• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.511-528
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• 2008

Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and $\upsilon$ be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple $\upsilon$-ideals $m\;=\;P_0\;{\supset}\;P_1\;{\supset}\;{\cdots}\;{\supset}\;P_t\;=\;P$ and all the other $\upsilon$-ideals are uniquely factored into a product of those simple ones [17]. Lipman further showed that the predecessor of the smallest simple $\upsilon$-ideal P is either simple or the product of two simple $\upsilon$-ideals. The simple integrally closed ideal P is said to be free for the former and satellite for the later. In this paper we describe the sequence of simple $\upsilon$-ideals when P is satellite of order 3 in terms of the invariant $b_{\upsilon}\;=\;|\upsilon(x)\;-\;\upsilon(y)|$, where $\upsilon$ is the prime divisor associated to P and m = (x, y). Denote $b_{\upsilon}$ by b and let b = 3k + 1 for k = 0, 1, 2. Let $n_i$ be the number of nonmaximal simple $\upsilon$-ideals of order i for i = 1, 2, 3. We show that the numbers $n_{\upsilon}$ = ($n_1$, $n_2$, $n_3$) = (${\lceil}\frac{b+1}{3}{\rceil}$, 1, 1) and that the rank of P is ${\lceil}\frac{b+7}{3}{\rceil}$ = k + 3. We then describe all the $\upsilon$-ideals from m to P as products of those simple $\upsilon$-ideals. In particular, we find the conductor ideal and the $\upsilon$-predecessor of the given ideal P in cases of b = 1, 2 and for b = 3k + 1, 3k + 2, 3k for $k\;{\geq}\;1$. We also find the value semigroup $\upsilon(R)$ of a satellite simple valuation ideal P of order 3 in terms of $b_{\upsilon}$.

• The Journal of Industrial Distribution & Business
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• v.12 no.6
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• pp.75-88
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• 2021

Purpose: This research aimed at exploring the functions of consumers' perceiving approach and avoidance roles and their feeling anger and disgust in the effect of the two types of self-discrepancy at social identity such as the ideal self-discrepancy and the ought self-discrepancy on within-self domain versus across-self domain consumption. Research design, data, and methodology - This study divided the self-discrepancy group into the ideal self-discrepancy and the ought self-discrepancy group as experimental groups for empirical study. Self-discrepancy type between-subjects design was used to develop two types of questionnaire according to the type of experimental groups. The platform, 'questionnaire stars' of 'WeChat' in China was used to collect 103 data from the ideal self-discrepancy group and 102 from the ought self-discrepancy group for empirical study. T-test and the structural equation model in Amos 21 were used to verify hypotheses developed through theoretical review. Results - First, ideal self-discrepancy positively affected the role-approaching goal and anger. Second, ought self-discrepancy positively affected the role-avoiding goal and disgust. Third, the role-approaching goal and anger positively influenced on the within- versus across- domain consumption. Fourth, the disgust negatively influenced on the within- versus across- domain consumption, however the role-avoiding goal did not influence on the consumption. Fifth, there was the mediation roles of anger (disgust) in the effects of ideal (ought) self-discrepancy on the consumption. Conclusions - When consumers feel anger at the ideal self- discrepancy induced by in-group, it is necessary for the marketers to promote their product brand used by the in-group. They should develop and advertise the messages priming the ideal self-discrepancy and the anger to increase the intent to purchase or use their product brand when the in-group members have used the brand by relating the brand to their social identity concerned with the ideal self-discrepancy. However, marketers should help consumers feel disgust by developing and advertising the messages expressing the ought self-discrepancy to lead the consumers to the place of purchasing or using their product brand when the members have used the brand based on keeping the consistence between the brand and other social identity not related to the ought self-discrepancy.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.653-663
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• 2022

We study cyclic codes of length n over 𝔽_2^t. Cyclic codes can be viewed as ideals in 𝓡_n = 𝔽_2^t [x]/(xⁿ − 1). It is known that there is a unique generating idempotent for each ideal. Let e(x) ∈ 𝓡_n. If t = 1 or t = 2, then there is a necessary and sufficient condition that e(x) is an idempotent. But there is no known similar result for t ≥ 3. In this paper we give an answer for this problem.

