• Korean Journal of Plant Resources
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• v.27 no.2
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• pp.133-154
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• 2014

We investigated the flora of Yeoseo-do (N $33^{\circ}58^{\prime}$, E $126^{\circ}55^{\prime}$), located in Wando-gun, Jeollanam-do, South Korea and discussed the vascular plants found there. Four separate field trips were completed from April to October of 2013. The vascular plants were summarized as 463 taxa; 112 families, 306 genera, 409 species, 6 subspecies, 42 varieties, 5 forms and 1 hybrids. The number of endemic species of Korea were 6 taxa, and 12 taxa designated by the Ministry of Environment as red data of endangered vascular plants were investigated in this region. There were a total of 98 taxa of floristic regional indicator plants and one taxon of level I endangered species, Neofinetia falcata (Thunb.) Hu, as designated by the Ministry of Environment. 33 taxa have shown their southern distributional limit ranges, and 10 taxa of halophytes were confirmed in the Yeoseo-do (Isl.). In additon, 27 taxa of the naturalized plants were recorded.

• Geomechanics and Engineering
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• v.11 no.6
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• pp.739-756
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• 2016

The shear strength reduction finite element method (SSRFEM) is a powerful tool for slope stability analysis. The factor of safety (FOS) of the slope can be easily calculated only through reducing effective cohesion (c′) and tangent of effective friction angle ($tan{\varphi}^{\prime}$) in equal proportion. However, this method may not be applicable to soil slope under wetting-drying cycles (WDCs), because the influence of WDCs on c′ and $tan{\varphi}^{\prime}$ may be different. To research the method of estimating FOS of soil slopes under WDCs, this paper presents an experimental study firstly to investigate the effects of WDCs on the parameters of shear strength and stiffness. Twelve silty clay samples were subjected to different number of WDCs and then tested with triaxial test equipment. The test results show that WDCs have a degradation effect on shear strength (${\sigma}_1-{\sigma}_3)_f$, secant modulus of elasticity ($E_s$) and c′ while little influence on ${\varphi}^{\prime}$. Hence, conventional SSRFEM which reduces c′ and $tan{\varphi}^{\prime}$ in equal proportion cannot be adopted to compute the FOS of slope under conditions of WDCs. The SSRFEM should be modified. In detail, c′ is merely reduced among shear strength parameters, and elasticity modulus is reduced correspondingly. Besides, a new approach based on sudden substantial changes in the displacement of marked nodes is proposed to identify the slope failure in SSRFEM. Finally, the modified SSRFEM is applied to compute the FOS of a slope example.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.115-128
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• 2015

Plumbing surfaces of links were introduced to study the geometry of the complement of the links. A basket surface is one of these plumbing surfaces and it can be presented by two sequential presentations, the first sequence is the flat plumbing basket code found by Furihata, Hirasawa and Kobayashi and the second sequence presents the number of the full twists for each of annuli. The minimum number of plumbings to obtain a basket surface of a knot is defined to be the basket number of the given knot. In present article, we first find a classification theorem about the basket number of knots. We use these sequential presentations and the classification theorem to find the basket number of all prime knots whose crossing number is 7 or less except two knots $7_1$ and $7_5$.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.623-631
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• 2001

Let $\kappa$ be a real abelian field of conductor f and $\kappa$(sub)$\infty$ = ∪(sub)n$\geq$0$\kappa$(sub)n be its Z(sub)p-extension for an odd prime p such that płf$\phi$(f). he aim of this paper is ot compute the cohomology groups of circular units. For m>n$\geq$0, let G(sub)m,n be the Galois group Gal($\kappa$(sub)m/$\kappa$(sub)n) and C(sub)m be the group of circular units of $\kappa$(sub)m. Let l be the number of prime ideals of $\kappa$ above p. Then, for mm>n$\geq$0, we have (1) C(sub)m(sup)G(sub)m,n = C(sub)n, (2) H(sup)i(G(sub)m,n, C(sub)m) = (Z/p(sup)m-n Z)(sup)l-1 if i is even, (3) H(sup)i(G(sub)m,n, C(sub)m) = (Z/P(sup)m-n Z)(sup l) if i is odd (※Equations, See Full-text).

