• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.391-399
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• 2003

Let (X,S,$\mu$) be a measure space and M be the vector space of all real valued S-measurable functions defined on (X,S,$\mu$). For $E\;{\in}\;S$ with $\mu(E)\;<\;{\infty}$, $d_E$ is a pseudometric on M. With the notion of D = {$d_E$\mid$E\;{\in}\;S,\mu(E)\;<\;{\infty}$}, in this paper we investigate some topological structure T of M. Indeed, we shall show that it is possible to define a complete invariant metric on M which is compatible with the topology T on M.

• 대한수학회지
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• 제33권1호
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• pp.169-181
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• 1996

Let $x : M^n \longrightarrow E^m$ be an isometric immersion of an n-dimensional connected Riemannian manifold into the m-dimensional Euclidean space. Then the metric tensor on $M^n$ is naturally induced from that of $E^m$.

• 호남수학학술지
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• 제35권4호
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• pp.647-655
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• 2013

We obtain $C^{\infty}$-continuous paths of explicit Riemannian metrics $g_t$, $0{\leq}t$ < ${\varepsilon}$, whose scalar curvatures $s(g_t)$ decrease, where $g_0$ is a flat metric, i.e. a metric with vanishing curvature. Most of them can exist on tori of dimension ${\geq}3$. Some of them yield scalar curvature decrease on a ball in the Euclidean space.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권2호
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• pp.742-762
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• 2015

In this study, we propose a distance metric learning approach called discriminant metric learning (DML) for face verification, which addresses a binary-class problem for classifying whether or not two input images are of the same subject. The critical issue for solving this problem is determining the method to be used for measuring the distance between two images. Among various methods, the large margin nearest neighbor (LMNN) method is a state-of-the-art algorithm. However, to compensate the LMNN's entangled data distribution due to high levels of appearance variations in unconstrained environments, DML's goal is to penalize violations of the negative pair distance relationship, i.e., the images with different labels, while being integrated with LMNN to model the distance relation between positive pairs, i.e., the images with the same label. The likelihoods of the input images, estimated using DML and LMNN metrics, are then weighted and combined for further analysis. Additionally, rather than using the k-nearest neighbor (k-NN) classification mechanism, we propose a verification mechanism that measures the correlation of the class label distribution of neighbors to reduce the false negative rate of positive pairs. From the experimental results, we see that DML can modify the relation of negative pairs in the original LMNN space and compensate for LMNN's performance on faces with large variances, such as pose and expression.

• Genomics & Informatics
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• 제18권1호
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• pp.2.1-2.11
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• 2020

In this paper, we propose a new approach to detecting outliers in a set of segmented genomes of the flu virus, a data set with a heterogeneous set of sequences. The approach has the following computational phases: feature extraction, which is a mapping into feature space, alignment-free distance measure to measure the distance between any two segmented genomes, and a mapping into distance space to analyze a quantum of distance values. The approach is implemented using supervised and unsupervised learning modes. The experiments show robustness in detecting outliers of the segmented genome of the flu virus.

• Journal of Electrical Engineering and Technology
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• 제10권3호
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• pp.1233-1243
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• 2015

The contrast enhancement is great challenge in the image processing when images are suffering from poor contrast problem. Therefore, in order to overcome this problem an automatic method is proposed for contrast enhancement of natural color images. The proposed method consist of two stages: in first stage lightness component in YIQ color space is normalized by sigmoid function after the adaptive histogram equalization is applied on Y component and in second stage automatic color contrast enhancement algorithm is applied on output of the first stage. The proposed algorithm is tested on different NASA color images, hyperspectral color images and other types of natural color images. The performance of proposed algorithm is evaluated and compared with the other existing contrast enhancement algorithms in terms of colorfulness metric and color enhancement factor. The higher values of colorfulness metric and color enhancement factor imply that the visual quality of the enhanced image is good. Simulation results demonstrate that proposed algorithm provides higher values of colorfulness metric and color enhancement factor as compared to other existing contrast enhancement algorithms. The proposed algorithm also provides better visual enhancement results as compared with the other existing contrast enhancement algorithms.

• Genomics & Informatics
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• 제17권1호
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• pp.4.1-4.7
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• 2019

In this paper, we propose a window-based mechanism visualization approach as an alternative way to measure the seriousness of the difference among data-insights extracted from a composite biodata point. The approach is based on two components: undirected graph and Mosaab-metric space. The significant application of this approach is to visualize the segmented genome of a virus. We use Influenza and Ebola viruses as examples to demonstrate the robustness of this approach and to conduct comparisons. This approach can provide researchers with deep insights about information structures extracted from a segmented genome as a composite biodata point, and consequently, to capture the segmented genetic variations and diversity (variants) in composite data points.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권2호
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• pp.127-138
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• 2015

The object of this paper is to emphasize the role of 'common limit range property' and utilize the same with variants of R-weakly commuting mappings for the existence of common fixed point under strict contractive conditions in metric spaces. We also furnish some interesting examples to validate our main result. Our results improve a host of previously known results including the ones contained in Pant [Contractive conditions and common fixed points, Acta Math. Acad. Paedagog. Nyhàzi. (N.S.) 24(2) (2008), 257-266 MR2461637 (2009h:54061)]. In the process, we also derive a fixed point result satisfying $\phi$-contractive condition.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권2호
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• pp.153-162
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• 2001

In this Paper, the notion of $\varepsilon$-Birkhoff orthogonality introduced by Dragomir [An. Univ. Timisoara Ser. Stiint. Mat. 29(1991), no. 1, 51-58] in normed linear spaces has been extended to metric linear spaces and a decomposition theorem has been proved. Some results of Kainen, Kurkova and Vogt [J. Approx. Theory 105 (2000), no. 2, 252-262] proved on e-near best approximation in normed linear spaces have also been extended to metric linear spaces. It is shown that if (X, d) is a convex metric linear space which is pseudo strictly convex and M a boundedly compact closed subset of X such that for each $\varepsilon$>0 there exists a continuous $\varepsilon$-near best approximation $\phi$ : X → M of X by M then M is a chebyshev set .

• 대한수학회논문집
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• 제15권3호
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• pp.533-540
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• 2000

In the present paper, we study a non-degenrate ruled surface along a null curve in a 3-dimensional Minkowski space E31, which is called a null scroll, an investigate some characterizations of null scrolls satisfying the condition H=AH, A Mat(3, ), where denotes the Laplacian of the surface with respect to the induced metric, H the mean curvature vector and Mat(3, ) the set of 3$\times$3-real matrices.