• The Journal of Korean Philosophical History
• /
• no.32
• /
• pp.185-213
• /
• 2011

This thesis is studing Kim Chi-in's Life and Confucianism-Buddhism-Taoism-Unity of Namhak lind on Jinan in Junbuk. He combined thought of Confucianism-Buddhism-Taoism and drawed up religious doctrine, after spotting internal and external troubles of nation. Kim Chi-in was influenced by Lee Un-gyu's thought of Confucianism-Buddhism-Taoism-Unity. He spoke with emphasis of Tao in doctrine through religious experience. The root of Tao originates in heaven. Although Tao was divided according to Confucianism, Buddhism and Taoism for the human's aspect of thought, it is ultimately the one. In time on explaining the one, he invoked 'eum(陰)', 'yang(陽)', 'che(體)'와 'yong(用)' as concepts of Neo-Confucianism. This ididn't incline to one side of Confucianism, Buddhism and Taoism. While he spoke with emphasis on Confucianism's ethics of 'yang' and 'yong' with Buddhism and Taoism's divine of 'eum' and 'che' as the center, he want to find pivot of thought. He especially seeked Younggamu(詠歌舞) of sing and dancing on training mind and body. This was that he let the people and scholars in retirement demand realization of Tao and aim at real virtue. The study of Kim Chi-in's thought and religion of Confucianism-Buddhism-Taoism-Unity will be an opportunity look around his identity for the traditional native thought and universality.

• Kyungpook Mathematical Journal
• /
• v.55 no.3
• /
• pp.587-595
• /
• 2015

In this article, we will examine the Diophantine equation $ax^6+by^3+cz^2=0$, for arbitrary rational integers a, b, and c in Gaussian integers and find all the solutions of this equation for many different values of a, b, and c. Moreover, two equations of the type $x^6{\pm}iy^3+z^2=0$, and $x^6+y^3{\pm}wz^2=0$ are also discussed, where i is the imaginary unit and w is a third root of unity.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.4
• /
• pp.1185-1196
• /
• 2016

We show a class of homogeneous polynomials of Fermat-Waring type such that for a polynomial P of this class, if $P(f_1,{\ldots},f_{N+1})=P(g_1,{\ldots},g_{N+1})$, where $f_1,{\ldots},f_{N+1}$; $g_1,{\ldots},g_{N+1}$ are two families of linearly independent entire functions, then $f_i=cg_i$, $i=1,2,{\ldots},N+1$, where c is a root of unity. As a consequence, we prove that if X is a hypersurface defined by a homogeneous polynomial in this class, then X is a unique range set for linearly non-degenerate non-Archimedean holomorphic curves.

• Journal of the Optical Society of Korea
• /
• v.20 no.1
• /
• pp.107-117
• /
• 2016

We develop a new method to globally calibrate the feature points that are derived from the binocular systems at different positions. A three-DOF (degree of freedom) global calibration system is established to move and rotate the 3D calibration board to an arbitrary position. A three-DOF global calibration model is constructed for the binocular systems at different positions. The three-DOF calibration model unifies the 3D coordinates of the feature points from different binocular systems into a unique world coordinate system that is determined by the initial position of the calibration board. Experiments are conducted on the binocular systems at the coaxial and diagonal positions. The experimental root-mean-square errors between the true and reconstructed 3D coordinates of the feature points are 0.573 mm, 0.520 mm and 0.528 mm at the coaxial positions. The experimental root-mean-square errors between the true and reconstructed 3D coordinates of the feature points are 0.495 mm, 0.556 mm and 0.627 mm at the diagonal positions. This method provides a global and accurate calibration to unity the measurement points of different binocular vision systems into the same world coordinate system.

• Journal of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.123-132
• /
• 2021

Let K be a number field and L a finite abelian extension of K. Let E be an elliptic curve defined over K. The restriction of scalars ResKLE decomposes (up to isogeny) into abelian varieties over K $$Res^L_KE{\sim}{\bigoplus_{F{\in}S}}A_F,$$ where S is the set of cyclic extensions of K in L. It is known that if L is a quadratic extension, then AL is the quadratic twist of E. In this paper, we consider the case that K is a number field containing a primitive third root of unity, $L=K({\sqrt[3]{D}})$ is the cyclic cubic extension of K for some D ∈ K×/(K×)3, E = Ea : y2 = x3 + a is an elliptic curve with j-invariant 0 defined over K, and EaD : y2 = x3 + aD2 is the cubic twist of Ea. In this case, we prove AL is isogenous over K to $E_a^D{\times}E_a^{D^2}$ and a property of the Selmer rank of AL, which is a cubic analogue of a theorem of Mazur and Rubin on quadratic twists.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1511-1522
• /
• 2022

Let H be a subgroup of $\mathbb{Z}^*_n$ (the multiplicative group of integers modulo n) and h₁, h₂, …, h_l distinct representatives of the cosets of H in $\mathbb{Z}^*_n$. We now define a polynomial J_n,H(x) to be $$J_{n,H}(x)=\prod^l_{j=1} \left( x-\sum_{h{\in}H} {\zeta}^{h_jh}_n\right)$$, where ${\zeta}_n=e^{\frac{2{\pi}i}{n}}$ is the nth primitive root of unity. Polynomials of such form generalize the nth cyclotomic polynomial $\Phi_n(x)={\prod}_{k{\in}\mathbb{Z}^*_n}(x-{\zeta}^k_n)$ as J_n,{1}(x) = Φ_n(x). While the nth cyclotomic polynomial Φ_n(x) is irreducible over ℚ, J_n,H(x) is not necessarily irreducible. In this paper, we determine the subgroups H for which J_n,H(x) is irreducible over ℚ.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.40 no.2
• /
• pp.264-272
• /
• 2015

