• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.437-448
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• 2007

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.

• Korean Journal of Radiology
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• 제22권8호
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• pp.1332-1340
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• 2021

Objective: To evaluate the feasibility of a new three-dimensional (3D) MR fingerprinting (MRF) technique for the prostate gland by conducting phantom and clinical studies. Materials and Methods: The new 3D MRF technique used in this study enables quick data acquisition and has a high resolution. For the phantom study, the MRF T1 and T2 values in an in-house phantom were compared with those of goldstandard mapping methods using linear regression analysis. For the clinical study, we evaluated 90 patients who underwent prostate imaging with MRF for suspected prostate cancer between September 2019 and February 2020. The mean T1 and T2 values were compared in the peripheral zone, transition zone, and focal lesions using paired t tests. The differences in the T1 and T2 values according to cancer aggressiveness were evaluated using one-way analysis of variance. Results: In the phantom study, the MRF T1 and T2 values showed a perfect correlation with the gold-standard T1 and T2 values (R > 0.99). In the clinical study, the T1 and T2 values in the peripheral zone were significantly higher than those in the transitional zone (p < 0.001, both). The T1 and T2 values in prostate cancer were significantly lower than those in the peripheral and transitional zones. The higher the grade of cancer, the lower the T2 values. Conclusion: The T1 and T2 values obtained from the 3D MRF showed a perfect correlation with the gold standard values in the phantom study. Differences in the T1 and T2 values among the different zones of the prostate gland were identified using 3D MRF in patients.

• Investigative Magnetic Resonance Imaging
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• 제22권2호
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• pp.86-93
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• 2018

Purpose: Imaging plays a significant role in diagnosing leptomeningeal metastases. However, the most appropriate sequence for the detection of leptomeningeal metastases has yet to be determined. This study compares the efficacies of contrast-enhanced T2 fluid attenuated inversion recovery (FLAIR) and contrast-enhanced 3D T1 black-blood fast spin echo (FSE) imaging for the detection of leptomeningeal metastases. Materials and Methods: Tube phantoms containing varying concentrations of gadobutrol solution were scanned using T2 FLAIR and 3D T1 black-blood FSE. Additionally, 30 patients with leptomeningeal metastases were retrospectively evaluated to compare conspicuous lesions and the extent of leptomeningeal metastases detected by T2 FLAIR and 3D T1 black-blood FSE. Results: The signal intensities of low-concentration gadobutrol solutions (< 0.5 mmol/L) on T2 FLAIR images were higher than in 3D T1 black-blood FSE. The T2 FLAIR sequences exhibited significantly greater visual conspicuity scores than the 3D T1 black-blood sequence in leptomeningeal metastases of the pial membrane of cistern (P = 0.014). T2 FLAIR images exhibited a greater or equal extent (96.7%) of leptomeningeal metastases than 3D T1 black-blood FSE images. Conclusion: Because of its high sensitivity even at low gadolinium concentrations, contrast-enhanced T2 FLAIR images delineated leptomeningeal metastases in a wider territory than 3D T1 black-blood FSE.

• 한국응용과학기술학회지
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• 제18권3호
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• pp.214-232
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• 2001

