• Journal of the Daesoon Academy of Sciences
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• v.23
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• pp.345-383
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• 2014

This article intends to examine the value of the world citizenship in the perspective from the root meaning that is stressed as the behavior style of Daesoon thoughts in relation with 'desirable attitude of life in education of morality. Traditional root meaning of Daesoon thoughts turned out to be proper moral behavior principle such as Yin Yang harmonious virtue, God Humane keeping unity, and conviviality with regrets settlement. Such three principles of Daesoon Thoughts show the characteristic of global code such as respect of life, solidarity unity, and tolerant trust. To revise the phenomenon of duality, and to realize the human awakening in radically changing reality, we need to cultivate world citizenship based on the root meaning of Daesoon thoughts. Daesoon thoughts covering the East and the West, especially the key features of religion, can cultivate the world view of citizenship in the era of plural society based on folk beliefs toward Gucheon Sangje faith as the essence of the multiplism. The world citizenship of human society is necessary to unite the world in the unified construction cooperative spirits. All beings need to be away from antagonistic confrontation with the practice of mutual conviviality. The diameter of acquired joining world citizenship can have the opportunity to realize of Gucheon Sangje's Heaven and earth construction. The root meaning of Daesoon thoughts can contribute to moral practicality with world citizenship by practice of heavenly truth and human truth. First, cultivating heavenly truth by means of insight can develope the profound world citizenship. Secondly, the solidarity of the public and private can cultivate public citizenship. Thirdly, in the crisis of the mankind, this awakening conviviality can be foundation for world citizenship of public communication. Fourthly, the spirit that would not deceive ownself can be contributed to cultivating the world citizenship by means of the process of internalizing Daesoon thoughts. Nowadays in the plural society demanding world citizenship, the public citizenship can deepen the spirit of respect of life, solidarity unity, and tolerant trust in the process of world citizenship cultivation. In the future, the world citizenship can be deepen the alternative of practice in the continuous cultivation of world citizenship. In this process, we can form the culture of coexistence which can contribute to human society as well as korean society by developing the value of living together happiness through the guide of this phonesis.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.449-454
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• 2012

In this paper, we find the minimal polynomial of a primitive root of unity over cyclotomic fields. From this, we factorize cyclotomic polynomials over cyclotomic fields and investigate the coefficients of ${\Phi}_{3n}(x)$ when 3∤$n$.

• The Pure and Applied Mathematics
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• v.23 no.1
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• pp.53-59
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• 2016

Let G be a finite group containing a non-abelian Sylow 2-subgroup. We elementarily show that every G-Galois field extension L/K has a hyperbolic trace form in the presence of root of unity.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.41-49
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• 2009

Let $\zeta$ be a fixed complex number. In this paper, we study the quantity $S(\zeta,\;n):=mas_{f{\in}{\Lambda}_n}\;|f(\zeta)|$, where ${\Lambda}_n$ is the set of all real polynomials of degree at most n-1 with coefficients in the interval [0, 1]. We first show how, in principle, for any given ${\zeta}\;{\in}\;{\mathbb{C}}$ and $n\;{\in}\;{\mathbb{N}}$, the quantity S($\zeta$, n) can be calculated. Then we compute the limit $lim_{n{\rightarrow}{\infty}}\;S(\zeta,\;n)/n$ for every ${\zeta}\;{\in}\;{\mathbb{C}}$ of modulus 1. It is equal to 1/$\pi$ if $\zeta$ is not a root of unity. If $\zeta\;=\;\exp(2{\pi}ik/d)$, where $d\;{\in}\;{\mathbb{N}}$ and k $\in$ [1, d-1] is an integer satisfying gcd(k, d) = 1, then the answer depends on the parity of d. More precisely, the limit is 1, 1/(d sin($\pi$/d)) and 1/(2d sin($\pi$/2d)) for d = 1, d even and d > 1 odd, respectively.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.9
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• pp.759-764
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• 2013

We present a square root algorithm in $F_q$ which generalizes Atkin's square root algorithm [9] for finite field $F_q$ of q elements where $q{\equiv}5$ (mod 8) and Kong et al.'s algorithm [11] for the case $q{\equiv}9$ (mod 16). Our algorithm precomputes ${\xi}$ a primitive $2^s$-th root of unity where s is the largest positive integer satisfying $2^s|q-1$, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favorably compared with the algorithms of Atkin, M$\ddot{u}$ller and Kong et al.

• Proceedings of the Korean Society of Computer Information Conference
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• 2023.07a
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• pp.163-164
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• 2023

실시간 3D 렌더링 게임의 제작 환경에서 캐릭터의 움직임은 모션 캡처(motion capture)를 통해 만들거나 애니메이터에 의해 제작된다. 걷기나 달리기 등 일정한 속도로 캐릭터가 움직이는 모션은 캐릭터가 제자리(in place)에서 움직이도록 한 뒤에 게임에서 프로그램에 의해 일정한 속도로 움직임으로써 구현할 수 있다. 하지만 일정하지 않은 속도로 움직이는 모션을 같은 방식으로 적용하면 캐릭터의 이동이 어색해진다. 이런 어색함을 보완하기 위해 언리얼이나 유니티 3D 등의 엔진에서는 루트 모션(root motion) 기능을 사용하고 있다. 그런데 루트 모션을 위한 계층 구조는 애니메이터의 작업 효율을 위한 계층 구조와 다른 측면이 있다. 본 논문에서는 3ds Max를 사용하여 애니메이터 친화적이고 루트 모션에도 적합한 캐릭터 리깅을 제시한다.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1025-1034
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• 2023

Let U be the restricted quantized enveloping algebra Ũ_q(𝖘𝖑₂) over an algebraically closed field of characteristic zero, where q is a primitive 𝑙-th root of unity (with 𝑙 being odd and greater than 1). In this paper we show that any indecomposable submodule of U under the adjoint action is generated by finitely many special elements. Using this result we describe all ideals of U. Moreover, we classify annihilator ideals of simple modules of U by generators.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.669-682
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• 2016

In this paper, we study the cellular structure of the G-edge colored partition algebras, when G is a finite group. Further, we classified all the irreducible representations of these algebras using their cellular structure whenever G is a finite cyclic group. Also we prove that the ${\mathbb{Z}}/r{\mathbb{Z}}$-Edge colored partition algebras are quasi-hereditary over a field of characteristic zero which contains a primitive $r^{th}$ root of unity.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.35-38
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• 1995

Let A be a symmetric positive definite Cartan matrix. As in [4], we denote by U the quantum group arising from A and $U_\lambda$ be the corresponding quantum group at a root of unity $\lambda$. In [4], Lusztig constructed irreducible highest weight $U_\lambda$-modules $L_\lambda(z)$ for $z \in Z^n$ and showed that $L_\lambda(z)$ is of finite dimension over C if and only if $z \in (Z^+)^n$.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.1005-1008
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• 1996

We consider the interval of a gain within which it is guaranteed that a feedback control system is stable. This paper presents the condition under which either a unity feedback control system is stable for a connected gain interval with a proportional compensator cascaded with an open loop forward transfer function. By the connected interval we mean that all the numbers between any two numbers in the connected interval belongs to the connected interval. The condition may be described by a frequency inequality in terms of the denominator and/or numerator of the closed loop transfer function. We also consider the conditions for the discrete-time control systems and the time delay continuous-time control systems. We show that this condition cannot be extended for the transfer function having complex coefficients via a counterexample.