• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1349-1357
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• 2022

Let 𝒜 = (A_n)_n≥0 be an increasing sequence of rings. We say that 𝓘 = (I_n)_n≥0 is an associated sequence of ideals of 𝒜 if I₀ = A₀ and for each n ≥ 1, I_n is an ideal of A_n contained in I_n+1. We define the polynomial ring and the power series ring as follows: $I[X]\, = \,\{\, f \,=\, {\sum}_{i=0}^{n}a_iX^i\,{\in}\,A[X]\,:\,n\,{\in}\,\mathbb{N},\,a_i\,{\in}\,I_i \,\}$ and $I[[X]]\, = \,\{\, f \,=\, {\sum}_{i=0}^{+{\infty}}a_iX^i\,{\in}\,A[[X]]\,:\,a_i\,{\in}\,I_i \,\}$. In this paper we study the Noetherian and the SFT properties of these rings and their consequences.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1285-1307
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• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.5
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• pp.196-208
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• 2005

In multiprocessor systems, interconnection network design is critical for overall system performance. Popular interconnection networks, which are generally considered, are meshes, rings, and hierarchical rings. In this paper, we propose (')Torus Ring('), which is a modified version of hierarchical ring. Torus Ring has the same complexity as the hierarchical rings, but the only difference is the way it connects the local rings. It has an advantage over the hierarchical rings when the destination of a packet is the neighbor local ring in the reverse direction. Though the average number of hops in Torus Ring is equal to that of the hierarchical rings when assuming the uniform distribution of each transaction, the benefits of the number of hops are expected to be larger because of the spatial locality in the real environment of parallel programming. In the simulation results, latencies in the interconnection network are reduced by up to 19$\%$, and the execution times are reduced by up to 10$\%$.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.23-27
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• 2004

We calculate dim $\hat{A}$ which is a completion of a Noetherian ring A with respect to I-adic topology. We do not use localization but power series techniques.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.7
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• pp.918-927
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• 1999

In the fully developed internal flow fields, there are complex transition flows caused by interaction of the cross flow and jet when jet is Injected Into the flow. These interactions are studied by means of the flow visualization methods. An instantaneous laser tomographic method is used to reveal the physical mechanism and the structure of vortices formation in the branch pipe flow. The velocity range of cross flow of the pipe is 0.7m/s and the corresponding Reynolds number $R_{cf}$, based on the duct height is $5.6{\times}10^3$, diameter/height ratios(d/H) 0.14 and velocity ratios 3.0. Oil mist with the size of $10{\mu}m$ diameter is used for the scattering particle. The instantaneous topological features of the vortex ring roll-up of the jet shear layer and characteristics of this flow are studied in detail by performing flow visualization in rectangular duct flow. It is found that the formation and roll-up of ring vortices is a periodic phenomenon. The detailed topology of the vortices in the near field of a cross -flow jet and the mechanism associated with them give enforced hints of vortex breakdown within the vortex system due to the interaction of the jet and the cross-flow.

• Journal of Korean Society for Quality Management
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• v.28 no.1
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• pp.105-118
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• 2000

In this paper, we consider an interconnection network, DRDT (Dual Receive Dual Transmit), that is a double-loop ring topology and adopts the concept of multiple packets transmission. For three types of DRDT configurations, we investigate some properties related to path sets and discuss the method for finding minimal path sets. Using the concept of the terminal reliability and the path sets approach, we evaluate the reliability of the DRDT networks and compare them with a single ring network and a unidirectional double-loop ring network.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.1
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• pp.22-34
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• 2002

In this paper, we consider ring embeding problem in faulty (n,k) star graphs which is recently proposed as an alternative interconnection network topology, By effectively utilizing such strategies as series of dimension expansions and even distribution of faulty nodes into sub-stars in graph itself. we prove that it is possible to construct a maximal fault-free ring excluding only faulty nodes when the number of faults is no more than n-3 and $n-k{\geq}2$, and also propose an algorithm which can embed the corresponding ring in (n.k)-star graphs This results will be applied into the multicasting applications that the underlying cycle properties on the multi-computer system.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.3
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• pp.403-408
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• 2008

The gyroscope is the sensor for detecting the rotation in inertial reference frame and constitute the navigation system together an accelerometer. As the inertial reference equipment for attitude determination and control in the satellite, the mechanical gyroscope has been used but it bring the disturbance for mass unbalance so the disturbance give a bad influence to the observation satellite mission because the mechanical gyroscope has the rotation parts. During the launch. The mechanical gyroscope is weak in vibration, shock and has the defect of narrow operating temperature range so it need the special design in integration. Recently the low orbit observation satellite for seeking the high pointing accuracy of image camera payload accept the FOG(Fiber Optic Gyro) or RLG(Ring Laser Gyro) for the attitude determination and control. The Ring Laser Gyro makes use of the Sanac effect within a resonant ring cavity of a He-Ne laser and has more accuracy than the other gyros. It need the 1000V DC to create the He-Ne plasma in discharge tube. In this paper, the design process of the High Voltage Power Supply for RLG(Ring Laser Gyroscope) is described. The specification for High Voltage Power Supply (HVPS) is proposed. Also, The analysis of flyback converter topology is explained. The Design for the HVPS is composed of the inverter circuit, feedback control circuit, high frequency switching transformer design and voltage doubler circuit.

• Proceedings of the KIEE Conference
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• 2008.07a
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• pp.1488-1490
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• 2008

The gyroscope is the sensor for detecting the rotation in inertial reference frame and constitute the navigation system together an accelerometer. As the inertial reference equipment for attitude determination and control in the satellite, the mechanical gyroscope has been used but it bring the disturbance for mass unbalance so the disturbance give a bad influence to the observation satellite mission because the mechanical gyroscope has the rotation parts. During the launch, The mechanical gyroscope is weak in vibration, shock and has the defect of narrow operating temperature range so it need the special design in integration. Recently the low orbit observation satellite for seeking the high pointing accuracy of image camera payload accept the FOG(Fiber Optic Gyro) or RLG(Ring Laser Gyro) for the attitude determination and control. The Ring Laser Gyro makes use of the Sanac effect within a resonant ring cavity of a He-Ne laser and has more accuracy than the other gyros. It need the 1000V DC to create the He-Ne plasma in discharge tube. In this paper, the design process of the High Voltage Power Supply for RLG(Ring Laser Gyroscope) is described. The specification for High Voltage Power Supply(HVPS) is proposed. Also, The analysis of flyback converter topology is explained. The Design for the HVPS is composed of the inverter circuit, feedback control circuit, high frequency switching transformer design and voltage doubler circuit.

• The KIPS Transactions:PartC
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• v.11C no.7 s.96
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• pp.895-904
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• 2004

Due to the frequent and unpredictable topology changes, multicast still remains as challenge and no one-size-fits-all protocol could serve all kinds of needs in mobile ad hoc network. In this paper, we propose a novel scheme of Hierarchical Eulerian Ring Oriented Multicast Architecture (HEROMA) over mobile ad hoc network. It has features that concentrate on efficiency and robustness simultaneously. It is also an application-driven proposal for hazard detection. Architectures including Eulerian ring, hierarchy and multicast agent are investigated in detail Simulation results different level of improvements on control traffic, end-to-end delay and packet delivery ratio by comparing with tree-based and mesh-based multicast protocols.