• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.175-180
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• 1991

In [3], [4] and [5], Hochster and Huneke introduced the notions of the tight closure of an ideal and of the weak F-regularity of a ring. This notion enabled us to give new proofs of many results in commutative algebra. A regular ring is known to be F-regular, and a Gorenstein local ring is proved to be F-regular provided that one ideal generated by a system of parameters (briefly s.o.p.) is tightly closed. In fact, a Gorenstein local ring is weakly F-regular if and only if there exists a system of parameters ideal which is tightly closed [3]. But we do not know whether this fact is true or not if a ring is not Gorenstein, in particular, a ring is a Cohen Macaulay (briefly C-M) local ring. In this paper, we will prove this in the case of an 1-dimensional C-M local ring. For this, we study the F-rationality and the normality of the ring. And we will also prove that a C-M local ring is to be Gorenstein under some additional condition about the tight closure.

• The KIPS Transactions:PartB
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• v.8B no.4
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• pp.395-402
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• 2001

본 논문에서는, 1차원 및 2차원 웨이브렛 함수를 전역통과필터(APF)와 지연기의 병렬접속에 위한 재귀형(IIR) 디지털 필터로 구성하는 방법을 제안한다. Mallat에 의하여 웨이브렛 변환과 필터뱅크가 밀접한 관계에 있다는 것이 알려졌고, 완전 재구성 필터뱅크로부터 웨이브렛 함수를 도출하는 다양한 방법이 알려져 있다. 그러나, 이러한 방법의 대부분은 비재귀형(FIR) 디지털 필터에 근거를 두는 것으로, 재귀형 디지털 필터에 의한 방법은 거의 제안되어 있지 않다. 재귀형 필터를 이용하는 장점은 비재귀형에 비하여 낮은 차수로 표현되는 점이다. 또 직교 웨이브렛 함수를 끌어내기 위한 직교조건을 용이하게 만족시킬 수 있다. 본 논문에서는 웨이브렛 함수에 요구되는 레귤레리티(Regularity)조건을 만족시키기 위하여, 최대 평탄성(Maximally Flat)을 부가한 새로운 1차원 및 2차원 재귀형 웨이브렛 함수의 도출법을 보인다.

• The Journal of Internal Korean Medicine
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• v.25 no.4
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• pp.158-166
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• 2004

Background & Object : The aim of this study was to investigate the usefulness of electrogastrography in the diagnosis field of traditional medicine through a study of the relationship between gastric motility and health condition based on oriental medicine diagnostic theory in functional dyspepsia. Method : 86 patients (male 27, female 59) with functional dyspepsia and 10 healthy control subjects (male 5, female 5) were involved in the investigation. The disease information of functional dyspepsia (based on Rome criteria II) was used for dyspeptic index and scores were obtained from the comprehensive diagnosis of Qui, Xue, Shui was applied as index for health condition, those were all investigated by questionnaire. Gastric motility were recorded and analyzed using electrogastrography in fasting and postprandial period. Results : The total score of comprehensive diagnosis of Qui Xue Shui was influenced by the number of functional dyspepsia symptoms (p=0.026). In terms of electrogastrographical parameters, both postpranial normal slow waves regularity(p=0.003) and power ratio (p=0.001) in the patients had the statistical significance and they showed an incremental inverse correlation with the number of symptoms. Dominant frequency and fasting normal slow waves regularity ratio had no statistical significance. Conclusion : Results suggest that electrogastrography is useful in evaluating the health condition of patient by comprehensive diagnosis of Qui Xue Sui.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.809-822
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• 2007

Certain weak type endpoint estimates are established for maximal commutators generated by $Calder\acute{o}n-Zygmund$ operators and $Osc_{exp}L^{\gamma}({\mu})$ functions for ${\gamma}{\ge}1$ under the condition that the underlying measure only satisfies some growth condition, where the kernels of $Calder\acute{o}n-Zygmund$ operators only satisfy the standard size condition and some $H\ddot{o}rmander$ type regularity condition, and $Osc_{exp}L^{\gamma}({\mu})$ are the spaces of Orlicz type satisfying that $Osc_{exp}L^{\gamma}({\mu})$ = RBMO(${\mu}$) if ${\gamma}$ = 1 and $Osc_{exp}L^{\gamma}({\mu}){\subset}RBMO({\mu})$ if ${\gamma}$ > 1.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1713-1726
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• 2018

We study the one-sided regularity of matrices in upper triangular matrix rings in relation with the structure of diagonal entries. We next consider a ring theoretic condition that ab being regular implies ba being also regular for elements a, b in a given ring. Rings with such a condition are said to be commutative at regular product (simply, CRP rings). CRP rings are shown to be contained in the class of directly finite rings, and we prove that if R is a directly finite ring that satisfies the descending chain condition for principal right ideals or principal left ideals, then R is CRP. We obtain in particular that the upper triangular matrix rings over commutative rings are CRP.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.753-760
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• 2013

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a bounded Lipschitz do-main under Dirichlet boundary condition. We present by a very simple argument that a strong solution exists globally when the product of $L^2$ norms of the initial velocity and the gradient of the initial velocity and $L^{p,2}$, $p{\geq}4$ norm of the forcing function are small enough. Our condition is scale invariant and implies many typical known global existence results for small initial data including the sharp dependence of the bound on the volumn of the domain and viscosity. We also present a similar result in the whole domain with slightly stronger condition for the forcing.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.195-210
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• 2007

This paper develops a consistent nonparametric test for Granger causality in the context of strong-mixing process, which covers a large class of stationary processes including ARMA and ARCH models. The previously proposed tests require absolute regularity ($\beta$-mixing) more stringent than the strong-mixing condition. We prove the consistency of the test under a high level assumption on the approximation error of U statistic by its projection. Due to the sample splitting, the test statistic we propose is asymptotically normally distributed under the null.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.635-641
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• 2014

The existence and the regularity of the particle trajectory flow X(x, t) along a velocity field u on $\mathbb{R}^n$ are discussed under the BMO-blow-up condition: $${\int}_{0}^{T}{\parallel}{\omega}({\tau}){\parallel}_{BMO}d{\tau}<{\infty}$$ of the vorticity ${\omega}{\equiv}{\nabla}{\times}u$. A comment on our result related with the mystery of turbulence is presented.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.31-48
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• 2006

In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

• Journal of Sasang Constitutional Medicine
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• v.30 no.1
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• pp.24-31
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• 2018

Objectives The purpose of this study is to find out whether there is any difference in lifestyle by health status in the same Sasang constitution type, and whether there is any difference in lifestyle by the Sasang constitution type in the same health condition. Methods We used collected the clinical data of Korean medicine Data Center (KDC). In this study, we used items of the lifestyle about meal and sleep (Meal regularity, Meal amount, Meal time, Dream, Sleep well, Hard to fall asleep, Shallow sleep, Nap, Sleep time, Quality of sleep) as variables. We found the differences of lifestyles using the Chi-square test and ANOVA. We analyzed using SPSS statistics 21.0 for Korean. Results & Conclusions When we compared the lifestyle by Sasang constitution type in each health status, there were differences in items of meal amount and nap. When we compared the lifestyle by health status in each Sasang constitution type, we found differences in items of meal regularity, sleep well, nap etc. However, in TE tpe, there was not these differences by health status.