• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.63-82
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• 2011

On the hyperbolic space $D^n$, codimension-one totally geodesic foliations of class $C^k$ are classified. Except for the unique parabolic homogeneous foliation, the set of all such foliations is in one-one correspondence (up to isometry) with the set of all functions z : [0, $\pi$] $\rightarrow$ $S^{n-1}$ of class $C^{k-1}$ with z(0) = $e_1$ = z($\pi$) satisfying |z'(r)| ${\leq}1$ for all r, modulo an isometric action by O(n-1) ${\times}\mathbb{R}{\times}\mathbb{Z}_2$. Since 1-dimensional metric foliations on $D^n$ are always either homogeneous or flat (that is, their orthogonal distributions are integrable), this classifies all 1-dimensional metric foliations as well. Equations of leaves for a non-trivial family of metric foliations on $D^2$ (called "fifth-line") are found.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.117-128
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• 2012

Using the concept of a g-monotone mapping we prove some common fixed point theorems for g-non-decreasing mappings which satisfy some generalized nonlinear contractions in partially ordered complete quasi b-metric spaces. The new theorems are generalizations of very recent fixed point theorems due to L. Ciric, N. Cakic, M. Rojovic, and J. S. Ume, [Monotone generalized nonlinear contractions in partailly ordered metric spaces, Fixed Point Theory Appl. (2008), article, ID-131294] and R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan [Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8].

• Honam Mathematical Journal
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• v.42 no.3
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• pp.621-643
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• 2020

Depending on the characteristic vector filed ζ, a generic lightlike submanifold M in an indefinite Kaehler manifold ${\bar{M}}$ with a semi-symmetric metric connection has various characterizations. In this paper, when the characteristic vector filed ζ belongs to the screen distribution S(TM) of M, we provide some characterizations of (Lie-) recurrent generic lightlike submanifold M in an indefinite Kaehler manifold ${\bar{M}}$ with a semi-symmetric metric connection. Moreover, we characterize various generic lightlike submanifolds in an indefinite complex space form ${\bar{M}}$ (c) with a semi-symmetric metric connection.

• East Asian mathematical journal
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• v.31 no.1
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• pp.65-75
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• 2015

In modern times, coupled fixed point theorems have been rigorously studied by many researchers in the milieu of partially ordered G-metric spaces using different contractive conditions. In this note, some coupled fixed point theorems using mixed monotone property in partially ordered G-metric spaces are obtained. Furthermore some theorems by omitting the completeness on the space and continuity conditions on function, are obtained. Our results partially generalize some existing results in the present literature. To exemplify our results and to distinguish them from the existing ones, we equip the article with suitable examples.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.4
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• pp.524-529
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• 2008

Park et.al.[10] defined the intuitionistic fuzzy metric space in which it is a little revised in Park[4], and Park et.a1.[7] proved a fixed point theorem of Banach for the contractive mapping of a complete intuitionistic fuzzy metric space. In this paper, we will establish common fixed point theorem for four self maps in intuitionistic fuzzy metric space. These results have been used to obtain translation and generalization of Grabiec's contraction principle.

• Korean Journal of Mathematics
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• v.32 no.3
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• pp.467-484
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• 2024

In this paper, following the pullback approach to global Finsler geometry, we investigate a coordinate-free study of Shen square metric in a more general manner. Precisely, for a Finsler metric (M, L) admitting a concurrent π-vector field, we study some geometric objects associated with ${\widetilde{L}}(x, y)={\frac{(L+{\mathfrak{B}}^2)}L}$ in terms of the objects of L, where ${\mathfrak{B}}$ is the associated 1-form. For example, we find the geodesic spray, Barthel connection and Berwald connection of ${\widetilde{L}}(x,y)$. Moreover, we calculate the curvature of the Barthel connection of ${\tilde{L}}$. We characterize the non-degeneracy of the metric tensor of ${\widetilde{L}}(x,y)$.

• Journal of Korea Society of Digital Industry and Information Management
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• v.7 no.3
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• pp.37-42
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• 2011

Nowadays software developers are moving from conventional software process technologies to the object-oriented paradigm. To develope the object-oriented softwares efficiently, various software metrics have been suggested. Coupling refers to the degree of independence between components of the system. It has long been well known that good software practice calls for minimizing coupling interaction. Many researches have been studied coupling metrics of the object- oriented systems. We review Chidamber and Kemerer's work & Li's work. In this paper, we study the coupling of the overall structures of object-oriented systems by analyzing the class diagram of UML. We propose four coupling metrics for object-oriented softwares. First, we use an established coupling metric for object- oriented systems as a basic coupling metric. Then we modify the basic coupling metric by including indirect coupling between classes, We also suggest two relative coupling metrics to measure coupling between subsystems. We investigate the theoretical soundness of the proposed metrics by the axioms of Briand et al. Finally, we apply the presented metrics to a practical case study. This coupling metric will be helpful to the software developers for their designing tasks by evaluating the coupling metric of the structures of object-oriented system and redesigning tasks of the system.

• Smart Media Journal
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• v.10 no.4
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• pp.45-54
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• 2021

The skin is the body's first line of defense against external infection. When a skin disease strikes, the skin's protective role is compromised, necessitating quick diagnosis and treatment. Recently, as artificial intelligence has advanced, research for technical applications has been done in a variety of sectors, including dermatology, to reduce the rate of misdiagnosis and obtain quick treatment using artificial intelligence. Although previous studies have diagnosed skin diseases with low incidence, this paper proposes a method to classify common illnesses such as warts and corns using a convolutional neural network. The data set used consists of 3 classes and 2,515 images, but there is a problem of lack of training data and class imbalance. We analyzed the performance using a deep metric loss function and a cross-entropy loss function to train the model. When comparing that in terms of accuracy, recall, F1 score, and accuracy, the former performed better.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.42 no.1
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• pp.31-38
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• 2017

In this paper, we have designed MIMO system using F-OFDM modulation. And then, we have evaluated and analyzed synchronization performance of the system. In this paper we have considered Schmidl's method, Minn's method, and Park's method. As simulation results, Schmidl's method has wide plateau of timing metric and Park's method has impulse-shape timing metric. Also, we can confirm that timing metric characteristic of synchronization estimator can be degraded by adjusting filter length of F-OFDM system. Especially, we can confirm that timing metric of synchronization estimator is shifted according to filter length of MIMO system using F-OFDM modulation and this timing metric movement can be compensated by using designed filter length.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.303-315
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• 2001

In this paper, we investigate the topology of complex Finsler manifolds. For a complex Finsler manifold (M, F), we introduce a certain condition on the Finsler metric F on M. This is a generalization of Kahler condition for the Hermitian metric. Under this condition, we can produce a Kahler metric on M. This enables us to use the usual techniques in the Kahler and Riemannian geometry. We show that if the holomorphic sectional curvature of $ M is\geqC^2>0\; for\; some\; c>o,\; then\; diam(M)\leq\frac{\pi}{c}$ and hence M is compact. This is a generalization of the Bonnet\`s theorem in the Riemannian geometry.