• Korean Journal of Radiology
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• v.23 no.6
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• pp.664-673
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• 2022

Objective: To evaluate the performance of baseline clinical characteristics and pretherapeutic histogram parameters derived from T2 mapping of the extraocular muscles (EOMs) in the prediction of treatment response to intravenous glucocorticoid (IVGC) therapy for active and moderate-to-severe thyroid-associated ophthalmopathy (TAO) and to investigate the effect of fat-suppression (FS) in T2 mapping in this prediction. Materials and Methods: A total of 79 patients clinically diagnosed with active, moderate-to-severe TAO (47 female, 32 male; mean age ± standard deviation, 46.1 ± 10 years), including 43 patients with a total of 86 orbits in the responsive group and 36 patients with a total of 72 orbits in the unresponsive group, were enrolled. Baseline clinical characteristics and pretherapeutic histogram parameters derived from T2 mapping with FS (i.e., FS T2 mapping) or without FS (i.e., conventional T2 mapping) of EOMs were compared between the two groups. Independent predictors of treatment response to IVGC were identified using multivariable analysis. Receiver operating characteristic (ROC) curve analysis was performed to evaluate the predictive performance of the prediction models. Differences between the models were examined using the DeLong test. Results: Compared to the unresponsive group, the responsive group had a shorter disease duration, lower kurtosis (FS-kurtosis), lower standard deviation, larger 75th, 90th, and 95th (FS-95th) T2 relaxation times in FS mapping and lower kurtosis in conventional T2 mapping. Multivariable analysis revealed that disease duration, FS-95th percentile, and FS-kurtosis were independent predictors of treatment response. The combined model, integrating all identified predictors, had an optimized area under the ROC curve of 0.797, 88.4% sensitivity, and 62.5% specificity, which were significantly superior to those of the imaging model (p = 0.013). Conclusion: An integrated combination of disease duration, FS-95th percentile, and FS-kurtosis was a potential predictor of treatment response to IVGC in patients with active and moderate-to-severe TAO. FS T2 mapping was superior to conventional T2 mapping in terms of prediction.

• East Asian mathematical journal
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• v.28 no.5
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• pp.597-604
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• 2012

Let C be a nonempty closed convex subset of real Hilbert space H and F = $\{S(t):t{\geq}0\}$ a nonexpansive self-mapping semigroup of C, and $f:C{\rightarrow}C$ is a fixed contractive mapping. Consider the process {$x_n$} : $$\{{x_{n+1}={\beta}_nx_n+(1-{\beta}_n)z_n\\z_n={\alpha}_nf(x_n)+(1-{\alpha}_n)S(t_n)P_C(x_n-r_nAx_n)$$. It is shown that {$x_n$} converges strongly to a common element of the set of fixed points of nonexpansive semigroups and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.665-678
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• 2019

We construct an iteration scheme involving a hybrid pair of mappings, one a single-valued asymptotically nonexpansive mapping t and the other a multivalued nonexpansive mapping T, in a complete CAT(0) space. In the process, we remove a restricted condition (called the end-point condition) from results of Akkasriworn and Sokhuma [1] and and use this to prove some convergence theorems. The results concur with analogues for Banach spaces from Uddin et al. [16].

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.215-231
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T:C{\rightarrow}{\mathcal{K}}(E)$ a multivalued nonself-mapping such that $P_T$ is nonexpansive, where $P_T(x)=\{u_x{\in}Tx:{\parallel}x-u_x{\parallel}=d(x,Tx)\}$. For $f:C{\rightarrow}C$ a contraction and $t{\in}(0,1)$, let $x_t$ be a fixed point of a contraction $S_t:C{\rightarrow}{\mathcal{K}}(E)$, defined by $S_tx:=tP_T(x)+(1-t)f(x)$, $x{\in}C$. It is proved that if C is a nonexpansive retract of E and $\{x_t\}$ is bounded, then the strong ${\lim}_{t{\rightarrow}1}x_t$ exists and belongs to the fixed point set of T. Moreover, we study the strong convergence of $\{x_t\}$ with the weak inwardness condition on T in a reflexive Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm. Our results provide a partial answer to Jung's question.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

• Investigative Magnetic Resonance Imaging
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• v.23 no.1
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• pp.17-25
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• 2019

