• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.543-549
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• 2001

We show that R[X] is a Krull (Resp. factorial) ring if and only if R is a normal Krull (resp, factorial) ring with a finite number of minimal prime ideals if and only if R is a Krull (resp. factorial) ring with a finite number of minimal prime ideals and R(sub)M is an integral domain for every maximal ideal M of R. As a corollary, we have that if R[X] is a Krull (resp. factorial) ring and if D is a Krull (resp. factorial) overring of R, then D[X] is a Krull (resp. factorial) ring.

• Journal of applied mathematics & informatics
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• v.3 no.1
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• pp.65-78
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• 1996

The properties of a toric variety have strong connection with the combinatorial structure of the corresponding fan and the rela-tions among the generators. Using this fact we have described explic-itly the Chow ring for a Q-factorial toric variety as the Stanley-Reisner ring for the corresponding fan modulo the linear equivalence relation. In this paper we calculate the Chow ring for 3-dimensional Q-factorial toric varieties having one bad isolated singularity.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.115-119
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• 2007

Let R be a Krull ring with the unique regular maximal ideal M. We show that R has a regular prime element and reg-$dimR=1{\Leftrightarrow}R$ is a factorial ring and reg-$dim(R)=1{\Rightarrow}M$ is invertible ${\Leftrightarrow}R{\varsubsetneq}[R:M]{\Leftrightarrow}M$ is divisorial ${\Leftrightarrow}$ reg-$htM=1{\Rightarrow}R$ is a rank one discrete valuation ring. We also show that if M is generated by regular elements, then R is a rank one discrete valuation ring ${\Rightarrow}$ R is a factorial ring and reg-dim(R)=1.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.319-323
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• 2013

Let D be a principal ideal domain, X be an indeterminate over D, D[X] be the polynomial ring over D, and $R_n=D[X]/(X^n)$ for an integer $n{\geq}1$. Clearly, $R_n$ is a commutative Noetherian ring with identity, and hence each nonzero nonunit of $R_n$ can be written as a finite product of irreducible elements. In this paper, we show that every irreducible element of $R_n$ is a primary element, and thus every nonunit element of $R_n$ can be written as a finite product of primary elements.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.189-196
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• 2009

Let D be an integral domain, and let U be a group of units of D. Let $D^*=D-\{0\}$ and ${\Gamma}=D^*/U$ be the commutative cancellative semigroup under aU+bU=abU. We prove that $Cl(D)=Cl({\Gamma})$ and that D is a PvMD (resp., GCD-domain, Mori domain, Krull domain, factorial domain) if and only if ${\Gamma}$ is a PvMS(resp., GCD-semigroup, Mori semigroup, Krull semigroup, factorial semigroup). Let U=U(D) be the group of units of D. We also show that if D is integrally closed, then $D[{\Gamma}]$, the semigroup ring of ${\Gamma}$ over D, is an integrally closed domain with $Cl(D[{\Gamma}])=Cl(D){\oplus}Cl(D)$; hence D is a PvMD (resp., GCD-domain, Krull domain, factorial domain) if and only if $D[{\Gamma}]$ is.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.455-462
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• 2013

Let D be an integral domain, S be a saturated multi-plicative subset of D such that $D_S$ is a factorial domain, $\{X_{\alpha}\}$ be a nonempty set of indeterminates, and $D[\{X_{\alpha}\}]$ be the polynomial ring over D. We show that S is a splitting (resp., almost splitting, t-splitting) set in D if and only if every nonzero prime t-ideal of D disjoint from S is principal (resp., contains a primary element, is t-invertible). We use this result to show that $D{\backslash}\{0\}$ is a splitting (resp., almost splitting, t-splitting) set in $D[\{X_{\alpha}\}]$ if and only if D is a GCD-domain (resp., UMT-domain with $Cl(D[\{X_{\alpha}\}]$ torsion UMT-domain).

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.1
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• pp.57-65
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• 2007

Along with the development of power electronics and magnetic materials, permanent magnet (PM) brushless direct current (BLDC) motors are now widely used in many fields of modern industry BLDC motors have many advantages such as high efficiency, large peak torque, easy control of speed, and reliable working characteristics. However, Compared with the other electric motors without a PM, BLDC motors with a PM have inherent cogging torque. It is often a principle source of vibration, noise and difficulty of control in BLDC motors. Cogging torque which is produced by the interaction of the rotor magnetic flux and angular variation in the stator magnetic reluctance can be reduced by sinusoidal air-gap flux density waveform due to reduction of variation of magnetic reluctance. Therefore, this paper will present a design method of magnetizing system for reduction of cogging torque and low manufacturing cost of BLDC motor with isotropic bonded neodynium-iron-boron (Nd-Fe-B) magnets in ring type by sinusoidal air-gap flux density distribution. An analytical technique of magnetization makes use of two-dimensional finite element method (2-D FEM) and Preisach model that expresses the hysteresis phenomenon of magnetic materials in order for accurate calculation. In addition, For optimum design of magnetizing fixture, Factorial design which is one of the design of experiments (DOE) is used.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.233-260
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• 2017

Let R be a factorial domain. In this work we investigate the connections between the arithmetic of Int(R) (i.e., the ring of integer-valued polynomials over R) and its monadic submonoids (i.e., monoids of the form {$g{\in}Int(R){\mid}g{\mid}_{Int(R)}f^k$ for some $k{\in}{\mathbb{N}}_0$} for some nonzero $f{\in}Int(R)$). Since every monadic submonoid of Int(R) is a Krull monoid it is possible to describe the arithmetic of these monoids in terms of their divisor-class group. We give an explicit description of these divisor-class groups in several situations and provide a few techniques that can be used to determine them. As an application we show that there are strong connections between Int(R) and its monadic submonoids. If $R={\mathbb{Z}}$ or more generally if R has sufficiently many "nice" atoms, then we prove that the infinitude of the elasticity and the tame degree of Int(R) can be explained by using the structure of monadic submonoids of Int(R).

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.601-607
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• 2011

Let D be an integral domain, X be an indeterminate over D, and D[X] be the polynomial ring over D. We show that D is an almost weakly factorial PvMD if and only if D + XDS[X] is an integrally closed almost GCD-domain for each (saturated) multiplicative subset S of D, if and only if $D+XD_1[X]$ is an integrally closed almost GCD-domain for any t-linked overring $D_1$ of D, if and only if $D_1+XD_2[X]$ is an integrally closed almost GCD-domain for all t-linked overrings $D_1{\subseteq}D_2$ of D.

• Design & Manufacturing
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• v.15 no.1
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• pp.41-47
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• 2021

The Fine Blanking process is an effective precision shearing process that can obtain a smooth cutting surface and high product precision through a single blanking process. It is widely used in various manufacturing fields. However, shearing through this fine blanking process is only intended to minimize burrs, die rolls and fracture surfaces and does not completely remove them. Therefore, it is necessary to study the minimization of burrs, die rolls and fracture surfaces in the fine blanking process. In this study, a study was conducted on the relationship between the fracture surface and process conditions that occurred during product production using the fine blanking process. For this purpose, the shape of the V-ring indenter, the distance to the punch, and the pressure force, clearance, shear rate, and physical properties of the material were selected as process and design variables, and the relationship with the fracture surface according to each process and design condition was tested. It was analyzed through the Experimental Design Method.