• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.817-828
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• 2005

In this note we show that there is an anti-symplectic involution $\sigma\;:\;X\;\to\;X$ on a simply-connected, closed, non-Kahler and symplectic 4-manifold X with a disjoint union of Riemann surfaces ${\amalg}^n_{i=1}{\Sigma}_i,\;n\;{\ge}\;2$ as a fixed point set. Also we show that its quotient X/$\sigma$ is homeomorphic to $\mathbb{CP}^2{\sharp}r\mathbb{CP}^2$ but not diffeomorphic to $\mathbb{CP}^2{\sharp}r\mathbb{CP}^2,\;r\;=\;b_2^-(X/{\sigma})$.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.347-355
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• 2001

Let ($X, \omega$) be a closed symplectic 4-manifold. Let a finite cyclic group G act semifreely, holomorphically on X as isometries with fixed point set $\Sigma$(may be empty) which is a 2-dimension submanifold. Then there is a smooth structure on the quotient X'=X/G such that the projection $\pi$:X$\rightarrow$X' is a Lipschitz map. Let L$\rightarrow$X be the Spin$^c$ -structure on X pulled back from a Spin$^c$-structure L'$\rightarrow$X' and b_2^$+(X')>1. If the Seiberg-Witten invariant SW(L')$\neq$0 of L' is non-zero and $L=E\bigotimesK^-1\bigotimesE$ then there is a G-invariant pseudo-holomorphic curve u:$C\rightarrowX$,/TEX> such that the image u(C) represents the fundamental class of the Poincare dual $c_1$(E). This is an equivariant version of the Taubes' Theorem.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.283-312
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• 2020

A sufficient condition for an Artinian complete intersection quotient S = 𝕜[x, y]/(x^m, yⁿ), where 𝕜 is an algebraically closed field of a prime characteristic, to have the strong Lefschetz property (SLP) was proved by S. B. Glasby, C. E. Praezer, and B. Xia in [3]. In contrast, we find a necessary and sufficient condition on m, n satisfying 3 ≤ m ≤ n and p > 2m-3 for S to fail to have the SLP. Moreover we find the Jordan types for S failing to have SLP for m ≤ n and m = 3, 4.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1387-1408
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• 2022

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :_R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N :_R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.895-903
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• 2023

In this paper, we give some results on 2-strongly Gorenstein projective modules and related rings. We first investigate the relationship between strongly Gorenstein projective modules and periodic modules and then give the structure of modules over strongly Gorenstein semisimple rings. Furthermore, we prove that a ring R is 2-strongly Gorenstein hereditary if and only if every ideal of R is Gorenstein projective and the class of 2-strongly Gorenstein projective modules is closed under extensions. Finally, we study the relationship between 2-Gorenstein projective hereditary and 2-Gorenstein projective semisimple rings, and we also give an example to show the quotient ring of a 2-Gorenstein projective hereditary ring is not necessarily 2-Gorenstein projective semisimple.

• Phonetics and Speech Sciences
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• v.15 no.4
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• pp.53-60
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• 2023

This study compared the absolute error of estimated fundamental frequency (AEF0) using voice - (VRP) and speech range profile (SRP) tasks across various etiological groups with voice disorders. Additionally, we explored the association between AEF0 and related voice parameters within each specific etiological group. The participants included 120 individuals, comprising 30 each from the functional (FUNC), organic (ORGAN), and eurological (NEUR) voice disorder groups, and a normal control group (NC). Each participant performed voice and SRP tasks, and the fundamental frequency of connected speech was measured using electroglottography (EGG). When comparing the AEF0 measures across the etiological groups, there were no differences in Grade and Severity among the patients. However, variations were observed in AEF0_VRP and AEF0_SUM. Specifically, AEF0_VRP was higher in the ORGAN group than in the FUNC and NC groups, whereas AEF0_SUM was higher in the ORGAN group than in the NC group. Furthermore, within FUNC and NEUR, AEF0 showed a positive correlation with Grade, while in ORGAN, it exhibited a positive correlation with the mean closed quotient (CQ). Attention should be paid to the application of AEF0 measures and related voice variables based on the etiological group. This study provides foundational information for the clinical application of AEF0 measures.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.723-744
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• 2010

