• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.687-700
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• 1994

Throughout this paper we will let H denote the complete Heyting algebra ($H, \vee, \wedge, *$) with order reversing involution *. 0 and 1 denote the supermum and the infimum of $\emptyset$, respectively. Given any set X, any element of $H^X$ is called H-fuzzy set (or, simply f.set) in X and will be denoted by small Greek letters, such as $\mu, \nu, \rho, \sigma$. $H^X$ inherits a structure of H with order reversing involution in natural way, by definding $\vee, \wedge, *$ pointwise (sam notations of H are usual). If $f$ is a map from a set X to a set Y and $\mu \in H^Y$, then $f^{-1}(\mu)$ is the f.set in X defined by f^{-1}(\mu)(x) = \mu(f(x))$. Also for $\sigma \in H^X, f(\sigma)$ is the f.set in Y defined by $f(\sigma)(y) = sup{\sigma(x) : f(x) = y}$ ([4]). A preorder R on a set X is reflexive and transitive relation on X, the pair (X,R) is called preordered set. A map $f$ from a preordered set (X, R) to another one (Y,T) is said to be preorder preserving (inverting) if for $x,y \in X, xRy$ implies $f(x)T f(y) (resp. f(y)Tf(x))$. For the terminology and notation, we refer to [10, 11, 13] for category theory and [7] for H-fuzzy semitopogenous spaces.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.51-61
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• 2022

Let G be a graph. Let f : V (G) → {0, 1, 2, …, k-1} be a map where k ∈ ℕ and k > 1. For each edge uv, assign the label |f(u) - f(v)|. f is called k-total difference cordial labeling of G if |t_df (i) - t_df (j) | ≤ 1, i, j ∈ {0, 1, 2, …, k - 1} where t_df (x) denotes the total number of vertices and the edges labeled with x. A graph with admits a k-total difference cordial labeling is called k-total difference cordial graphs. In this paper we investigate the 4-total difference cordial labeling behaviour of shell butterfly graph, Lilly graph, Shackle graphs etc..

• 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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1803-1825
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• 2017

Let X be a smooth scheme with an action of an algebraic group G. We establish an equivalence of two categories related to the corresponding moment map ${\mu}:T^{\ast}X{\rightarrow}g^{\ast}$ - the derived category of G-equivariant coherent sheaves on the derived fiber ${\mu}^{-1}(0)$ and the derived category of G-equivariant matrix factorizations on $T^{\ast}X{\times}g$ with potential given by ${\mu}$.

• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.223-230
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• 2007

We give an answer to the following question: Question. Let S be a subset of [0,1] containing a maximal element m > 0 and let C :=$\{I_{t}\;{\mid}\;t{\in}S\}$ be a decreasing chain of ideals of a BCK/BCI-algebra X. Then does there exists a fuzzy ideal ${\mu}(X)=S\;and\;C_{\mu}=C?$.

• Proceedings of the PSK Conference
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• 2001.04a
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• pp.119.2-119.2
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• 2001

• Journal of Korea Multimedia Society
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• v.11 no.5
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• pp.692-702
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• 2008

Path planning is gaining more weight in computer games and virtual reality as the number of self-moving characters increases. In the roadmap approach, the map of possible paths is built in advance to plan paths for a character, whose advantage is to provide high-quality paths. On the other hand, a disadvantage is that the road map doesn't reflect properties of characters such as their sizes because they move on the same map once the road map is constructed. In this paper we propose an efficient method to build a different road map for each character so that it can use its own map for path-planning. This method is efficient because the whole map is built once by applying the Visibility Graph regardless of the number of characters and walkable paths are incrementally inserted according to the sizes of characters. The effects of using separate roadmaps are demonstrated through simulations and the trade-offs accompanied with these effects are analyzed.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.287-297
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• 2015

In this paper, we investigate $T_1$ Boolean subalgebras of the Boolean algebra consisting all regular closed sets in a space and their Wallman covers. In particular, we will give sufficient and necessary conditions of spaces X satisfying ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$.

• Korean Journal of Radiology
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• v.23 no.11
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• pp.1078-1088
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• 2022

Objective: To develop and validate a model using radiomics features from apparent diffusion coefficient (ADC) map to diagnose local tumor recurrence in head and neck squamous cell carcinoma (HNSCC). Materials and Methods: This retrospective study included 285 patients (mean age ± standard deviation, 62 ± 12 years; 220 male, 77.2%), including 215 for training (n = 161) and internal validation (n = 54) and 70 others for external validation, with newly developed contrast-enhancing lesions at the primary cancer site on the surveillance MRI following definitive treatment of HNSCC between January 2014 and October 2019. Of the 215 and 70 patients, 127 and 34, respectively, had local tumor recurrence. Radiomics models using radiomics scores were created separately for T2-weighted imaging (T2WI), contrast-enhanced T1-weighted imaging (CE-T1WI), and ADC maps using non-zero coefficients from the least absolute shrinkage and selection operator in the training set. Receiver operating characteristic (ROC) analysis was used to evaluate the diagnostic performance of each radiomics score and known clinical parameter (age, sex, and clinical stage) in the internal and external validation sets. Results: Five radiomics features from T2WI, six from CE-T1WI, and nine from ADC maps were selected and used to develop the respective radiomics models. The area under ROC curve (AUROC) of ADC radiomics score was 0.76 (95% confidence interval [CI], 0.62-0.89) and 0.77 (95% CI, 0.65-0.88) in the internal and external validation sets, respectively. These were significantly higher than the AUROC values of T2WI (0.53 [95% CI, 0.40-0.67], p = 0.006), CE-T1WI (0.53 [95% CI, 0.40-0.67], p = 0.012), and clinical parameters (0.53 [95% CI, 0.39-0.67], p = 0.021) in the external validation set. Conclusion: The radiomics model using ADC maps exhibited higher diagnostic performance than those of the radiomics models using T2WI or CE-T1WI and clinical parameters in the diagnosis of local tumor recurrence in HNSCC following definitive treatment.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.149-156
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• 2019

Let G be a (p, q) graph. Let $f:V(G){\rightarrow}\{1,2,{\ldots},k\}$ be a map where $k{\in}{\mathbb{N}}$ and k > 1. For each edge uv, assign the label gcd(f(u), f(v)). f is called k-Total prime cordial labeling of G if ${\mid}t_f(i)-t_f(j){\mid}{\leq}1$, $i,j{\in}\{1,2,{\ldots},k\}$ where $t_f$(x) denotes the total number of vertices and the edges labelled with x. A graph with a k-total prime cordial labeling is called k-total prime cordial graph. In this paper we investigate the 4-total prime cordial labeling of some graphs.