CTA ester bonds in TG molecules were not attacked by pancreatic lipase and lipases produced by microbes such as Candida cylindracea, Chromobacterium viscosum, Geotricum candidium, Pseudomonas fluorescens, Rhizophus delemar, R. arrhizus and Mucor miehei. An aliquot of total TG of all the seed oils and each TG fraction of the oils collected from HPLC runs were deuterated prior to partial hydrolysis with Grignard reagent, because CTA molecule was destroyed with treatment of Grignard reagent. Deuterated TG (dTG) was hydrolyzed partially to a mixture of deuterated diacylglycerols (dDG), which were subsequently reacted with (S)-(+)-1-(1-naphthyl)ethyl isocyanate to derivatize into dDG-NEUs. Purified dDG-NEUs were resolved into 1, 3-, 1, 2- and 2, 3-dDG-NEU on silica columns in tandem of HPLC using a solvent of 0.4% propan-1-o1 (containing 2% water)-hexane. An aliquot of each dDG-NEU fraction was hydrolyzed and (fatty acid-PFB ester). These derivatives showed a diagnostic carboxylate ion, $(M-1)^{-}$, as parent peak and a minor peak at m/z 196 $(PFB-CH_{3})^{-}$ on NICI mass spectra. In the mass spectra of the fatty acid-PFB esters of dTGs derived from the seed oils of T. kilirowii and M. charantia, peaks at m/z 285, 287, 289 and 317 were observed, which corresponded to $(M-1)^{-}$ of deuterized oleic acid ($d_{2}-C_{18:0}$), linoleic acid ($d_{4}-C_{18:0}$), punicic acid ($d_{6}-C_{18:0}$) and eicosamonoenoic acid ($d_{2}-C_{20:0}$), respectively. Fatty acid compositions of deuterized total TG of each oil measured by relative intensities of $(M-1)^-$ ion peaks were similar with those of intact TG of the oils by GLC. The composition of fatty acid-PFB esters of total dTG derived from the seed oils of T. kilirowii are as follows; $C_{16:0}$, 4.6 mole % (4.8 mole %, intact TG by GLC), $C_{18:0}$, 3.0 mole % (3.1 mole %), $d_{2}C_{18:0}$, 11.9 mole % (12.5 mole %, sum of $C_{18:1{\omega}9}$ and $C_{18:1{\omega}7}$), $d_{4}-C_{18:0}$, 39.3 mole % (38.9 mole %, sum of $C_{18:2{\omega}6}$ and its isomer), $d_{6}-C_{18:0}$, 41.1 mole % (40.5 mole %, sum of $C_{18:3\;9c,11t,13c}$, $C_{18:3\;9c,11t,13r}$ and $C_{18:3\;9t,11t,13c}$), $d_{2}-C_{20:0}$, 0.1 mole % (0.2 mole % of $C_{20:1{\omega}9}$). In total dTG derived from the seed oils of M. charantia, the fatty acid components are $C_{16:0}$, 1.5 mole % (1.8 mole %, intact TG by GLC), $C_{18:0}$, 12.0 mole % (12.3 mole %), $d_{2}-C_{18:0}$, 16.9 mole % (17.4 mole %, sum of $C_{18:1{\omega}9}$), $d_{4}-C_{18:0}$, 11.0 mole % (10.6 mole %, sum of $C_{18:2{\omega}6}$), $d_{6}-C_{18:0}$, 58.6 mole % (57.5 mole %, sum of $C_{18:3\;9c,11t,13t}$ and $C_{18:3\;9c,11t,13c}$). In the case of Aleurites fordii, $C_{16:0}$; 2.2 mole % (2.4 mole %, intact TG by GLC), $C_{18:0}$; 1.7 mole % (1.7 mole %), $d_{2}-C_{18:0}$; 5.5 mole % (5.4 mole %, sum of $C_{18:1{\omega}9}$), $d_{4}-C_{18:0}$ ; 8.3 mole % (8.5 mole %, sum of $C_{18:2{\omega}6}$), $d_{6}-C_{18:0}$; 82.0 mole % (81.2 mole %, sum of $C_{18:3\;9c,11t,13t}$ and $C_{18:3 9c,11t,13c})$. In the stereospecific analysis of fatty acid distribution in the TG species of the seed oils of T. kilirowii, $C_{18:3\;9c,11t,13r}$ and $C_{18:2{\omega}6}$ were mainly located at sn-2 and sn-3 position, while saturated acids were usually present at sn-1 position. And the major molecular species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})_{2}$ and $(C_{18:1{\omega}9})(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})$ were predominantly composed of the stereoisomer of $sn-1-C_{18:2{\omega}6}$, $sn-2-C_{18:3\;9c,11t,13c}$, $sn-3-C_{18:3\;9c,11t,13c}$, and $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:2{\omega}6}$, $sn-3-C_{18:3\;9c,11t,13c}$, respectively, and the minor TG species of $(C_{18:2{\omega}6})_{2}(C_{18:3\;9c,11t,13c})$ and $ (C_{16:0})(C_{18:3\;9c,11t,13c})_{2}$ mainly comprised the stereoisomer of $sn-1-C_{18:2{\omega}6}$, $sn-2-C_{18:2{\omega}6}$, $sn-3-C_{18:3\;9c,11t,13c}$ and $sn-1-C_{16:0}$, $sn-2-C_{18:3\;9c,11t,13c}$, $sn-3-C_{18:3\;9c,11t,13c}$. The TG of the seed oils of Momordica charantia showed that most of CTA, $C_{18:3\;9c,11t,13r}$, occurred at sn-3 position, and $C_{18:2{\omega}6}$ was concentrated at sn-1 and sn-2 compared to sn-3. Main TG species of $(C_{18:1{\omega}9})(C_{18:3\;9c,11t,13t})_{2}$ and $(C_{18:0})(C_{18:3\;9c,11t,13t})_{2}$ were consisted of the stereoisomer of $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ and $sn-1-C_{18:0}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$, respectively, and minor TG species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})_{2}$ and $(C_{18:1{\omega}9})(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})$ contained mostly $sn-1-C_{18:2{\omega6}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ and $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:2{\omega}6}$, $sn-3-C_{18:3\;9c,11t,13t}$. The TG fraction of the seed oils of Aleurites fordii was mostly occupied with simple TG species of $(C_{18:3\;9c,11t,13t})_{3}$, along with minor species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13t})_{2}$, $(C_{18:1{\omega}9})(C_{18:3\;9c,11t,13t})_{2}$ and $(C_{16:0})(C_{18:3\;9c,11t,13t})$. The sterospecific species of $sn-1-C_{18:2{\omega}6}$, $sn-2-C_{18:3\;9c,11t,13t}$, sn-3-C_{18:3\;9c,11t,13t}$, $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ and $sn-1-C_{16;0}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ are the main stereoisomers for the species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13t})_2$, $(C_{18:1{\omega}9})(C_{18:3\;9c,11t,13t})_{2}$ and $(C_{16:0})(C_{18:3\;9c,11t,13t})$, respectively.