In this paper, we analyze the statistical characteristic and describe the anti-interference performance of the signal for the LPI-applied GNSS using encrypted spreading code. To do this, we analyze the correlation property of encrypted sequences theoretically having various symbol sets over complex root of unity. We derive the degradation of anti-interference performance of encrypted sequences comparing with Gold and Zadoff-Chu sequences using theoretical and experimental methods.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.1137-1150
• /
• 2022

Consider the quantum algebra U_q(sl₂) over field 𝓕 (char(𝓕) = 0) with equitable generators x^±1, y and z, where q is fixed nonzero, not root of unity scalar in 𝓕. Let V denote a finite dimensional irreducible module for this algebra. Let Λ ∈ End(V), and let {A₁, A₂, A₃} = {x, y, z}. First we show that if Λ, A₁ is a Leonard pair, then this Leonard pair have four types, and we show that for each type there exists a Leonard pair Λ, A₁ in which Λ is a linear combination of 1, A₂, A₃, A₂A₃. Moreover, we use Λ to construct 𝚼 ∈ U_q(sl₂) such that 𝚼, A^-1₁ is a Leonard pair, and show that 𝚼 = I + A₁Φ + A₁ΨA₁ where Φ and Ψ are linear combination of 1, A₂, A₃.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.1
• /
• pp.172-181
• /
• 1993

Pseudo-Brayton cycle is defined as an ideal Brayton cycle admitting the difference between heat capacities of working fluid during heating and cooling processes. The endo-pseudo-Brayton cycle which is a pseudo-Brayton cycle with heat transfer processes is analyzed with the consideration of maximum power conditions and the results were compared with those of the endo-Carnot cycle and endo-Brayton cycle. As results, the maximum power is an extremum with respect to the cycle temperature and the flow heat capacities of heating and cooling processes. At the maximum power condition, the heat capacity of the cold side is smaller than that of heat sink flow. And the heat capacity of endo-Brayton cycle is always between those of heat source and sink flows and those of the working fluids of pseudo-Brayton cycle. There is another optimization problem to decide the distribution of heat transfer capacity to the hot and cold side heat exchangers. The ratios of the capacies of the endo-Brayton and the endo-pseudo-Braton cycles at the maximum power condition are just unity. With the same heat source and sink flows and with the same total heat transfer caqpacities, the maximum power output of the Carnot cycle is the least as expected, but the differences among them were small if the heat transfer capacity is not so large. The thermal efficiencies of the endo-Brayton and endo-Carnot cycle were proved to be 1-.root.(T$_{7}$/T$_{1}$) but it is not applicable to the pseudo-Brayton case, instead it depends on comparative sizes of heat capacities of the heat source and sink flow.w.

• Journal of the Daesoon Academy of Sciences
• /
• v.34
• /
• pp.107-139
• /
• 2020

This paper primarily focuses on the highest deity, the Upper Thearch of the Nine Heavens (officially translated as 'The Supreme God of the Ninth Heaven'), in the Korean new religious movement (NRM) Daesoon Jinrihoe and the true minister of the myriad spirits in the Taiwanese NRM, Yiguan Dao, the Upper Thearch of Manifest Luminosity. As the two both serve as highly representative "Upper Thearch" beliefs in emerging NRMs, I attempt a comparative analysis of the source of these beliefs, their characteristics, and the links that exist between them. On the basis of ancient Chinese classics and Daoist texts, along with Daesoon Jinrihoe's scriptures and works from Yiguan Dao's Canon, I try to understand the distinguishing features of cosmological ideas from both religious movements. For example, because the Upper Thearch of the Nine Heavens could not bear to see the human realm growing ever more disordered and in order to improve worldly conditions, he traveled to the harmonized realm of deities, and therefore descended into the world to make a great itineration and enlighten the people through his teachings. In the end, he came to Korea and was reborn as Kang Jeungsan (secular name: Kang Il-Sun) in Gaekmang Village. In the Human Realm, he spread his transformative teachings to the people which were later became the doctrines of the Virtuous Concordance of Yin and Yang, Harmonious Union between Divine Beings and Human Beings, the Resolution of Grievances for Mutual Beneficence, and Perfected Unification (jingyeong 真境) with the Dao. Yiguan Dao; however, explains that the source of humanity is the "Heaven of Principle" (Litian 理天), and people are "Buddha's Children of the Original Embryo" (Yuantai Fozi 原胎佛子), created by the Upper Thearch of Manifest Luminosity, who came to world to govern and impart spiritual refinement, before returning to his native place in the Heaven of Principle. Yet, because he became infatuated with the world of mortals, he forgot the path of his return. Therefore, the Eternal Mother sent Maitreya Buddha, the Living Buddha Jigong 濟公, and the Bodhisattva of Moon Wisdom (Yuehui pusa 月慧菩薩) to descend to the human world and teach the people, so that they may acknowledge the Eternal Mother as the root of return, achieve their return to the origin, and go back to the home of the Eternal Mother in the Heaven of Principle. Both Daesoon Jinrihoe and Yiguan Dao refer to their highest deity, the true ministers of the myriad spirits, with the simple title "Upper Thearch." This phenomenon also has some ties to God in the western Biblical tradition but also has some key differences. In investigating the sources of these two deities, we find that they likely took shape during the Yinshang (殷商) period and have some relationship to the Upper Thearch of Chinese antiquity. The questions raised in this research are quite interesting and deserving of deeper comparative study.