• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2035-2045
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• 2015

Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with special invariants. In the present paper we give the complete classification of Chen meridian surfaces and meridian surfaces with parallel normal bundle.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.547-557
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• 2018

We establish some characterizations of isoparametric surfaces in the three-dimensional Euclidean space, which are associated with the Laplacian operator defined by the so-called II-metric on surfaces with non-degenerate second fundamental form and the elliptic linear Weingarten metric on surfaces in the three-dimensional Euclidean space. We also study a Ricci soliton associated with the elliptic linear Weingarten metric.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.668-677
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• 2023

In this study, we bring forth a new general formula for inextensible flows of Euclidean curves as regards modified orthogonal frame (MOF) in E³. For an inextensible curve flow, we provide the necessary and sufficient conditions, which are denoted by a partial differential equality containing the curvatures and torsion.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.849-866
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• 2024

In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.259-284
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• 2024

In present study, we introduce ruled surfaces whose base curve is the Salkowski curve in Euclidean 3-space and whose generating lines consist of the Frenet vectors of this curve (tangent, principal normal and binormal vectors). Then, we produce regular surfaces from a vector with real coefficients, which is a linear combination of these vectors, and we examine some special cases for these surfaces. Moreover, we present some geometric properties and graphics of all these surfaces.

• International Journal of CAD/CAM
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• v.5 no.1
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• pp.59-68
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• 2005

Euclidean Voronoi diagram of spheres in 3-dimensional space has not been explored as much as it deserves even though it has significant potential impacts on diverse applications in both science and engineering. In addition, studies on the data structure for its topology have not been reported yet. Presented in this, paper is the topological representation for Euclidean Voronoi diagram of spheres which is a typical non-manifold model. The proposed representation is a variation of radial edge data structure capable of dealing with the topological characteristics of Euclidean Voronoi diagram of spheres distinguished from those of a general non-manifold model and Euclidean Voronoi diagram of points. Various topological queries for the spatial reasoning on the representation are also presented as a sequence of adjacency relationships among topological entities. The time and storage complexities of the proposed representation are analyzed.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.42 no.5
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• pp.69-78
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• 2005

It is crucial to compute the Euclidean distance between two vectors efficiently in high dimensional space for multimedia information retrieval. In this paper, we propose an effective method for approximating the Euclidean distance between two high-dimensional vectors. For this approximation, a previous method, which simply employs norms of two vectors, has been proposed. This method, however, ignores the angle between two vectors in approximation, and thus suffers from large approximation errors. Our method introduces an additional vector called a reference vector for estimating the angle between the two vectors, and approximates the Euclidean distance accurately by using the estimated angle. This makes the approximation errors reduced significantly compared with the previous method. Also, we formally prove that the value approximated by our method is always smaller than the actual Euclidean distance. This implies that our method does not incur any false dismissal in multimedia information retrieval. Finally, we verify the superiority of the proposed method via performance evaluation with extensive experiments.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.509-518
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• 1995

Let $M^n$ be a hypersurface in the Euclidean space $R^{n+1}$ with position vector field x and unit normal vector field G.

• International Journal of Advanced Culture Technology
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• v.9 no.3
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• pp.298-304
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• 2021

Currently, to prevent the spread of COVID-19 virus infection, gathering of more than 5 people in the same space is prohibited. The purpose of this paper is to measure the distance between objects using the Yolov5 model for processing real-time images with OpenCV in order to restrict the distance between several people in the same space. Also, Utilize Euclidean distance calculation method in DeepSORT and OpenCV to minimize occlusion. In this paper, to detect the distance between people, using the open-source COCO dataset is used for learning. The technique used here is using the YoloV5 model to measure the distance, utilizing DeepSORT and Euclidean techniques to minimize occlusion, and the method of expressing through visualization with OpenCV to measure the distance between objects is used. Because of this paper, the proposed distance measurement method showed good results for an image with perspective taken from a higher position than the object in order to calculate the distance between objects by calculating the y-axis of the image.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.198-214
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• 2023

In the present paper, we investigate homothetic motions determined by quaternions, which is a general form of our previous paper [20]. We introduce a transition between homothetic motions in 3D and 4D Euclidean and Lorentzian spaces. In other words, we give a new method that works as a handy tool for obtaining Lorentzian homothetic motions from Euclidean homothetic motions. Moreover, some remarkable properties of homothetic motions, which are given in former studies on this subject, are also examined by dual transformations. Then, we present applications and visualize them with 3D-plots. Finally, we investigate homothetic motions in dual spaces because of the importance in many fields related to kinematics.