• 대한수학회지
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• 제31권3호
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• pp.367-373
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• 1994

Let us consider the Cauchy problem $$ {\rho_t + \upsilon \cdot \nabla\rho = 0 {\rho[\upsilon_t + (\upsilon \cdot \nabla)\upsilon] + \nabla p + \rho f {div \upsilon = 0 (1.1) {\rho$\mid$_t = 0 = \rho_0(x) {\upsilon$\mid$_t = 0 = \upsilon_0(x) $$ in $Q_T = R^3 \times [0,T]$, where $f(x,t), \rho_0(x) and \upsilon_0(x)$ are given, while the density $\rho(x,t)$, the velocity vector $\upsilon(x,t) = (\upsilon^1(x,t),\upsilon^2(x,t),\upsilon^3(x,t))$ and the pressure p(x,t) are unknowns. The equations $(1.1)_1 - (1.1)_3$ describe the motion of a nonhomogeneous ideal incompressible fluid.

• 한국버섯학회지
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• 제13권4호
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• pp.301-304
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• 2015

본 연구는 잎새버섯 병 재배시 적합한 배지조성비율을 구명하고자 수행되었다. 배지조성은 참나무톱밥: 옥수수피: 건비지를 건물중량 비율로 T1처리(67:11:22), T2처리(68:15:17), T3처리(74:14:12)의 3처리를 두고 시험한 결과, 발이율은 T1처리에서 72.6%, T2처리에서 72.1%로 두 처리 간 유의적 차이가 없었으나 T3처리에서는 65.8%로서 다른 두 처리에 비하여 낮았다. 이병률은 T2처리에서 4.1%, T3처리에서 3.7%인데 비하여 T1처리에서는 9.8%로 가장 높았다. 수확률은 T1처리에서 64.1%, T3처리에서 63.6%인데 비하여 T2처리에서는 70.5%로 가장 높았다. 병당 자실체 중량은 T1처리에서 85.5 g, T2처리에서 83.3 g으로 두 처리 간 유의적 차이가 없었으나 T3처리에서는 72.4 g으로 다른 두 처리에 비하여 낮았다. 입병 수 10,000병 기준으로 재배 시 수량은 T2처리에서 587 kg으로 T1처리 및 T3처리에 비하여 각각 7% 및 28%가 높았다. 따라서 잎새버섯 병재배 시 적합한 배지조성비율은 건조중량비율로 참나무톱밥: 옥수수피: 건비지가 68:15:17인 것으로 나타났다.

