• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.393-401
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• 1997

Let $A_1,A_2,\cdots,A_m$ and $B_1,B_2,\cdots,B_n$ be two sequences of events on a given probability space. Let $X_m$ and $Y_n$, respectively, be the number of those $A_i$ and $B_j$, which occur we establish new upper and lower bounds on the probability $P(X=r, Y=t)$ which improve upper bounds and classical lower bounds in terms of the bivariate binomial moment $S_{r,t},S_{r+1,t},S_{r,t+1}$ and $S_{r+1,t+1}$.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.565-570
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• 2012

In this note we investigate Weyl's theorem for *-paranormal operators on a separable infinite dimensional Hilbert space. We prove that if T is a *-paranormal operator satisfying Property $(E)-(T-{\lambda}I)H_T(\{{\lambda}\})$ is closed for each ${\lambda}{\in}{\mathbb{C}}$, where $H_T(\{{\lambda}\})$ is a local spectral subspace of T, then Weyl's theorem holds for T.

• Investigative Magnetic Resonance Imaging
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• v.25 no.2
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• pp.118-128
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• 2021

Purpose: To investigate the value of MR textural analysis, including use of diffusion-weighted imaging (DWI) to differentiate malignant from benign soft-tissue tumors on 3T MRI. Materials and Methods: We enrolled 69 patients (25 men, 44 women, ages 18 to 84 years) with pathologically confirmed soft-tissue tumors (29 benign, 40 malignant) who underwent pre-treatment 3T-MRI. We calculated MR texture, including mean, standard deviation (SD), skewness, kurtosis, mean of positive pixels (MPP), and entropy, according to different spatial-scale factors (SSF, 0, 2, 4, 6) on axial T1- and T2-weighted images (T1WI, T2WI), contrast-enhanced T1WI (CE-T1WI), high b-value DWI (800 sec/mm²), and apparent diffusion coefficient (ADC) map. We used the Mann-Whitney U test, logistic regression, and area under the receiver operating characteristic curve (AUC) for statistical analysis. Results: Malignant soft-tissue tumors had significantly lower mean values of DWI, ADC, T2WI and CE-T1WI, MPP of ADC, and CE-T1WI, but significantly higher kurtosis of DWI, T1WI, and CE-T1WI, and entropy of DWI, ADC, and T2WI than did benign tumors (P < 0.050). In multivariate logistic regression, the mean ADC value (SSF, 6) and kurtosis of CE-T1WI (SSF, 4) were independently associated with malignancy (P ≤ 0.009). A multivariate model of MR features worked well for diagnosis of malignant soft-tissue tumors (AUC, 0.909). Conclusion: Accurate diagnosis could be obtained using MR textural analysis with DWI and CE-T1WI in differentiating benign from malignant soft-tissue tumors.

• Proceedings of the Korean Magnestics Society Conference
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• 1992.10a
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• pp.38-39
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• 1992

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.1025-1050
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• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.129-132
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• 2001

In this paper, in order to control uncertain missile autopilot, an adaptive fuzzy control(AEC) scheme via parallel distributed compensation(PDC) is developed for the multi-input/multi-output plants represented by the Takagi-Sugeno(T-S) fuzzy model. Moreover adaptive law is designed so that the plant output tracks the stable reference model(SRM), From the simulations results, we can conclude that the suggested scheme can effectively solve the control problems of uncertain missile systems based on T-S fuzzy model.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.261-278
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• 2017

In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy alpha generalized closed and open sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy alpha generalized continuous mappings and then investigate some of their properties.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.717-734
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• 2015

In this paper, we provide a classification of arithmetic functions in terms of identically-free-distributedness, determined by a fixed prime. We show then such classifications are free from the choice of primes. In particular, we obtain that the algebra $A_p$ of equivalence classes under the quotient on A by the identically-free-distributedness is isomorphic to an algebra $\mathbb{C}^2$, having its multiplication $({\bullet});(t_1,t_2){\bullet}(s_1,s_2)=(t_1s_1,t_1s_2+t_2s_1)$.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.565-571
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• 2006

In this paper, we present the explicit formula of the generalized inverse $A^{(2)}_{T,S}$, and we apply this result to solve restricted linear equation $Ax+y=b$, $x{\in}T$, $y{\in}S$ and $Ax+By=b$, $x{\in}T$, $y{\in}S$.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.12
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• pp.4760-4765
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• 2010

Time out-medium access control (T-MAC) protocol is one of the well-known MAC protocols designed for wireless sensor networks (WSN), and is proposed to enhance the poor performance of the S-MAC protocol. In this paper, we are reviewed about security vulnerability in T-MAC, and analyzed the power which is consumed at each stage of T-MAC protocol according to vulnerability of denial of service (DoS) and replay problem. From our analytical results, it can be considered the need of power efficient authentication scheme which provides the reliability, efficiency, and security for a general T-MAC communication. This is the case study of possible DoS vulnerability and its power consumption in T-MAC.