• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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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.

• Honam Mathematical Journal
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• v.33 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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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.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2000.10a
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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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• v.27 no.3
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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.

• Journal of the Korean Geographical Society
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• v.50 no.4
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• pp.431-449
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• 2015

Philosophical roots and discussion frames of neoliberalism are very heterogeneous and approaches to neoliberalism including anarchism, post-neoliberalism also take diverse stances. Even if neoliberalism is losing legitimacy and stability through the global financial crisis, 2008, spatial perspective is becoming more and more important as neoliberalism constantly evolve with creating immense variations. Especially, urban space has become strategically crucial arenas as spatio-temporal strategies and generative nodes for reproduction of neoliberalism. Urban enclosure plays a key role in the specific process of neoliberal urbanization as a kind of capitalist formal and real subsumption. Contemporary capitalism continuously has been sustaining the accumulation by dispossession based on urban enclosure through reshaping the primitive accumulation mechanism. These enclosures are embodied by the change of public use concept from public ownership to economic benefits and public-private taking for private capital. Urban enclosure promotes reification deepening the separation and alienation of workers from the means of production and survival, and interdiction from free place appropriation, transformation of urban economy to patrimonial forms. Also it is pervasive in a daily life space and everyday experience in the city, and private tangled social rules dominate public space and the publicity of space.