• 한국방사선학회논문지
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• 제16권2호
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• pp.115-122
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• 2022

본 연구는 후각망울(Olfactory Bulb) 검사 시 SPACE 3D T2 기법의 Turbo Factor 값을 변화하여 검사 한 후 2D TSE T2와 비교하여 진단능과 화질의 변화를 알아보고자 한다. 연구 결과 정성적, 정량적 분석 결과 SPACE 3D T2 기법이 2D TSE T2 기법과 비교 시 통계적으로 유의한 차이가 있음을 알 수 있었으며, 결론적으로 Turbo Factor값을 적절하게 변화 시킨 SPACE 3D T2 기법은 검사시간을 단축시키면서 2D TSE T2기법과 비교하여 화질이 증가 된 영상을 획득할 수 있으므로 임상적으로 충분한 진단적 가치가 있다고 사료된다.

• 대한수학회보
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• 제43권4호
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• pp.831-839
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• 2006

By relaxing the requirements for a sequence of functions to be a delta sequence, a space of Boehmians on the torus ${\beta}(T^d)$ is constructed and studied. The space ${\beta}(T^d)$ contains the space of distributions as well as the space of hyperfunctions on the torus. The Fourier transform is a continuous mapping from ${\beta}(T^d)$ onto a subspace of Schwartz distributions. The range of the Fourier transform is characterized. A necessary and sufficient condition for a sequence of Boehmians to converge is that the corresponding sequence of Fourier transforms converges in $D'({\mathbb{R}}^d)$.

• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.223-233
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• 1998

This paper is concerned with the problem of existence of solutions to the initial value problem u'(t) = A(t, u(t)), u(a) = z in a probabilistic normed space where $A : [a,b)\;{\times}\;D->E$ is continuous, D is a closed subset of a probabilistic normed space E, and $z\;{\in}\;D$. With a dissipative type condition on A, we estabilish sufficient conditions for this initial value problem to have a solution.

• 한국우주과학회:학술대회논문집(한국우주과학회보)
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• 한국우주과학회 2009년도 한국우주과학회보 제18권2호
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• pp.36.3-37
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• 2009

This is an attempt to improve a formula to predict variations of geomagnetic storm indices (Dst) from solar wind parameters. A formula which is most widely accepted was given by Burton et al. (1975) over 30 years ago. Their formula is: dDst*/dt = Q(t) - Dst*(t)/$\tau$, where Q(t) is the Dst injection rate given by the convolution of dawn-to-dusk electric field generated by southward solar wind magnetic field and some response function. However, they did not clearly specify the response function. As a result, misunderstanding seems to be prevailing that the injection rate is proportional to the dawn-to-dusk electric field. In this study we tried to determine the response function by examining 12 intense geomagnetic storms with minimum Dst < -200 nT for which solar wind data are available. The method is as follows. First we assume the form of response function that is specified by several time constants, so that we can calculate the injection rate Q1(t) from the solar wind data. On the other hand, Burton et al. expression provide the observed injection rate Q2(t) = dDst*/dt + Dst*(t)/$\tau$. Thus, it is possible to determine the time constants of response function by a least-squares method to minimize the difference between Q1(t) and Q2(t). We have found this simple method successful enough to reproduce the observed Dst variations from the corresponding solar wind data. The present result provides a scheme to predict the development of Dst 30 minutes to 1 hour in advance by using the real time solar wind data from the ACE spacecraft.

• 대한수학회보
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• 제44권4호
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• pp.807-816
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• 2007

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

• Investigative Magnetic Resonance Imaging
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• 제22권4호
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• pp.229-239
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• 2018

Purpose: To assess the diagnostic performance in detecting rotator cuff tears at 3T of non-arthrographic shoulder magnetic resonance imaging (MRI) using 3D isotropic turbo spin-echo (TSE-SPACE) sequence as compared with 2D sequences. Materials and Methods: Seventy-four patients who were arthroscopically confirmed to have underwent non-arthrographic shoulder MRI with 2D sequences and TSE-SPACE were included. Three independent readers retrospectively scored supraspinatus and infraspinatus tendon (SST-IST) and subscapularis tendon (SCT) tears on 2D sequences and TSE-SPACE. Results: The mean sensitivity, specificity, and accuracy of the three readers were 95%, 100%, and 95% on TSE-SPACE and 99%, 93%, and 98% on 2D sequences for detecting SST-IST tears, respectively, whereas those were 87%, 49%, and 68% on TSESPACE and 88%, 66%, and 77% on 2D sequences for detecting SCT tears, respectively. There was no statistical difference between the two sequences, except for in the specificity of one reader for detecting SCT tears. The mean AUCs of the three readers on TSE-SPACE and 2D sequences were 0.96 and 0.98 for detecting SST-IST tears, respectively, which were not significantly different, while those were 0.71 and 0.82 for detecting SCT tears, respectively, which were significantly different (P < 0.05). Conclusion: TSE-SPACE may have accuracy and reliability comparable to conventional 2D sequences for SST-IST tears at non-arthrographic 3T shoulder MRI, whereas TSE-SPACE was less reliable than conventional 2D sequences for detecting SCT tears.

