• Bulletin of the Korean Mathematical Society
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• 제31권2호
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• pp.210-214
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• 1994

The purpose of this paper is to investigate the relationship between the depths of the Rees algebra R[It] and the associated graded ring g $r_{I}$(R) of an ideal I in a local ring (R,m) of dim(R) > 0. The relationship between the Cohen-Macaulayness of these two rings has been studied extensively. Let (R, m) be a local ring and I an ideal of R. An ideal J contained in I is called a reduction of I if J $I^{n}$ = $I^{n+1}$ for some integer n.geq.0. A reduction J of I is called a minimal reduction of I. The reduction number of I with respect to J is defined by (Fig.) S. Goto and Y.Shimoda characterized the Cohen-Macaulay property of the Rees algebra of the maximal ideal of a Cohen-Macaulay local ring in terms of the Cohen-Macaulay property of the associated graded ring of the maximal ideal and the reduction number of that maximal ideal. Let us state their theorem.m.m.

• The Journal of Korean Institute of Communications and Information Sciences
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• 제11권5호
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• pp.297-306
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• 1986

This paper surveys circuit switching local area networks(LANs) whit topology of ring, mesh, bus and star. Emphasis of this study is given on the conceptual switching technologies of these LANs.

• Journal of the Korean Mathematical Society
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• 제43권4호
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• pp.871-883
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• 2006

We show that the Auslander index is the same as the column invariant over Gorenstein local rings. We also show that Ding's conjecture ([13]) holds for an isolated non-Gorenstein ring A satisfying a certain condition which seems to be weaker than the condition that the associated graded ring of A is Cohen-Macaulay.

• The Journal of Korean Institute of Communications and Information Sciences
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• 제17권8호
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• pp.796-804
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• 1992

This paper presents a design of a backbone network which uses a rigister-Insertion ring structure, The introduction of a high speed register in sertton backbone ring enables high performance inter-network 4ommunicatlons In a simple and modular structure at low cost and Its concurrent communications.. Two or more bridge nodes can be used to construct a register Insertion backbone ring network. The high bandwidth of the backbone ring sup ports heavy traffic for Inter-segment Eornrnunicatlons. The bridge node does both local address filtering to block data entering the ring and remote address filtering to block data entering the local LAN segment . Title local address greatly reduces the rate on the backbone ring and the remote address filterlng greatly reduces the traffic rate on each LAN segment. An feature makes the network the network reconflguratlon simpler and transparent to users. A throughput analysis Is used to deterrune the bandwidth of the backbone rlr)g transmission medium.

• Bulletin of the Korean Mathematical Society
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• 제39권1호
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• pp.1-8
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• 2002

We characterize the commutative Artinian rings R every proper quotient ring (respectively every proper ideal) in which is invariant with respect to all derivations.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.53-69
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• 2020

Let (A, M) ⊂ (B, N) be commutative quasi-local rings. We consider the property that there exists a ring D such that A ⊆ D ⊂ B and the extension D ⊂ B is inert. Examples show that the number of such D may be any non-negative integer or infinite. The existence of such D does not imply M ⊆ N. Suppose henceforth that M ⊆ N. If the field extension A/M ⊆ B/N is algebraic, the existence of such D does not imply that B is integral over A (except when B has Krull dimension 0). If A/M ⊆ B/N is a minimal field extension, there exists a unique such D, necessarily given by D = A + N (but it need not be the case that N = MB). The converse fails, even if M = N and B/M is a finite field.

• Bulletin of the Korean Mathematical Society
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• 제54권1호
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• pp.319-329
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• 2017

Let I denote an ideal of a Noetherian local ring (R, m). Let M denote a finitely generated R-module. We study the endomorphism ring of the local cohomology module $H^c_I(M)$, c = grade(I, M). In particular there is a natural homomorphism $$Hom_{\hat{R}^I}({\hat{M}}^I,\;{\hat{M}}^I){\rightarrow}Hom_R(H^c_I(M),\;H^c_I(M))$$, $where{\hat{\cdot}}^I$ denotes the I-adic completion functor. We provide sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals $J{\subset}I$ with the property grade(I, M) = grade(J, M). Our results extends constructions known in the case of M = R (see e.g. [8], [17], [18]).

• Nuclear Engineering and Technology
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• 제56권2호
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• pp.485-497
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• 2024

Ring beam is the main anchorage zone of the tendons in the nuclear power prestressed concrete containment vessel (PCCV). Its safety is crucial and has a great influence on the overall performance of PCCV. In this paper, two half-scale ring beams were tested to investigate the mechanical performance of the anchorage zone in the PCCV under multidirectional pressure. The effect of working condition with different tension sequences was investigated. Additionally, a half axisymmetric plane model of the containment was established by the finite element simulation to further predict the experimental responses and propose the local reinforcement design in the anchorage zone of the ring beam. The results showed that the ultimate load of the specimens under both working conditions was greater than the nominal ultimate tensile force. The original reinforcement design could meet the bearing capacity requirements, but there was still room for optimization. The ring beam was generally under pressure in the anchorage area, while the splitting force appeared in the under-anchor area, and the spalling force appeared in the corner area of the tooth block, which could be targeted for local strengthening design.

• Bulletin of the Korean Mathematical Society
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• 제56권3호
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• pp.659-666
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• 2019

In this paper, we consider a conjecture of I. N. Herstein for local commutators of symmetric elements and unitary elements of division rings. For example, we show that if D is a finite dimensional division ring with involution ${\star}$ and if $a{\in}D^*=D{\setminus}\{0\}$ such that local commutators $axa^{-1}x^{-1}$ at a are radical over the center F of D for every $x{\in}D^*$ with $x^{\star}=x$, then either $a{\in}F$ or ${\dim}_F\;D=4$.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 한국소음진동공학회 2008년도 추계학술대회논문집
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• pp.228-229
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• 2008

In this study, we propose an effective method to improve the clarity and period of the beat in a ring structure. Ring is an simplified model of a Korean bell, in which beating vibration and sound are very important features. An equivalent ring theory is applied and finite element analysis on the equivalent ring is performed to determine the condition of the asymmetric element for the clear and proper period beat. The clarity and the period of the beat are improved by attacking asymmetric mass and decreasing local thickness. Using the equivalent ring, the amount and position of the local variation for the required beat condition are determined and the results are verified by experiment.