this reason we study the graded analogue of ${\star}-quasi-Pr{\ddot{u}}fer$ domains called $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. We study several ring-theoretic properties of $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. As an application we give new characterizations of UMt-domains. In particular it is shown that R is a $gr-t-quasi-Pr{\ddot{u}}fer$ domain if and only if R is a UMt-domain if and only if RP is a $quasi-Pr{\ddot{u}}fer$ domain for each homogeneous maximal t-ideal P of R. We also show that R is a UMt-domain if and only if H is a t-splitting set in R[X] if and only if each prime t-ideal Q in R[X] such that $Q{\cap}H ={\emptyset}$ is a maximal t-ideal.

• 대한화학회지
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• 제56권6호
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• pp.720-724
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• 2012

Under pseudo-first order conditions, the monomeric species of Cr(VI) was found to be kinetically active in the absence of phenanthroline (phen) whereas in the phen-promoted path, the Cr(VI)-phen complex undergoes a nucleophilic attack by etane-1,2-diol to form a ternary complex which subsequently experience a redox decomposition leading to hydroxy ethanal and Cr(III)-phen complex. The effect of the cationic surfactant (CPC), anionic surfactant (SDS) and neutral surfactant (TX-100) on the unpromoted and phen-promoted path have been studied. Micellar effects have been explained by considering the preferential partitioning of reactants between the micellar and aqueous phase. Combination of TX-100 and phenanthroline will be the ideal for chromic acid oxidation of ethane-1,2-diol in aqueous media.

• 한국자동차공학회논문집
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• 제12권2호
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• pp.83-90
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• 2004

A flywheel-driven rapid compression and expansion machine is developed and utilized for experimental study of homogeneous charge compression ignition combustion. Compression ignition of homogeneous charge in IC engines offers possibilities of realizing ultra-lean engine operation with greatly reduced NOx and particulate formation. Fundamental investigations are carried out in order to better understand this ideal engine combustion mechanism. Perfectly premixed propane-air mixtures of various equivalence ratio are compression-ignited in the rapid compression and expansion machine, and the characteristics of the auto-ignition and the following combustion process are analyzed.

• 대한수학회논문집
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• 제11권4호
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• pp.887-893
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• 1996

Let (R,m) be a Cohen-Macaulay local ring with an infinite residue field and let $J = (a_1, \cdots, a_l)$ be a minimal reduction of an equimultiple ideal I of R. In this paper we shall prove that the following conditions are equivalent: (1) $I^2 = JI$. (2) $gr_I(R)/mgr_I(R)$ is Cohen-Macaulay with minimal multiplicity at its maximal homogeneous ideal N. (3) $N^2 = (a'_1, \cdots, a'_l)N$, where $a'_i$ denotes the images of $a_i$ in I/mI for $i = 1, \cdots, l$.

• Investigative Magnetic Resonance Imaging
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• 제20권1호
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• pp.44-52
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• 2016

Purpose: To quantitatively and qualitatively compare fat-suppressed MRI quality using iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) with that using frequency selective fat-suppression (FSFS) T2- and postcontrast T1-weighted fast spin-echo images of the head and neck at 3T. Materials and Methods: The study was approved by our Institutional Review Board. Prospective MR image analysis was performed in 36 individuals at a single-center. Axial fat suppressed T2- and postcontrast T1-weighted images with IDEAL and FSFS were compared. Visual assessment was performed by two independent readers with respect to; 1) metallic artifacts around oral cavity, 2) susceptibility artifacts around upper airway, paranasal sinus, and head-neck junction, 3) homogeneity of fat suppression, 4) image sharpness, 5) tissue contrast of pathologies and lymph nodes. The signal-to-noise ratios (SNR) for each image sequence were assessed. Results: Both IDEAL fat suppressed T2- and T1-weighted images significantly reduced artifacts around airway, paranasal sinus, and head-neck junction, and significantly improved homogeneous fat suppression in compared to those using FSFS (P < 0.05 for all). IDEAL significantly decreased artifacts around oral cavity on T2-weighted images (P < 0.05, respectively) and improved sharpness, lesion-to-tissue, and lymph node-to-tissue contrast on T1-weighted images (P < 0.05 for all). The mean SNRs were significantly improved on both T1- and T2-weighted IDEAL images (P < 0.05 for all). Conclusion: IDEAL technique improves image quality in the head and neck by reducing artifacts with homogeneous fat suppression, while maintaining a high SNR.

• 충청수학회지
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• 제27권4호
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• pp.563-569
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• 2014

We investigate a minimal set of generators of a homogeneous ideal of a curve of degree d on a linearly normal smooth surface scroll W in $P^r$ whose arithmetic genus is maximal among curves of degree d on W.

• 대한수학회보
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• 제58권6호
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• pp.1401-1407
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• 2021

Let R be a commutative G-graded ring with a nonzero unity. In this article, we introduce the concept of graded radically principal ideals. A graded ideal I of R is said to be graded radically principal if Grad(I) = Grad(〈c〉) for some homogeneous c ∈ R, where Grad(I) is the graded radical of I. The graded ring R is said to be graded radically principal if every graded ideal of R is graded radically principal. We study graded radically principal rings. We prove an analogue of the Cohen theorem, in the graded case, precisely, a graded ring is graded radically principal if and only if every graded prime ideal is graded radically principal. Finally we study the graded radically principal property for the polynomial ring R[X].

• 대한수학회지
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• 제57권1호
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• pp.145-169
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• 2020

Let k be a field of characteristic 0. Let ${\mathfrak{C}}=Spec(k[x,y]/{\langle}f{\rangle})$ be a weighted homogeneous plane curve singularity with tangent space ${\pi}_{\mathfrak{C}}:T_{{\mathfrak{C}}/k}{\rightarrow}{\mathfrak{C}$. In this article, we study, from a computational point of view, the Zariski closure ${\mathfrak{G}}({\mathfrak{C}})$ of the set of the 1-jets on ${\mathfrak{C}}$ which define formal solutions (in F[[t]]² for field extensions F of k) of the equation f = 0. We produce Groebner bases of the ideal ${\mathcal{N}}_1({\mathfrak{C}})$ defining ${\mathfrak{G}}({\mathfrak{C}})$ as a reduced closed subscheme of $T_{{\mathfrak{C}}/k}$ and obtain applications in terms of logarithmic differential operators (in the plane) along ${\mathfrak{C}}$.

• 농촌계획
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• 제4권1호
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• pp.15-21
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• 1998

The purpose of the study is to identify a basic spatial unit for rural village redevelopment plan. An ideal spatial unit need to satisfy three basic premises: to be homogeneous as rural community, to be appropriate to implement the project, and to be compatible with regional planning systems. A spatial unit could, empirically, be defined based on the homogeneity at first, and then appropriateness and compatibility could be used to adjust its boundary. Mitan-Myun(13 villages), Pyungchang County, Dochuck-Myun(15 villages), Kwangju County, and Chuksan-Myun(28 villages), Kimje City in Korea were selected as case study areas. The degree of interrelationship between all possible pairs in each Myun was measured using spatial, socio-cultural, and economic indicators. Multidimensional Scaling(MDS) was used to identify a homogeneous spatial unit, and then indicators representing appropriateness and compatibility were used to adjust the identified boundary. New districts which have two or three villages were suggested as a reasonable spatial unit for rural village redevelopment, and its boundary roughly overlaps with Bup-Jeong-Ri(法定里: a legally defined village).