• 충청수학회지
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• 제26권2호
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• pp.323-342
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• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $Xn:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}:C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\cdots},x(t_n),x(t_{n+1}))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions which have the form $${\int}_{L_2[0,t]}{{\exp}\{i(v,x)\}d{\sigma}(v)}{{\int}_{\mathbb{R}^r}}\;{\exp}\{i{\sum_{j=1}^{r}z_j(v_j,x)\}dp(z_1,{\cdots},z_r)$$ for $x{\in}C[0,t]$, where $\{v_1,{\cdots},v_r\}$ is an orthonormal subset of $L_2[0,t]$ and ${\sigma}$ and ${\rho}$ are the complex Borel measures of bounded variations on $L_2[0,t]$ and $\mathbb{R}^r$, respectively. We then investigate the inverse transforms of the function with their relationships and finally prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the products of the conditional Fourier-Feynman transforms of each function.

• 대한수학회논문집
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• 제11권1호
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• pp.71-79
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• 1996

In this paper, we prove for a nonexpansive mapping T that under certain conditions the trajectory $t \to G_t(x), t \in [0,1]$, defined by the equation $G_t(x) = (1 - t)x + tTG_t(x)$ strongly converges to a fixed point of T as $t \to 1^{-1}$.

• 한국의학물리학회지:의학물리
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• 제21권4호
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• pp.348-353
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• 2010

임상적용 전 단계에서 마우스와 같은 작은 설치류를 이용한 신경학적 실험의 필요성이 높아지면서 임상용 3T MRI를 이용한 마우스 뇌 영상의 요구가 높아지고 있다. 본 연구에서는 임상용 3T MRI를 이용한 마우스 뇌 영상의 가능성과 기술적인 적용과 최적화에 대해 알아보고자 하였다. 20~25g 체중 마우스 3마리에서 임상용 3T MRI를 이용하여 T1 강조영상(T1WI), T2 강조영상(T2WI), FLAIR (Fluid Attenuated Inversion Recovery) 영상, 가돌리늄 조영 T1 강조영상(Gd-T1WI), 확산 강조영상(DWI)을 시행하였다. 대상이 되었던 마우스 1마리는 뇌 경색을 유발시키지 않았으며 2마리는 우측 중대뇌동맥을 결찰하여 일측 뇌경색을 유발하고 1시간, 24시간, 72시간에 각각의 MRI 영상을 시행하였으며 각 영상에서 마우스 뇌의 striatum, 뇌실, 대뇌 피질의 해부학적 구별, 뇌 경색 부위의 진단 가능성 등을 분석하였다. T2WI에서 마우스 뇌의 striatum, 뇌실, 대뇌 피질의 해부학적 구별이 모두 가능하였고 T1WI, FLAIR, DWI 영상에서는 위의 해부학적 경계부위의 해상도는 감소하였다. 뇌경색 부위는 경색 후 1시간, 24시간, 72시간 영상 모두에서 발견되었고 T2WI, FLAIR에서는 24시간, 72시간에서만 구분되었다. 임상용 3T MRI를 이용한 마우스 뇌 영상에서 해부학적 부위의 구별이 가능하였고 특히 DWI를 이용하여 급성기 뇌 경색의 진단이 가능하였다. 앞으로 기술적인 적용과 최적화를 위한 노력이 계속 진행된다면 임상 실험에 큰 도움을 줄 수 있을 것이라 생각된다.

• 한국환경과학회지
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• 제32권11호
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• pp.853-856
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• 2023

This study assesses the palatability of regular canine diets and seven types of black soldier fly-based canine diets when fed to dogs. Sixteen dogs of two types were included in this study: 8 poodles (average weight 2.7 kg ± 0.5) and 8 bichons frises(average weight 2.0 kg ± 0.5). For intake and first choice, two-bowl tests, adhering to standards of canine palatability, were conducted every two days for a total of 14 days by comparing between the control and each treatment. Data, including total intake and total first choice were collected and accumulated for a total of 58 days. This encompassed 14 days of data on comparison between control and treatments, and 44 days of data on comparison among treatment groups (e.g., T1 vs T2) of black soldier fly-based canine diets. Significance differences in canine palatability was observed in treatments (p<0.05), except for the control and T2 results. Among the two-bowl tests, T1 and T2 exhibited the lowest intake and first choices. In particular, the palatability of canine diets ranked in the order T6 > T3 > T7 > T4 > T5 compared to each control. The total intake demonstrated in the following ranking: T6 > T3 > T7 > T5 > Control > T4 > T2 > T1. The total first choice was highest for T6, followed by T3, T7, T5, T4, Control, T2, and T1. In conclusion, insect diets with higher protein content such as T6, T3, and T7 representing as black soldier fly-based canine diets exhibit higher intake and first choice preferences in canines.