• Bulletin of the Korean Chemical Society
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• 제27권1호
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• pp.39-43
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• 2006

The relaxed torsional potential of a liquid crystalline polymer containing an ester functional group in a mesogenic unit (hereafter 12-4 oligomer) has been calculated with the ab initio self-consistent-field using 6-31G$^*$ basis set. GIAO^{13}C NMR chemical shifts also have been calculated at the B3LYP/6-31G$^*$ level of theory for each conformational structure obtained from torsional potential calculation. The results show that the phenyl ring-ester linkages are coplanar with the dihedral angle of about 0$^{\circ}$ and the ring-ring linkages in the biphenyl groups are tilted with the dihedral angle of around 43-44$^{\circ}$ in the lowest energy conformer. The biphenyl ring has a comparatively lower energy barrier of internal rotation potential in the ring-ring than that of phenyl ring-ester. The ^{13}C chemical shifts of carbonyl carbons were found to move to upfield due to $\pi$ -conjugation with phenyl ring and slightly affected about 0.5 ppm by dihedral angle of the ring-ring linkage.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.367-377
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• 2024

Let G = (V, E) be a graph with p-vertices and q-edges and let R^◦ be a finite zero ring of order n. An injective function f : V (G) → {r₁, r₂, _…, r_k}, where r_i ∈ R^◦ is called vertex pair sum k-zero ring labeling, if it is possible to label the vertices x ∈ V with distinct labels from R^◦ such that each edge e = uv is labeled with f(e = uv) = [f(u) + f(v)] (mod n) and the edge labels are distinct. A graph admits such labeling is called vertex pair sum k-zero ring graph. The minimum value of positive integer k for a graph G which admits a vertex pair sum k-zero ring labeling is called the vertex pair sum k-zero ring index denoted by 𝜓_pz(G). In this paper, we defined the vertex pair sum k-zero ring labeling and applied to some graphs.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1999년도 하계학술대회 논문집 D
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• pp.1686-1688
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• 1999

The FLR(Field Limiting Ring) structure with a buried ring is proposed to improve breakdown voltage. The breakdown characteristics of proposed structure is verified by two-dimensional device simulator. ATLAS. It has shown that the breakdown voltage of the proposed structure is increased by 11 % compared with that of the FLR.

• 대한수학회보
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• 제53권1호
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• pp.195-204
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• 2016

We prove, in this note, that a Zabavsky ring R is an elementary divisor ring if and only if R is a $B{\acute{e}}zout$ ring. Many known results are thereby generalized to much wider class of rings, e.g. [4, Theorem 14], [7, Theorem 4], [9, Theorem 1.2.14], [11, Theorem 4] and [12, Theorem 7].

• 대한수학회보
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• 제53권6호
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• pp.1613-1615
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• 2016

It is proved that $k[X_1,{\ldots},X_v ]$ localized at the ideal ($X_1,{\ldots},X_v$ ), where k is a field and $X_1,{\ldots},X_v$ indeterminates, is not weakly quasi-complete for $v{\geq}2$, thus proving a conjecture of D. D. Anderson and solving a problem from "Open Problems in Commutative Ring Theory" by Cahen, Fontana, Frisch, and Glaz.

• Korean Journal of Mathematics
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• 제25권4호
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• pp.587-606
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• 2017

This paper is a continuation of study semi-potentness endomorphism rings of module. We give some other characterizations of endomorphism ring to be semi-potent. New results are obtained including necessary and sufficient conditions for the endomorphism ring of semi(injective) projective module to be semi-potent. Finally, we characterize a module M whose endomorphism ring it is semi-potent via direct(injective) projective modules. Several properties of the endomorphism ring of a semi(injective) projective module are obtained. Besides to that, many necessary and sufficient conditions are obtained for semi-projective, semi-injective modules to be semi-potent and co-semi-potent modules.

• Korean Journal of Mathematics
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• 제17권3호
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• pp.233-236
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• 2009

We investigate in this paper some equivalent conditions for right principally quasi-Baer rings to be reflexive. Using these results we are able to prove that if R is a reflexive right principally quasi-Baer ring then R is a left principally quasi-Baer ring. In addition, for an idempotent reflexive principally quasi-Baer ring R we show that R is prime if and only if R is torsion free.

• 대한수학회지
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• 제45권3호
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• pp.741-756
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• 2008

In this paper, we introduce a new class of rings, SB-rings. We establish various properties of this concept. These shows that, in several respects, SB-rings behave like rings satisfying unit 1-stable range. We will give necessary and sufficient conditions under which a semilocal ring is a SB-ring. Furthermore, we extend these results to exchange rings with all primitive factors artinian. For such rings, we observe that the concept of the SB-ring coincides with Goodearl-Menal condition. These also generalize the results of Huh et al., Yu and the author on rings generated by their units.

• 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.

• 대한수학회논문집
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• 제33권4호
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• pp.1103-1112
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• 2018

We study the structure of a generalization of right nilpotent-duo rings in relation with powers of elements. Such a ring property is said to be weakly right nilpotent-duo. We find connections between weakly right nilpotent-duo and weakly right duo rings, in several algebraic situations which have roles in ring theory. We also observe properties of weakly right nilpotent-duo rings in relation with their subrings and extensions.