• Journal of the Korean Society of Costume
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• v.54 no.3
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• pp.43-51
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• 2004

The purpose of this study was to compare ideal clothing and actual clothing behavior between Korean and Japanese college students. 185 Korean students and 91 Japanese students were used into data analysis from October to December. 2000. The age range was 18 to 28 years. The results were as followed. 1) Japanese students wanted to wear fitted clothing styles with revealing the body, while Koreans wanted to wear not only fitted styles but also relaxed and coved body styles. 2) Korean students wore more loose styles and fitted upper styles and pants than Japanese students. On the other hand, Japanese students wore fitted clothing styles and skirt. 3) Japanese students showed higher correlation between ideal clothing styles and actual clothing styles than Koreans. This means that although Koreans want to wear ideal styles, they don't wear those styles much. 4) Overweight students tended to avoid wearing fitted and revealed body styles, pursuing more loose and coved body styles. This tendency showed stronger to Koreans than Japanese students.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.397-420
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• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.

• Transactions of Materials Processing
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• v.13 no.6 s.70
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• pp.540-545
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• 2004

Ever since the ideal forming theory has been developed for process design purposes, application has been limited to sheet forming and, fur bulk forming, to two-dimensional steady flow. Here, application for the non-steady case was performed under the plane-strain condition based on the theory previously developed. In the ideal flow, material elements deform following the minimum plastic work path (or mostly proportional true strain path) so that the ideal plane-stram flow can be effectively described using the two-dimensional orthogonal convective coordinate system. Besides kinematics, fur a prescribed final part shape, schemes to optimize a preform shape out of a class of initial configurations and also to define the evolution of shapes and boundary tractions were developed. Discussions include the two problematic issues on internal tractions and the non-monotonous straining. For demonstration purposes, numerical calculations were made for a bulk part under forging.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.127-135
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m. Then we say that I is an equimultiple good ideal in A, if I contains a reduction Q = ( $a_1$, $a_2$,ㆍㆍㆍ, $a_{s}$ ) generated by s elements in A and G(I) =(equation omitted)$_{n 0}$ $I^{n}$ / $I^{n＋1}$ of I is a Gorenstein ring with a(G(I)) = 1 - s, where s = h $t_{A}$ I and a(G(I)) denotes the a-invariant of G(I). Let $X_{A}$$^{s}$ denote the set of equimultiple good ideals I in A with h $t_{A}$ I = s, R(I) = A [It] be the Rees algebra of I, and $K_{R(I)}$ denote the canonical module of R(I). Let a I such that $I^{n＋l}$ = a $I^{n}$ for some n$\geq$0 and $\mu$$_{A}$(I)$\geq$2, where $\mu$$_{A}$(I) denotes the number of elements in a minimal system of generators of I. Assume that A/I is a Cohen-Macaulay ring. We show that the following conditions are equivalent. (1) $K_{R(I)}$(equation omitted)R(I)＋as graded R(I)-modules. (2) $I^2$ = aI and aA : I$\in$ $X^1$$_{A}$._{A}$./.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.387-391
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• 2004

Let A be Noetherian ring, a= (${\tau}_1..., \tau_n$ an ideal of A and $C_{A}$ be category of A-modules and A-homomorphisms. We show that the connected left sequences of covariant functors ${limH_i(K.(t^t,-))}_{i\geq0}$ and ${lim{{Tor^A}_i}(\frac{A}{a^f}-)}_{i\geq0}$ are isomorphic from $C_A$ to itself, where $\tau^t\;=\;{{\tau_^t}_1$, ㆍㆍㆍ${\tau^t}_n$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.629-636
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• 1999

We introduce Lipschitz algebras of differentiable functions of a perfect compact plane set X and extend the definition to Lipschitz algebras of infinitely differentiable functions of X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.653-661
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• 2010

Let R be a ring, and let $\Psi$(R) be the ideal generated by the set {x $\in$R | 1 + sxt $\in$ R is unit-regular for all s, t $\in$ R}. We show that $\Psi$(R) has "radical-like" property. It is proven that $\Psi$(R) has stable range one. Thus, diagonal reduction of matrices over such ideal is reduced.