We discuss recent advances in Gd-based $T_1$-weighted MR contrast agents for the mapping of cellular pH. The pH plays a critical role in various biological processes. During the past two decades, several MR contrast agents of strategic importance for pH-mapping have been developed. Some of these agents shed light on the pH fluctuation in the tumor microenvironment. A pH-responsive self-assembled contrast agent facilitates the visualization of tumor size as small as $3mm^3$. Optimization of various parameters is crucial for the development of pH-responsive contrast agents. In due course, the new contrast agents may provide significant insight into pH fluctuations in the human body.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.275-285
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• 1997

Let E be a uniformly convex Banach space with a uniformly G$\hat{a}teaux differentiable norm, C a nonempty closed convex subset of $E, T : C \to E$ a nonexpansive mapping, and Q a sunny nonexpansive retraction of E onto C. For $u \in C$ and $t \in (0,1)$, let $x_t$ be a unique fixed point of a contraction $R_t : C \to C$, defined by $R_tx = Q(tTx + (1-t)u), x \in C$. It is proved that if ${x_t}$ is bounded, then the strong $lim_{t\to1}x_t$ exists and belongs to the fixed point set of T. Furthermore, the strong convergence of ${x_t}$ in a reflexive and strictly convex Banach space with a uniformly G$\hat{a}$teaux differentiable norm is also given in case that the fixed point set of T is nonempty.

• Journal of the Korean Society of Industry Convergence
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• v.24 no.1
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• pp.69-77
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• 2021

The widely used low-cost design methodology for IoT devices is very popular. In such a networked device, memory is composed of flash memory, SRAM, DRAM, etc., and because it processes a large amount of data, memory design is an important factor for system performance. Therefore, each device selects optimized design factors such as function, performance and cost according to market demand. The design of a memory architecture available for low-cost IoT devices is very limited with the configuration of SRAM, flash memory, and DRAM. In order to process as much data as possible in the same space, an architecture that supports parallel processing units is usually provided. Such parallel architecture is a design method that provides high performance at low cost. However, it needs precise software techniques for instruction and data mapping on the parallel architecture. This paper proposes an instruction/data mapping method to support optimized parallel processing performance. The proposed method optimizes system performance by actively using hardware and software parallelism.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.799-813
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• 2012

In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

• Korean Journal of Radiology
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• v.22 no.4
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• pp.535-546
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• 2021

Objective: To evaluate the feasibility of texture analysis on non-contrast-enhanced T1 maps of cardiac magnetic resonance (CMR) imaging for the diagnosis of myocardial injury in acute myocardial infarction (MI). Materials and Methods: This study included 68 patients (57 males and 11 females; mean age, 55.7 ± 10.5 years) with acute ST-segment-elevation MI who had undergone 3T CMR after a percutaneous coronary intervention. Forty patients of them also underwent a 6-month follow-up CMR. The CMR protocol included T2-weighted imaging, T1 mapping, rest first-pass perfusion, and late gadolinium enhancement. Radiomics features were extracted from the T1 maps using open-source software. Radiomics signatures were constructed with the selected strongest features to evaluate the myocardial injury severity and predict the recovery of left ventricular (LV) longitudinal systolic myocardial contractility. Results: A total of 1088 segments of the acute CMR images were analyzed; 103 (9.5%) segments showed microvascular obstruction (MVO), and 557 (51.2%) segments showed MI. A total of 640 segments were included in the 6-month follow-up analysis, of which 160 (25.0%) segments showed favorable recovery of LV longitudinal systolic myocardial contractility. Combined radiomics signature and T1 values resulted in a higher diagnostic performance for MVO compared to T1 values alone (area under the curve [AUC] in the training set; 0.88, 0.72, p = 0.031: AUC in the test set; 0.86, 0.71, p = 0.002). Combined radiomics signature and T1 values also provided a higher predictive value for LV longitudinal systolic myocardial contractility recovery compared to T1 values (AUC in the training set; 0.76, 0.55, p < 0.001: AUC in the test set; 0.77, 0.60, p < 0.001). Conclusion: The combination of radiomics of non-contrast-enhanced T1 mapping and T1 values could provide higher diagnostic accuracy for MVO. Radiomics also provides incremental value in the prediction of LV longitudinal systolic myocardial contractility at six months.