• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.1-5
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• 2012

We study surfaces of revolution in the three dimensional Euclidean space $\mathbb{R}^3$ with two distinct axes of revolution. As a result, we prove that if a connected surface in the three dimensional Euclidean space $\mathbb{R}^3$ admits two distinct axes of revolution, then it is either a sphere or a plane.

• 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.

• 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.

• Journal of applied mathematics & informatics
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• v.42 no.5
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• pp.1007-1023
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• 2024

In this paper we are able to define a standard fractional vector cross product(SFVCP) of two vectors in a Euclidean 3-space where it satisfies all the conditions of geometrical reality. For γ = 1 this definition satisfies the conditions of standard vector cross product(SVCP). The formulae for euclidean norm and fractional triple vector cross product of two vectors with standard fractional vector cross product are presented. Fractional curl and divergence of an electromagnetic vector field are presented using the new definition. All the properties are further supported with particular cases at γ = 0, γ = 1 and examples on standard orthogonal basis in R³. This concept has application in electrodynamics, elastodynamics, fluid flow etc.

• 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 Astronomy and Space Sciences
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• v.19 no.1
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• pp.1-6
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• 2002

Recently, one interesting possibility is proposed that a magnetar can be a progenitor of short and hard gamma-ray bursts (GRBs). If this is true, one may expect that the short and hard GRBs, at least some of GRBs in this class, are distributed in the Euclidean space and that the angular position of these GRBs is correlated with galaxy clusters. Even though it is reported that the correlation is statistically marginal, the observed value of < $V/V_{max}$ > deviates from the Euclidean value. The latter fact is often used as evidence against a local extragalactic origin for short GRB class. We demonstrate that GRB sample of which the value of < $V/V_{max}$ > deviates from the Euclidean value can be spatially confined within the low value of z. We select very short bursts (TgO < 0.3 sec) from the BATSE 4B catalog. The value of < $V/V_{max}$ > of the short bursts is 0.4459. Considering a conic-beam and a cylindrical beam for the luminosity function, we deduce the corresponding spatial distribution of the GRB sources. We also calculate the fraction of bursts whose redshifts are larger than a certain redshift z', i.e. f>z'. We find that GRBs may be distributed near to us, despite the non-Euclidean value of < $V/V_{max}$ >. A broad and uniform beam pattern seems compatible with the magnetar model in that the magnetar model requires a small $z_{max}$.

• 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.

• 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.