• 대한수학회지
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• 제45권6호
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• pp.1561-1576
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• 2008

In this paper we shall prove some weighted norm inequalities of the form $${\int}_{R^n}\;|Tf(x)|^pu(x)dx\;{\leq}\;C_p\;{\int}_{R^n}\;|f(x)|^pNu(x)dx$$ for certain rough singular integral T and maximal singular integral $T^*$. Here u is a nonnegative measurable function on $R^n$ and N denotes some maximal operator. As a consequence, some vector valued inequalities for both T and $T^*$ are obtained. We shall also get a boundedness result of T on the Triebel-Lizorkin spaces.

• 대한수학회지
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• 제34권3호
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• pp.543-551
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• 1997

We prove a norm inequality of the form $\left\$\mid$ \upsilon \right\$\mid$ \leq (r - 1) \left\$\mid$ u \right\$\mid$_p, 1 < p < \infty$, between a non-negative subharmonic function u and a smooth function $\upsilon$ satisfying $$\mid$\upsilon(0)$\mid$ \leq u(0), $\mid$\nabla\upsilon$\mid$ \leq \nabla u$\mid$$ and $\mid$\Delta\upsilon$\mid$ \leq \alpha\Delta u$, where $\alpha$ is a constant with $0 \leq \alpha \leq 1$. This inequality extends Burkholder's inequality where $\alpha = 1$.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2001년도 춘계학술대회 학술발표 논문집
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• pp.231-235
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• 2001

순수한 부울 검색 시스템은 문서와 질의 사이의 유사도를 나타내는 문서값을 계산할 수 없기 때문에, 검색된 문서들을 질의를 만족하는 정보에 따라 정렬할 수 없다. 부울 검색 시스템의 이러한 단점을 보완하는 방법으로 MMM 모델, Paice 모델, P-norm 모델이 개발되었다. 본 논문에서는 높은 검색 효과를 제공하는 질의분해 적합성 피드백(QSRF) 모델을 제안한다. 질의 분해 적합성 피드백 모델의 연산 특성이 MMM, Paice, P-norm 모델보다 우수함을 설명하고, 또한 성능 비교를 통하여 이를 입증한다.

• 통합자연과학논문집
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• 제6권4호
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• pp.251-255
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• 2013

For the mean vector of a p-variate normal distribution ($p{\geq}4$), the optimal estimation within the class of modified James-Stein type decision rules under the quadratic loss is given when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}{\theta}-\bar{\theta}1{\parallel}$ it known.

• Korean Journal of Acupuncture
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• 제30권4호
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• pp.305-318
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• 2013

Objectives : The aim of this study was to examine the effect of electroacupuncture(EA) at an acupoint, HT8(Sobu), on normal humans by using power spectral analysis. We examined the effect on the Heart Rate Variability(HRV), and the balance of the autonomic nervous system. Methods : Thirty-two healthy volunteers participated in this study. EEG(Electroencephalogram) power spectrum exhibits site-specific and state-related differences in specific frequency bands. A thirty-two channel EEG study was carried out on thirty-two subjects(14 males; mean age=23.5 years old, 18 females; mean age=21.5 years old). HRV and EEG were simultaneously recorded before and after acupuncture. Results : In the ${\alpha}$(alpha) band, during the HT8-acupoint treatment, the power values in the ${\alpha}$(alpha) band significantly decreased(p<0.05) at 28 channels. In the ${\beta}$(beta) band significantly decreased(p<0.05) at 26 channels. In ${\delta}$(delta) band significantly decreased(p<0.05) at 18 channels. In ${\theta}$(theta) band significantly decreased(p<0.05) at 20 channels. ${\alpha}/{\beta}$ values were increased at 6 channels and decreased at 10 channels.${\beta}/{\theta}$ values were increased at 10 channels and decreased at 19 channels. Mean-RR(RR-interval), Complexity, RMSSD(Root mean square of successive differences), SDSD(Standard deviations differences between adjacent normal R-R intervals), norm HF showed a significantly increased and mean-HRV, norm LF, LHR(LF/HF Ratio) showed a significantly decreased after HT8-acupoint treatment(p<0.05). Conclusions : These results suggest that EA at the HT8 mostly causes significant changes on alpha(28 channels), beta(26 channels), delta(18 channels), theta(20 channels) bands and mean-HRV, mean-RR, complexity, RMSSD, SDSD, norm LF, norm HF and LHR. If practicing EA at the HT8, it will regulate the function of the cerebral cortex, decrease activity of the sympathetic and increase parasympathetic nervous activity.