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.407-416
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• 2013

Let E be an elliptic curve over $\mathbb{Q}$ and $p$ be a prime of good supersingular reduction for E. Although the Iwasawa theory of E over the cyclotomic ${\mathbb{Z}}_p$-extension of $\mathbb{Q}$ is well known to be fundamentally different from the case of good ordinary reduction at p, we are able to combine the method of our earlier paper with the theory of Kobayashi [5] and Pollack [8], to give an explicit upper bound for the number of copies of ${\mathbb{Q}}_p/{\mathbb{Z}}_p$ occurring in the $p$-primary part of the Tate-Shafarevich group of E over $\mathbb{Q}$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1981-1988
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• 2013

We say a positive integer n satisfies the Lehmer property if ${\phi}(n)$ divides n - 1, where ${\phi}(n)$ is the Euler's totient function. Clearly, every prime satisfies the Lehmer property. No composite integer satisfying the Lehmer property is known. In this article, we show that every composite integer of the form $D_{p,n}=np^n+1$, for a prime p and a positive integer n, or of the form ${\alpha}2^{\beta}+1$ for ${\alpha}{\leq}{\beta}$ does not satisfy the Lehmer property.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.479-487
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• 2004

Let G be a finite group and N be a normal subgroup of G. We denote by ncc(N) the number of conjugacy classes of N in G and N is called n-decomposable, if ncc(N) = n. Set $K_{G}\;=\;\{ncc(N)$\mid$N{\lhd}G\}$. Let X be a non-empty subset of positive integers. A group G is called X-decomposable, if KG = X. In this paper we characterise the {1, 3, 4}-decomposable finite non-perfect groups. We prove that such a group is isomorphic to Small Group (36, 9), the $9^{th}$ group of order 36 in the small group library of GAP, a metabelian group of order $2^n{2{\frac{n-1}{2}}\;-\;1)$, in which n is odd positive integer and $2{\frac{n-1}{2}}\;-\;1$ is a Mersenne prime or a metabelian group of order $2^n(2{\frac{n}{3}}\;-\;1)$, where 3$\mid$n and $2\frac{n}{3}\;-\;1$ is a Mersenne prime. Moreover, we calculate the set $K_{G}$, for some finite group G.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.97-111
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• 2015

Let R be a commutative ring with $1{\neq}0$. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b, $c{\in}R$ and $0{\neq}abc{\in}I$, then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sqrt{I}$. A number of results concerning weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.

• Journal of Species Research
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• v.6 no.spc
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• pp.67-70
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• 2017

Three ciliate species, Australocirrus australis (Foissner, 1995) Kumar and Foissner, 2015, Rimaleptus longitrichus ($Vd^{\prime}a{\check{c}}n{\acute{y}}$ and Foissner, 2008) $Vd^{\prime}a{\check{c}}n{\acute{y}}$ and Foissner, 2012, and Frontonia subtropica Pan et al., 2013, that were previously unreported in Korea were collected from terrestrial and marine habitats in Korea. Using live observation and protargol impregnation, the three species were identified using a combination of the following characteristics: Australocirrus australis, the distance between the anterior pretransverse cirrus and the anteriormost transverse cirrus (0.6-2.1% of body length) and the arrangement of the transverse cirri (oblique row); Rimaleptus longitrichus, the arrange of contractile vacuoles and longitudinal ciliary rows anteriorly spaced; Frontonia subtropica, number of somatic kineties (approximately 115 rows) and vestibular kineties (5 rows).

• ETRI Journal
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• v.28 no.6
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• pp.745-760
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• 2006

In this paper, we particularly deal with no $F_p$-rational two-torsion elliptic curves, where $F_p$ is the prime field of the characteristic p. First we introduce a shift product-based polynomial transform. Then, we show that the parities of (#E - 1)/2 and (#E' - 1)/2 are reciprocal to each other, where #E and #E' are the orders of the two candidate curves obtained at the last step of complex multiplication (CM)-based algorithm. Based on this property, we propose a method to check the parity by using the shift product-based polynomial transform. For a 160 bits prime number as the characteristic, the proposed method carries out the parity check 25 or more times faster than the conventional checking method when 4 divides the characteristic minus 1. Finally, this paper shows that the proposed method can make CM-based algorithm that looks up a table of precomputed class polynomials more than 10 percent faster.