• 대한수학회논문집
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• 제34권1호
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• pp.185-202
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• 2019

In this paper, we investigate many types of stability, like (uniform stability, exponential stability and h-stability) of the first order dynamic equations of the form $$\{u^{\Delta}(t)=Au(t)+f(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ and $$\{u^{\Delta}(t)=Au(t)+f(t,u),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ in terms of the stability of the homogeneous equation $$\{u^{\Delta}(t)=Au(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ where f is rd-continuous in $t{\in}{\mathbb{T}}$ and with values in a Banach space X, with f(t, 0) = 0, and A is the generator of a $C_0$-semigroup $\{T(t):t{\in}{\mathbb{T}}\}{\subset}L(X)$, the space of all bounded linear operators from X into itself. Here D(A) is the domain of A and ${\mathbb{T}}{\subseteq}{\mathbb{R}}^{{\geq}0}$ is a time scale which is an additive semigroup with property that $a-b{\in}{\mathbb{T}}$ for any $a,b{\in}{\mathbb{T}}$ such that a > b. Finally, we give illustrative examples.

• Investigative Magnetic Resonance Imaging
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• 제20권2호
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• pp.81-87
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• 2016

Purpose: To analyze the feasibility of three-dimensional (3D) diffusion-weighted (DW) PSIF (reversed FISP [fast imaging with steady-state free precession]) sequence in order to evaluate peripheral nerves in the elbow. Materials and Methods: Ten normal, asymptomatic volunteers were enrolled (6 men, 4 women, mean age 27.9 years). The following sequences of magnetic resonance images (MRI) of the elbow were obtained using a 3.0-T machine: 3D DW PSIF, 3D T2 SPACE (sampling perfection with application optimized contrasts using different flip angle evolution) with SPAIR (spectral adiabatic inversion recovery) and 2D T2 TSE (turbo spin echo) with modified Dixon (m-Dixon) sequence. Two observers used a 5-point grading system to analyze the image quality of the ulnar, median, and radial nerves. The signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) of each nerve were measured. We compared 3D DW PSIF images with other sequences using the Wilcoxon-signed rank test and Friedman test. Inter-observer agreement was measured using intraclass correlation coefficient (ICC) analysis. Results: The mean 5-point scores of radial, median, and ulnar nerves in 3D DW PSIF (3.9/4.2/4.5, respectively) were higher than those in 3D T2 SPACE SPAIR (1.9/2.8/2.8) and 2D T2 TSE m-Dixon (1.7/2.8/2.9) sequences (P < 0.05). The mean SNR in 3D DW PSIF was lower than 3D T2 SPACE SPAIR, but there was no difference between 3D DW PSIF and 2D T2 TSE m-Dixon in all of the three nerves. The mean CNR in 3D DW PSIF was lower than 3D T2 SPACE SPAIR and 2D T2 TSE m-Dixon in the median and ulnar nerves, but no difference among the three sequences in the radial nerve. Conclusion: The three-dimensional DW PSIF sequence may be feasible to evaluate the peripheral nerves around the elbow in MR imaging. However, further optimization of the image quality (SNR, CNR) is required.

• 대한수학회지
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• 제53권4호
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• 호남수학학술지
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• 제32권3호
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• pp.441-451
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• 2010

In this paper we evaluate the analogue of Wiener integral ${\int\limits}_{C[0,t]}x(t_1){\cdots}x(t_n)d\omega_\rho(x)$ where 0 = $t_0$ < $t_1$ $\cdots$ < $t_n$ $\leq$ t and the Paley-Wiener-Zygmund integral ${\int\limits}_{C[0,t]}$ exp $({\int\limits}_0^t h(s)\tilde{d}x(s))d\omega_\rho(x)$ is the analogue of Wiener measure space.