• Journal for History of Mathematics
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• v.33 no.3
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• pp.155-165
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• 2020

Pythagorean theorem is a proposition on the relationship between the lengths of three sides of a right triangle. It is well known that Pythagorean theorem for Euclidean geometry deforms into an interesting form in non-Euclidean geometry. In this paper, we investigate a new perspective that replaces right triangles with 'proper triangles' so that Pythagorean theorem extends to non-Euclidean geometries without any modification. This is seen from the perspective that a rectangle is an equiangular quadrilateral, and a right triangle is a half of a rectangle. Surprisingly, a proper triangle (defined by Paolo Maraner), which is a half of an equiangular quadrilateral, satisfies Pythagorean theorem in many geometries, including hyperbolic geometry and spherical geometry.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.12 no.3
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• pp.417-424
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• 2001

This paper proposes new symbol mapping method that can enhance the performance of trellis coded M-ary PSK compared with conventional symbol mapping methods in AWGN environment. Since the basic criteria of TCM design is Maximum Euclidean distance in AWGN, conventional symbol mapping method keep this basic criteria. In this paper, proposed new symbol mapping method uses both Euclidean distance and Hamming distance to design, while conventional methods make use of only optimal Euclidean distance. New symbol mapping method show the better BER performance than the other through computer simulation and error equations.

• Development and Reproduction
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• v.21 no.4
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• pp.435-440
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• 2017

The author performed PCR-based genetic platform to measure the hierarchical dendrogram of Euclidean genetic distances of Korean scallop populations (KSP), particularly for Chlamys farreri, which was further compared with those of the Chinese scallop populations (CSP), by employing the with specifically designed oligonucleotide primer sets. The scallop is economically and ecologically very important bivalves in South Korea. Relatively, individuals of KSP population were fairly distantly related to that of CSP population, as shown in the hierarchical dendrogram of Euclidean genetic distances. Comparatively, individuals of KSP population were fairly distantly related to that of CSP population. Thus analysis of genetic difference between scallop populations could provide important statistics for fishery and aquaculture. Overall the results showed specific and/or conserved genetic loci between scallop populations. Information on the genetic distance of the bivalve would be helpful to understand scallop expansion or conservation in the coastal regions of South Korea. Specific markers developed by the author will be useful for the analysis of scallop population genetics and distribution in coastal region.

• The Mathematical Education
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• v.4 no.1
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• pp.1-15
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• 1966

In accordance with the tendency of Modern Mathematics laying emphasis on Mathematical structure, that is, on axioms, it is necessary for students to be interested in structure of Geometry on Mathematics Education. In fact, it is of importance not only to obtain new ideas but also to forget old ones in the development of Mathematics. Most students do not understand the Mathematical significance of axioms, and do not know what Mathemetical truth is. Now Non-Euclidean Geometry offers opportunity to understand the essence of Mathematics better, and is no less effective than Euclidean Geometry in training student in logical inference. This thesis is a study with regard to what should be taught and how student should be guided at High school Mathematics. Chiefly Hyperbolic Geometry is discussed in connection with Abosolute Geometry. As Non-Euclidean Geometry has not appeared in our curriculum, some experiments are required before putting it into actual curriculum to find out how much students understand and how much pedagogically useful it can be. This is only a. presentation of a tentative plan, which needs to be criticized by many teachers.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.507-528
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• 2006

In this paper we show that the Koecher's Jordan automorphic generators of one variable on an irreducible symmetric cone are enough to determine the elements of scalar multiple of the Jordan identity on the attached simple Euclidean Jordan algebra. Its various geometric, Jordan and Lie theoretic interpretations associated to the Cartan-Hadamard metric and Cartan decomposition of the linear automorphisms group of a symmetric cone are given with validity on infinite-dimensional spin factors

• 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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.10a
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• pp.981-984
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• 2009

In this paper, We design RS(255,239) decoder with modified Euclidean algorithm, which show polynomic coefficient state machine instead of calculating coefficients of modified Euclidean algorithm. This design can reduce complexity and implement High-speed Read Solomon decoder. Additionally, we have synthesized with Xilinx XC4VLX60. From synthesis, it can operate at clock frequency of 77.4MHz, and gate count is 20,710.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.419-431
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• 2022

Mannheim introduced the concept of a pair of curves, called as Mannheim partner curves, in 1878. Until now, Mannheim partner curves have been studied widely in the literature. In this study, we take into account of this concept according to Positional Adapted Frame (PAF) for the particles moving in the 3-dimensional Euclidean space. We introduce a new type special trajectory pairs which are called Mannheim partner P-trajectories in the Euclidean 3-space. The relationships between the PAF elements of this pair are investigated. Also, the relations between the Serret-Frenet basis vectors of Mannheim partner P-trajectories are given. Afterwards, we obtain the necessary conditions for one of these trajectories to be an osculating curve and for other to be a rectifying curve. Moreover, we provide an example including an illustrative figure.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.310-324
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• 2022

In this paper, we define timelike curves in R⁴₂ and characterize such curves in terms of Frenet frame. Also, we examine the timelike helices of R⁴₂, taking into account their curvatures. In addition, we study timelike slant helices, timelike B₁-slant helices, timelike B₂-slant helices in four dimensional semi-Euclidean space, R⁴₂. And then we obtain an approximate solution for the timelike B₁ slant helix with Taylor matrix collocation method.

• 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.