• 대한수학회논문집
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• 제28권2호
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• pp.231-241
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• 2013

On the framework of the 2-adic group $\mathcal{Z}_2$, we study a Sobolev-like inequality where we estimate the $L^2$ norm by a geometric mean of the BV norm and the $\dot{B}_{\infty}^{-1,{\infty}}$ norm. We first show, using the special topological properties of the $p$-adic groups, that the set of functions of bounded variations BV can be identified to the Besov space ˙$\dot{B}_1^{1,{\infty}}$. This identification lead us to the construction of a counterexample to the improved Sobolev inequality.

• 대한수학회지
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• 제55권2호
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• pp.313-326
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• 2018

The paper studies some new ${\mathbb{C}}^n$-generalizations of Bergman type operators introduced by Shields and Williams depending on a normal pair of weight functions. We find the values of parameter ${\beta}$ for which these operators are bounded on mixed norm spaces L(p, q, ${\beta}$) over the unit ball in ${\mathbb{C}}^n$. Moreover, these operators are bounded projections as well, and the images of L(p, q, ${\beta}$) under the projections are found.

• 대한수학회논문집
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• 제9권3호
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• pp.731-737
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• 1994

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measures on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$- algebras of F. If $r > 0$, let $J = [-r, 0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert_C = sup_{s \in J} $\mid$\gamma(x)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E and F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$ with the norm $\Vert T \Vert = sup {$\mid$T(x)$\mid$_F : x \in E, $\mid$x$\mid$_E \leq 1}$.

• Structural Engineering and Mechanics
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• 제82권6호
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• pp.771-783
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• 2022

Structural damage identification (SDI) methods have been proposed to monitor the safety of structures. However, the traditional SDI methods using modal parameters, such as natural frequencies and mode shapes, are not sensitive enough to structural damage. To tackle this problem, this paper proposes a new SDI method based on transmissibility assurance criterion (TAC) and weighted Schatten-p norm regularization. Firstly, the transmissibility function (TF) has been proved a useful damage index, which can effectively detect structural damage under unknown excitations. Inspired by the modal assurance criterion (MAC), TF and MAC are combined to construct a new damage index, so called as TAC, which is introduced into the objective function together with modal parameters. In addition, the weighted Schatten-p norm regularization method is adopted to improve the ill-posedness of the SDI inverse problem. To evaluate the effectiveness of the proposed method, some numerical simulations and experimental studies in laboratory are carried out. The results show that the proposed method has a high SDI accuracy, especially for weak damages of structures, it can precisely achieve damage locations and quantifications with a good robustness.

• 통합자연과학논문집
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• 제10권1호
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• pp.33-39
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• 2017

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-q{\geq}3)$, $q=rank(P_V)$ with a projection matrix $P_v$ under the quadratic loss, based on a sample $X_1$, $X_2$, ${\cdots}$, $X_n$. We find a James-Stein type decision rule which shrinks towards projection vector when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}{\theta}-P_V{\theta}{\parallel}$ is restricted to a known interval, where $P_V$ is an idempotent and projection matrix and rank $(P_V)=q$. In this case, we characterize a minimal complete class within the class of James-Stein type decision rules. We also characterize the subclass of James-Stein type decision rules that dominate the sample mean.