• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.329-352
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• 2019

In this paper, we study conformally flat (${\alpha}$, ${\beta}$)-metrics in the form $F={\alpha}(1+{\sum_{j=1}^{m}}\;a_j({\frac{\beta}{\alpha}})^j)$ with $m{\geq}2$, where ${\alpha}$ is a Riemannian metric and ${\beta}$ is a 1-form on a smooth manifold M. We prove that if such conformally flat (${\alpha}$, ${\beta}$)-metric F is of weakly isotropic scalar curvature, then it must has zero scalar curvature. Moreover, if $a_{m-1}a_m{\neq}0$, then such metric is either locally Minkowskian or Riemannian.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.193-203
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• 2023

In view of solution to the Hilbert fourth problem, the present study engages to investigate the projectively flat special (𝛼, 𝛽)-metric and the generalised first approximate Matsumoto (𝛼, 𝛽)-metric, where 𝛼 is a Riemannian metric and 𝛽 is a differential one-form. Further, we concluded that 𝛼 is locally Projectively flat and have 𝛽 is parallel with respect to 𝛼 for both the metrics. Also, we obtained necessary and sufficient conditions for the aforementioned metrics to be locally projectively flat.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.503-521
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• 2001

A change of Finsler metric L(x,y)longrightarrowL(x,y) is called a Randers change of L, if L(x,y) = L(x,y) +$\rho$(x,y), where $\rho$(x,y) = $\rho$(sub)i(x)y(sup)i is a 1-form on a smooth manifold M(sup)n. Let us consider the special Randers change of Finsler metric LlongrightarrowL = L + $\beta$ by $\beta$. On the basis of this special Randers change, the purpose of the present paper is devoted to studying the conditions for Finsler space F(sup)n which are transformed by a special Randers change of Finsler spaces F(sup)n with ($\alpha$,$\beta$)-metrics of Douglas type to be also of Douglas type, and vice versa.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.425-441
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• 2006

We have two concepts of Douglas spaces and Lands-berg spaces as generalizations of Berwald spaces. S. Bacso gave the definition of a weakly-Berwald space [2] as another generalization of Berwald spaces. In the present paper, we find the conditions that the Finsler space with an (${\alpha},{\beta}$)-metric be a weakly-Berwald space and the Finsler spaces with some special (${\alpha},{\beta}$)-metrics be weakly-Berwald spaces, respectively.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.45-52
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• 2004

The theory of m-th root metric has been developed by H. Shimada [8], and applied to the biology [1] as an ecological metric. The purpose of this paper is to introduce the m-th root Finsler metrics which admit ($\alpha,\;\beta$)-types. Especially in cases of m = 3, 4, we give the condition for Finsler spaces with such metrics to be locally Minkowski spaces.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1335-1349
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• 2020

In this paper, we give an equivalent characterization for general (α, β)-metrics with reversible geodesics when the dimension of the manifold is greater than 2.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1231-1240
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• 2018

In this paper, we characterize the conformal transformations between two almost regular (${\alpha},{\beta}$)-metrics. Suppose that F is a non-Riemannian (${\alpha},{\beta}$)-metric and is conformally related to ${\widetilde{F}}$, that is, ${\widetilde{F}}=e^{{\kappa}(x)}F$, where ${\kappa}:={\kappa}(x)$ is a scalar function on the manifold. We obtain the necessary and sufficient conditions of the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature. Further, when both F and ${\widetilde{F}}$ are regular, the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature must be a homothety.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.611-622
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• 2023

In this paper, we prove that every weakly Einstein slope metric, which is conformally flat on a manifold M of dimension n ≥ 3, is either a locally Minkowski metric or a Riemannian metric. We also prove the same result for conformally flat weakly Einstein Kropina metrics.

• Journal of the Korea Safety Management & Science
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• v.15 no.2
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• pp.243-253
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• 2013

This research paper introduces the application and implementation of medical decision metrics that classifies medical decision-making into four different metrics using statistical diagnostic tools, such as confusion matrix, normal distribution, Bayesian prediction and Receiver Operating Curve(ROC). In this study, the metrics are developed based on cross-section study, cohort study and case-control study done by systematic literature review and reformulated the structure of type I error, type II error, confidence level and power of detection. The study proposed implementation strategies for 10 quality improvement activities via 14 medical decision metrics which consider specificity and sensitivity in terms of ${\alpha}$ and ${\beta}$. Examples of ROC implication are depicted in this paper with a useful guidelines to implement a continuous quality improvement, not only in a variable acceptance sampling in Quality Control(QC) but also in a supplier grading score chart in Supplier Chain Management(SCM) quality. This research paper is the first to apply and implement medical decision-making tools as quality improvement activities. These proposed models will help quality practitioners to enhance the process and product quality level.

• Biomedical Science Letters
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• v.24 no.4
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• pp.418-425
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• 2018

Amyloid brain positron emission tomography (PET) images are visually and subjectively analyzed by the physician with a lot of time and effort to determine the ${\beta}$-Amyloid ($A{\beta}$) deposition. We designed a convolutional neural network (CNN) model that predicts the $A{\beta}$-positive and $A{\beta}$-negative status. We performed 18F-florbetaben (FBB) brain PET on controls and patients (n=176) with mild cognitive impairment and Alzheimer's Disease (AD). We classified brain PET images visually as per the on the brain amyloid plaque load score. We designed the visual geometry group (VGG16) model for the visual assessment of slice-based samples. To evaluate only the gray matter and not the white matter, gray matter masking (GMM) was applied to the slice-based standard samples. All the performance metrics were higher with GMM than without GMM (accuracy 92.39 vs. 89.60, sensitivity 87.93 vs. 85.76, and specificity 98.94 vs. 95.32). For the patient-based standard, all the performance metrics were almost the same (accuracy 89.78 vs. 89.21), lower (sensitivity 93.97 vs. 99.14), and higher (specificity 81.67 vs. 70.00). The area under curve with the VGG16 model that observed the gray matter region only was slightly higher than the model that observed the whole brain for both slice-based and patient-based decision processes. Amyloid brain PET images can be appropriately analyzed using the CNN model for predicting the $A{\beta}$-positive and $A{\beta}$-negative status.