The aim of this study was to find the effects of open-ended problems on mathematical creativity and brain function. In this study, one class of first grade students were allocated randomly into two groups. Each group solved different problems. The experimental group solved the open-ended problems and the comparison group solved the closed-problems. Mathematical creativity was tested by the paper test. And Brain function was tested by an EEG(electroencephalogram) tester. The results of this study are as follows. Firstly, this study analyzed how the open-ended problems are effective on mathematical creativity. This analysis showed that it had a meaningful influence on the mathematical creativity(p=0.46). Accordingly, we could find out that open-ended problems make the student connect the mathematical concept and idea and think variously. Secondly, this study analyzed the effect of open-ended problems on brain function. This analysis showed that it did not have a meaningful influence on the brain function(p=.073) statistically but the experimental group's evaluation was higher than comparison groups' at the post-test. It also had a meaningful influence on the brain attention quotient(left) (p=.007), attention quotient(right) (p=.023) and emotion tendency quotient(p=.025). As a result of such tests, we could find out that open-ended problems are effective on brain function, especially on the attention ability. With the use of the open-ended problems, students could show quick understanding and response. An emotion tendency is also developed in the process. Because various answers are accepted, the students gain an internal reward at the process of finding an answer. Putting the above results together, we could find that open-ended problem is effective on mathematical creativity and brain function.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.907-913
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• 2010

Let D be an integrally closed domain with quotient field K, * be a star operation on D, X, Y be indeterminates over D, $N_*\;=\;\{f\;{\in}\;D[X]|\;(c_D(f))^*\;=\;D\}$ and $R\;=\;D[X]_{N_*}$. Let b be the b-operation on R, and let $*_c$ be the star operation on D defined by $I^{*_c}\;=\;(ID[X]_{N_*})^b\;{\cap}\;K$. Finally, let Kr(R, b) (resp., Kr(D, $*_c$)) be the Kronecker function ring of R (resp., D) with respect to Y (resp., X, Y). In this paper, we show that Kr(R, b) $\subseteq$ Kr(D, $*_c$) and Kr(R, b) is a kfr with respect to K(Y) and X in the notion of [2]. We also prove that Kr(R, b) = Kr(D, $*_c$) if and only if D is a $P{\ast}MD$. As a corollary, we have that if D is not a $P{\ast}MD$, then Kr(R, b) is an example of a kfr with respect to K(Y) and X but not a Kronecker function ring with respect to K(Y) and X.

• Journal of Biomedical Engineering Research
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• v.25 no.5
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• pp.343-349
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• 2004

Electroglottograph(EGG) is a signal recorded from the vocal cord vibration by measuring electrical impedance across the vocal folds through the neck skin. The purpose of this study was to develop EGG system and to evaluate possibility for the application on speech analysis and laryngeal disease diagnosis. EGG system was composed of two pairs of ring electrodes, tuned amplifier, phase sensitive detector, low pass filter, and auto-gain controller. It was designed to extract electric impedance after detecting by amplitude modulation method with 2.7MHz carrier signal. Extracted signals were transmitted through line-in of PC sound card, sampled and quantized. Closed Quotient(CQ), Speed Quotient(SQ), Speed Index(SI), fundamental frequency of vocal cord vibration(F0), pitch variability of vocal fold vibration (Jitter), and peak-to-peak amplitude variability of vocal fold vibration(Shimmer) were analyzed as EGG parameters. Experimental results were as follows: the faster vocal fold vibration, the higher values in CQ parameter and the lower values in SQ and SI parameters. EGG and speech signals had the same fundamental frequency. CQ, SQ, and SI were significantly different between normal subjects and patients with laryngeal cancer. These results suggest that it is possible to implement portable EGG system to monitor the function of vocal cord and to test functional changes of the glottis.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.427-436
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• 2005

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 v 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 v-ideals $m=P_0\;{\supset}\;P_1\;{\supset}\;{\cdotS}\;{\supset}\;P_t=P$ and all the other v-ideals are uniquely factored into a product of those simple ones. It then was also shown by Lipman that the predecessor of the smallest simple v-ideal P is either simple (P is free) or the product of two simple v-ideals (P is satellite), that the sequence of v-ideals between the maximal ideal and the smallest simple v-ideal P is saturated, and that the v-value of the maximal ideal is the m-adic order of P. Let m = (x, y) and denote the v-value difference |v(x) - v(y)| by $n_v$. In this paper, if the m-adic order of P is 2, we show that $O(P_i)\;=\;1\;for\;1\;{\leq}\;i\; {\leq}\;{\lceil}\;{\frac{b+1}{2}}{\rceil}\;and\;O(P_i)\;=2\;for\;{\lceil}\;\frac{b+3}{2}\rceil\;{\leq}\;i\;\leq\;t,\;where\;b=n_v$. We also show that $n_w\;=\;n_v$ when w is the prime divisor associated to a simple v-ideal $Q\;{\supset}\;P$ of order 2 and that w(R) = v(R) as well.