• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.197-224
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• 2019

Let A be a $JB^*$-triple with Banach dual space $A^*$ and bi-dual the $JBW^*$-triple $A^{**}$. Elements x of $A^*$ of norm one may be regarded as normalised 'Q-measures' defined on the complete ortho-lattice ${\tilde{\mathcal{U}}}(A^{**})$ of tripotents in $A^{**}$. A Q-measure x possesses a support e(x) in ${\tilde{\mathcal{U}}}(A^{**})$ and a compact support $e_c(x)$ in the complete atomic lattice ${\tilde{\mathcal{U}}}_c(A)$ of elements of ${\tilde{\mathcal{U}}}(A^{**})$ compact relative to A. Necessary and sufficient conditions for an element v of ${\tilde{\mathcal{U}}}_c(A)$ to be a compact support tripotent $e_c(x)$ are given, one of which is related to the Q-covering numbers of v by families of elements of ${\tilde{\mathcal{U}}}_c(A)$.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.707-717
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• 1997

The square of Brownian density process $Q^\lambda$ is defined where $\lambda$ is a parameter. Applying limit theorems of stochastic integrals w.r.t. martingale measure, we prove a weak limit theorem for $Q^\lambda$ in $D_{S'(R^d)}[0,1]$.

• Proceedings of the Korea Society for Simulation Conference
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• 1999.10a
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• pp.62-62
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• 1999

In this paper, we propose a new technique of estimating tail of steady-state queue length distribution; Pr(Q>q), fo ATM multiplexer. Pr(Q>q) is a fundamental measure of network congestion. Assessing Pr(Q>q) properly is crucial for design and control of ATM networks. Data traffic pattern of high-speed networks is highly correlated and bursty. Estimating Pr(Q>q) is very difficult because of correlation and burstiness. We estimate entropy(rate-function) using large deviation principles and threshold bootstrap. Simulation studies are conducted to compare the performance of an existing method and our new method.

• Journal of Biomedical Engineering Research
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• v.31 no.1
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• pp.27-32
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• 2010

Noninvasive detection of patients with probable Alzheimer's disease (AD) is of great importance for assisting a medical doctor's decision for early treatment of AD patients. In the present study, we have extracted quantitative electroencephalogram (qEEG) variables, which can be potentially used to diagnose AD, from resting eyes-closed continuous EEGs of 22 AD patients and 27 age-matched normal control (NC) subjects. We have extracted qEEG variables from mean phase coherence (MPC) and EEG coherence, evaluated for all possible combinations of electrode pairs. Preliminary trials to discriminate the two groups with the extracted qEEG variables demonstrated that the use of MPC as a supplementary or alternative measure for the EEG coherence may enhance the accuracy of noninvasive diagnosis of AD.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.155-162
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• 1995

Let $\mu$ be a positive Borel measure on $R^n$ which is positive on cubes. For any cube $Q \subset R^n$, a Borel measurable nonnegative function $\varphi_Q$, supported and positive a.e. with respect to $\mu$ in Q, is given. We consider a maximal function $$ M_{\mu}f(x) = sup \int \varphi Q$\mid$f$\mid$d_{\mu} $$ where the supremum is taken over all $\varphi Q$ such that $x \in Q$.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1073-1097
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• 2022

In this paper, we shall be concerned with evaluation of multifractal Hausdorff measure 𝓗^q,t_𝜇 and multifractal packing measure 𝓟^q,t_𝜇 of Cartesian product sets by means of the measure of their components. This is done by investigating the density result introduced in [34]. As a consequence, we get the inequalities related to the multifractal dimension functions, proved in [35], by using a unified method for all the inequalities. Finally, we discuss the extension of our approach to studying the multifractal Hewitt-Stromberg measures of Cartesian product sets.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.469-479
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• 2003

Let B be the open unit ball in $C^{n}$ and ${\mu}_{q}$(q > -1) the Lebesgue measure such that ${\mu}_{q}$(B) ＝ 1. Let ${L_{a,q}}^2$ be the subspace of ${L^2(B,D{\mu}_q)$ consisting of analytic functions, and let $\overline{{L_{a,q}}^2}$ be the subspace of ${L^2(B,D{\mu}_q)$) consisting of conjugate analytic functions. Let $\bar{P}$ be the orthogonal projection from ${L^2(B,D{\mu}_q)$ into $\overline{{L_{a,q}}^2}$. The little Hankel operator ${h_{\varphi}}^{q}\;:\;{L_{a,q}}^2\;{\rightarrow}\;{\overline}{{L_{a,q}}^2}$ is defined by ${h_{\varphi}}^{q}(\cdot)\;=\;{\bar{P}}({\varphi}{\cdot})$. In this paper, we will find the necessary and sufficient condition that the little Hankel operator ${h_{\varphi}}^{q}$ is bounded(or compact).

• The Journal of the Acoustical Society of Korea
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• v.27 no.1
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• pp.26-32
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• 2008

UBSS (unde-determined blind source separation) is composed of the stages of BMMR (blind mixing matrix recovery) and BSR (blind source recovery). Generally, these two stages are executed using the sparseness of the observed data, and their performance is influenced by the accuracy of the measure of the sparseness. In this paper, as introducing the measure of the sparseness using the Gini coefficient to BSR stage, we obtained more accurate measure of the sparseness and better performance of BSR than methods using the $l_1$-norm, $l_q$-norm, and hyperbolic tangent, which was confirmed via computer simulations.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.39-44
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• 1996

Throughout this paper $Z^p, Q_p$ and C_p$ will denote the ring of p-adic rational integers, the field of p-adic rational numbers and the completion of the algebraic closure of $Q_p$, respectively. Let $v_p$ be the normalized exponential valuation of $C_p$ with $$\mid$p$\mid$_p = p^{-v_p (p)} = p^{-1}$. We set $p^* = p$ for any prime p > 2 $p^* = 4 for p = 2$.

• Journal of the Korean Society of Physical Medicine
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• v.5 no.1
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• pp.71-79
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• 2010

Purpose : To investigate of gait change as Q-angle in chronic knee osteoarthritis patients. Methods : Participated osteoarthritis disease patients(n=16) and normal adults(n=16). gait measure was used by GaitRite and Q-angle measure was used by tape measur