• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.506-509
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• 2006

Shaped Sound Focusing is defined as the generation of acoustically bright shape in space using multiple sources. The acoustically bright shape is a spatially focused region with relatively high acoustic potential energy level. In view of the energy transfer, acoustical focusing is essential because acoustic energy is very small to use other type of energy. Practically, focused sound shape control not a point is meaningful because there are so many needs to enlarge the focal region especially in clinical uses and others. If focused sound shape can be controlled, it offers various kinds of solutions for clinical uses and others because a regional focusing is essentially needed to reduce a treatment time and enhance the performance of transducers. For making the shaped-sound field, control variables, such as a number of sources, excitation frequency, source positioning, etc., should be taken according to geometrical sound shape. To verify these relations between them, wavenumber domain matching method is suggested because wavenumber spectrum can provide the information of control variables of sources. In this paper, the procedures of shaped sound focusing using wavenumber domain matching and relations between control variables and geometrical sound shape are covered in case of an acoustical ring.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.16 no.2
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• pp.81-87
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• 2017

The pipe connection process using a clamping ring is used for joining small pipes in the refrigerator and air-conditioner industries instead of the brazing process, which induces inevitable thermal deformation in the pipes. However, few studies have been carried out on the process to select optimal parameters in joining pipes, and studies on the relation between the process parameters of the connection and connecting force of the joint have not been conducted. In this study, the connection process of pipes with the clamping ring was modeled using the finite element method (FEM) and analyzed to obtain the contact stress distribution between the pipes with which the connecting force of the joint was estimated. Considering the characteristics of pipe connection, the process was modeled and simulated in a two-dimensional axisymmetric solution domain. With the numerical model, the effect of ring shape on the connection was studied by adding a projection to the end of a ring or changing the length of a ring. The results of the analyses revealed that the contact stress distribution could be predicted with the suggested model. The effect of the ring shape was also presented. The effect of any combination of process parameters could be easily estimated through the related analyses.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.539-558
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• 2019

An ideal of a commutative ring is called a d-ideal if it contains the annihilator of the annihilator of each of its elements. Denote by DId(A) the lattice of d-ideals of a ring A. We prove that, as in the case of f-rings, DId(A) is an algebraic frame. Call a ring homomorphism "compatible" if it maps equally annihilated elements in its domain to equally annihilated elements in the codomain. Denote by $SdRng_c$ the category whose objects are rings in which the sum of two d-ideals is a d-ideal, and whose morphisms are compatible ring homomorphisms. We show that $DId:\;SdRng_c{\rightarrow}CohFrm$ is a functor (CohFrm is the category of coherent frames with coherent maps), and we construct a natural transformation $RId{\rightarrow}DId$, in a most natural way, where RId is the functor that sends a ring to its frame of radical ideals. We prove that a ring A is a Baer ring if and only if it belongs to the category $SdRng_c$ and DId(A) is isomorphic to the frame of ideals of the Boolean algebra of idempotents of A. We end by showing that the category $SdRng_c$ has finite products.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1447-1455
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• 2016

In this note, we mainly discuss the Gorenstein $Pr{\ddot{u}}fer$ domains. It is shown that a domain is a Gorenstein $Pr{\ddot{u}}fer$ domain if and only if every finitely generated ideal is Gorenstein projective. It is also shown that a domain is a PID (resp., Dedekind domain, $B{\acute{e}}zout$ domain) if and only if it is a Gorenstein $Pr{\ddot{u}}fer$ UFD (resp., Krull domain, GCD domain).

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.185-193
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• 2010

Let D be an integral domain, and let ${\bar{D}}$ be the integral closure of D. We show that if D is an almost pseudo-valuation domain (APVD), then D is a quasi-$Pr{\ddot{u}}fer$ domain if and only if D=P is a quasi-$Pr{\ddot{u}}fer$ domain for each prime ideal P of D, if and only if ${\bar{D}}$ is a valuation domain. We also show that D(X), the Nagata ring of D, is a locally APVD if and only if D is a locally APVD and ${\bar{D}}$ is a $Pr{\ddot{u}}fer$ domain.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.711-719
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• 2018

In this paper we define and study a new kind of dimension called, semisimple dimension, that measures how far a module is from being semisimple. Like other kinds of dimensions, this is an ordinal valued invariant. We give some interesting and useful properties of rings or modules which have semisimple dimension. It is shown that a noetherian module with semisimple dimension is an artinian module. A domain with semisimple dimension is a division ring. Also, for a semiprime right non-singular ring R, if its maximal right quotient ring has semisimple dimension as a right R-module, then R is a semisimple artinian ring. We also characterize rings whose modules have semisimple dimension. In fact, it is shown that all right R-modules have semisimple dimension if and only if the free right R-module ${\oplus}^{\infty}_{i=1}$ R has semisimple dimension, if and only if R is a semisimple artinian ring.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.1
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• pp.120-126
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• 2013

This paper proposes a novel scheme of fault detection and self-recovery for space-borne dual ring counters subject to transient faults. The considered ring counter is equipped with hardware redundancy, but it has a limited output domain where direct access to the current state is unavailable. We employ the theory of corrective control to detect any transient fault occurring to the counter bits and to realize immediate self-recovery of the ring counter back to the normal state. The structure of the fault-tolerant controller is designed to be minimal regardless of the counter size. To validate the applicability, we implement the proposed system on a commercial FGPA board.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1321-1334
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• 2023

An idempotent e of a ring R is called right (resp., left) semicentral if er = ere (resp., re = ere) for any r ∈ R, and an idempotent e of R∖{0, 1} will be called right (resp., left) quasicentral provided that for any r ∈ R, there exists an idempotent f = f(e, r) ∈ R∖{0, 1} such that er = erf (resp., re = fre). We show the whole shapes of idempotents and right (left) semicentral idempotents of upper triangular matrix rings and polynomial rings. We next prove that every nontrivial idempotent of the n by n full matrix ring over a principal ideal domain is right and left quasicentral and, applying this result, we can find many right (left) quasicentral idempotents but not right (left) semicentral.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.503-512
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• 1999

Over a field k, every schur k-algebra is a cyclotomic algebra due to Brauer-Witt theorem. Similarly every projective Schur k-division algebra is itself a radical algebra by Aljadeff-Sonn theorem. We study the two theorems over a certain commutative ring, and prove similar results over regular domain containing a field.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.649-657
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• 2018

Let R be a commutative ring. In this paper, the w-projective Basis Lemma for w-projective modules is given. Then it is shown that for a domain, nonzero w-projective ideals and nonzero w-invertible ideals coincide. As an application, it is proved that R is a Krull domain if and only if every submodule of finitely generated projective modules is w-projective.