• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.435-442
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• 2017

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}$ (p ${\geq}$ 3) under the quadratic loss from multi-variate normal population. We find a James-Stein type estimator which shrinks towards the projection vectors when the underlying distribution is that of a variance mixture of normals. In this case, the norm ${\parallel}{\theta}-K{\theta}{\parallel}$ is known where K is a projection vector with rank(K) = q. The class of this type estimator is quite general to include the class of the estimators proposed by Merchand and Giri (1993). We can derive the class and obtain the optimal type estimator. Also, this research can be applied to the simple and multiple regression model in the case of rank(K) ${\geq}2$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.3-8
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• 2007

In this paper a generalized parametric mean length $L(P^{\nu},\;R)$ has been defined and bounds for $L(P^{\nu},\;R)$ are obtained in terms of generalized R-norm information measure.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.11-21
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• 1998

A condition for a certain maximal operator to be of strong type (p,p) is characterized in terms of Carleson measure.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.225-237
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• 2019

We introduce a larger ideal ${\mathcal{N}}_{wp}$ of the ideal of p-nuclear operators. We obtain isometric representations of the injective and surjective hulls of ${\mathcal{N}}_{wp}$ and study them.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.841-852
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• 2019

We establish the generalized Myers theorem for Finsler manifolds under integral Ricci curvature bound. More precisely, we show that the forward complete Finsler n-manifold whose part of Ricci curvature less than a positive constant is small in $L^p$-norm (for p > n/2) have bounded diameter and finite fundamental group.

• Toxicological Research
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• v.34 no.4
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• pp.363-370
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• 2018

Many studies reported reduced antioxidant capacity in the vasculature under hypertensive conditions. However, little is known about the effects of antihypertensive treatments on the regulation of vascular antioxidant enzymes. Thus, we hypothesized that antihypertensive treatments prevent the reduction of antioxidant enzyme activity and expression in the small vessels of angiotensin II-induced hypertensive rats (ANG). We observed the small mesenteric arteries and small renal vessels of normotensive rats (NORM), ANG, and ANG treated with a triple antihypertensive therapy of reserpine, hydrochlorothiazide, and hydralazine (ANG + TTx). Systolic blood pressure was increased in ANG, which was attenuated by 2 weeks of triple therapy (127, 191, and 143 mmHg for NORM, ANG, and ANG + TTx, respectively; p < 0.05). Total superoxide dismutase (SOD) activity in the small mesenteric arteries of ANG was lower than that of NORM. The protein expression of SOD1 was lower in ANG than in NORM, whereas SOD2 and SOD3 expression was not different between the groups. Reduced SOD activity and SOD1 expression in ANG was not restored in ANG + TTx. Both SOD activity and SOD isoform expression in the small renal vessels of ANG were not different from those of NORM. Interestingly, SOD activity in the small renal vessels was reduced by TTx. Between groups, there was no difference in catalase activity or expression in both the small mesenteric arteries and small renal vessels. In conclusion, SOD activity in the small mesenteric arteries decreased by angiotensin II administration, but not by hypertension, which is caused by decreased SOD1 expression.

• Journal of the Korean Mathematical Society
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• v.28 no.1
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• pp.79-86
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• 1991

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.163-176
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• 2001

We examine Orlicz-type integral inequalities for operators and obtain as a corollary a characterization of such inequalities for the Hardy-Littlewood maximal operator extending the well-known L(sup)p-norm inequalities.

• Korean Journal of Mathematics
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• v.12 no.2
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• pp.193-200
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• 2004

We shall introduce the notion of the windowed Fourier transform in $\mathbb{Q}_p$ and show that, for any given function $g{\in}L^2(\mathbb{Q}_p)$ of norm, the windowed Fourier transform of $f$ with respect to $g$ be a function of norms, and moreover be expressible to a summation form. The results obtained in this paper will be usable to the field of research in data compression for signal processing according to the following scheme.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1025-1031
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• 2017

We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.