• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제4권1호
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• pp.29-38
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• 2000

In this paper, we consider a criterion on primitive roots modulo p where p is the prime of the form $p=2^kq+1$, q odd prime. For such p we also consider the least primitive root modulo p. Also, we deal with certain isomorphism classes of elliptic curves over finite fields.

• 대한수학회논문집
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• 제28권1호
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• pp.71-77
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• 2013

Consider a multiplicative group of integers modulo $n$, denoted by $\mathbb{Z}_n^*$. Any element $a{\in}\mathbb{Z}_n^*$ is said to be a semi-primitive root if the order of $a$ modulo $n$ is ${\phi}(n)/2$, where ${\phi}(n)$ is the Euler phi-function. In this paper, we discuss some interesting properties of the multiplicative groups of integers possessing semi-primitive roots and give its applications to solving certain congruences.

• 호남수학학술지
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• 제33권2호
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• pp.181-186
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• 2011

Consider a multiplicative group of integers modulo n, denoted by $\mathbb{Z}_n^*$. Any element $a{\in}\mathbb{Z}_n^*$ n is said to be a semi-primitive root if the order of a modulo n is $\phi$(n)/2, where $\phi$(n) is the Euler phi-function. In this paper, we classify the multiplicative groups of integers having semi-primitive roots and give interesting properties of such groups.

• 대한수학회논문집
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• 제32권1호
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• pp.1-6
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• 2017

In this paper, the fundamental theorem of Galois Theory is used to generalize cyclotomic polynomials and construct irreducible polynomials associated with the n-th primitive roots of unity.

• 대한수학회논문집
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• 제20권2호
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• pp.247-257
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• 2005

In this paper we calculate two special types of multiple zeta values, $\zeta(\{4\iota+2\}_n)\;and\;\zeta(\{4\iota\}_n)$ using the primitive roots of unity, which may be simpler and easier.

• 한국농공학회:학술대회논문집
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• 한국농공학회 2000년도 학술발표회 발표논문집
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• pp.78-83
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• 2000

Over twenty thousand types of bryohytes are existed in the world. Bryophytes are generally considered to be primitive plants and seriously neglected by even in botany area. Bryophytes includes mosses, liverworts, and hornworts. They thrive in humid environments and require water to survive. Some types, however, can recover after serious dehydration, even after years of complete dehydration. They generally absorb water and nutrients not from roots which is called rhizoid, but through entire body. The rhizoids are nonchlorophyllose fillamentous branches and attach the body to substratum such as soil and rocks. The attachment of mosses in soil surface provides a good protection from soil erosion by runoff water. In this presentation, reviewed and discussed are ecological characteristics and engineering perspectives of mosses, particularly with respect to soil and water conservation.

• Journal of Plant Biology
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• 제27권3호
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• pp.149-162
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• 1984

Anatomical characters of the secondary xylem in roots of Lauraceae, including 6 genera and 13 species grown in Korea, were studied systematically. Lauraceors members studied anatomically possess characters of the secondary xylem that are in the main more specialized than those found in the primitive angiosperm families. The specialized characters are as follows; (1) mostly solitary pores with some radially multiples, (2) mostly simple perforation plates and partially scalariform perforation plates in all species, (3) slightly oblique end wall of vessel element, (4) predominantly alternate intervascular pitting, (5) paratracheal axial parenchyma in all species, (6) heterogeneous II or III vascular rays. It is considered that the series of specialization in this family from the perforation plates and angle of end wall to the vessel axis is as follows; MachiluslongrightarrowNeolitsealongrightarrowLinderalongrightarrowCinammomumlongrightarrowIozostelongrightarrowLitsea.

• 대한지리학회지
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• 제50권4호
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• pp.431-449
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• 2015

신자유주의의 사상적 기원과 논의구도는 매우 이질적이며, 접근방법도 아나키즘, 탈신자유주의를 포함하여 매우 다양하다. 2008년 금융위기를 계기로 신자유주의는 그 정당성과 안정성을 상실하기는 했지만 여전히 광범위한 변이들을 창출하면서 진화하고 있기 때문에 신자유주의 분석에서 공간적 관점의 중요성이 커지고 있다. 특히 신자유주의의 시공간 전략과 시스템 재생산을 위한 생성적 거점으로서 도시 공간이 핵심 무대가 되었다. 자본의 형식적 실질적 공간포섭으로서 신자유주의 도시화의 구체적 전개과정에서 가장 중요한 수단이 도시 인클로저이다. 현대 자본주의는 도시 인클로저를 통해 시초축적기의 원리를 현대적으로 재구성하여 탈취 기반 축적을 지속하고 있다. 이러한 도시 인클로저는 공적소유라는 본래의 공익개념으로부터 경제적 공익개념으로의 해석 변경과 사적자본의 이익을 위한 공용수용을 통해서 이루어지고 있다. 도시 인클로저는 생산 및 생존수단으로부터 노동자의 분리 소외를 더욱 심화시키는 물상화, 자유로운 장소향유의 제지, 세습가산제 형태로의 도시경제 전환을 동반하면서 인클로저의 일상화를 촉진하고 있고, 사적이익으로 뒤얽힌 사회적 규범들이 공적공간과 공간의 공공성을 지배하도록 만든다.