• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.753-771
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• 2015

A complete invariant defined for (closed connected orientable) 3-manifolds is an invariant defined for the 3-manifolds such that any two 3-manifolds with the same invariant are homeomorphic. Further, if the 3-manifold itself can be reconstructed from the data of the complete invariant, then it is called a characteristic invariant defined for the 3-manifolds. In a previous work, a characteristic lattice point invariant defined for the 3-manifolds was constructed by using an embedding of the prime links into the set of lattice points. In this paper, a characteristic rational invariant defined for the 3-manifolds called the characteristic genus defined for the 3-manifolds is constructed by using an embedding of a set of lattice points called the PDelta set into the set of rational numbers. The characteristic genus defined for the 3-manifolds is also compared with the Heegaard genus, the bridge genus and the braid genus defined for the 3-manifolds. By using this characteristic rational invariant defined for the 3-manifolds, a smooth real function with the definition interval (-1, 1) called the characteristic genus function is constructed as a characteristic invariant defined for the 3-manifolds.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.917-930
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• 2009

We find all distinct representatives of isomorphism classes of genus-3 pointed trigonal curves and compute the number of isomorphism classes of a special class of genus-3 pointed trigonal curves including that of Picard curves over a finite field F of characteristic 2.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.145-155
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• 2015

In this paper, we study the bounds of the coefficients of the characteristic polynomial of the Frobenius endomorphism of the Jacobian of dimension three over a finite field. We provide explicitly computable bounds for the coefficients of the characteristic polynomial. In addition, we present the counting points algorithm for computing a group of the Jacobian of genus 3 hyperelliptic curves over a finite field with large characteristic. Based on these bounds, we found an efficient search space that was used in the counting points algorithm on genus 3 curves. The algorithm was explained and verified through simple examples.

• Proceedings of the Korean Information Science Society Conference
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• 1999.10a
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• pp.643-645
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• 1999

타원곡선에 이어 초타원곡선을 공개키 암호시스템에 적용하는 방법이 Koblitz에 의해 제안되었다. 이를 위해 우선 곡선을 선택해야 하는데, 선택될 곡선은 현재까지 알려진 공격에 대해 안전하여야 한다. 본 논문에서는 초타원 암호시스템(hyperelliptic cryptosystem을 구성하기 위해 genus 2인 초타원곡선 v2+v=u5+u3+u와 특성계수(characteristic) 3인 기본 체(field)를 선택하고, 이로써 만들어질 암호시스템이 안전함을 보인다.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.1-12
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• 2003

L. H. Encinas, A. J. Menezes, and J. M. Masque in [2] proposed a classification of isomorphism classes of hyperelliptic curve of genus 2 over finite fields with characteristic different from 2 and 5. Y. Choie and D. Yun in [1] obtained for the number of isomorphic classes of hyperelliptic curves of genus 2 over $F_q$ using direct counting method. In this paper we will classify the isomorphism classes of hyperelliptic curves of genus 2 over $F_{2^n}$ for odd n, represented by an equation of the form $y^2+a_5y=x^5+a_8x+a_{10}(a_5{\neq}0)$.

• The Bulletin of The Korean Astronomical Society
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• v.38 no.2
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• pp.56.2-56.2
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• 2013

We study the three-dimensional genus topology of large-scale structure using the CMASS Data Release 11 sample of the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS). The CMASS sample yields a genus curve that is characteristic of one produced by Gaussian random-phase initial conditions. The data thus supports the standard model of inflation where random quantum fluctuations in the early universe produced Gaussian random-phase initial conditions. Modest deviations in the observed genus from random phase are as expected from the nonlinear evolution of structure. We construct mock SDSS CMASS surveys along the past light cone from the Horizon Run 3 (HR3) N-body simulations, where gravitationally bound dark matter subhalos are identified as the sites of galaxy formation. We study the genus topology of the HR3 mock surveys with the same geometry and sampling density as the observational sample, and the observed genus topology to be consistent with LCDM as simulated by the HR3 mock samples.

• Animal Systematics, Evolution and Diversity
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• v.35 no.3
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• pp.114-122
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• 2019

A new species belonging to the genus Cyclopinopsis Smirnov, 1935 (Cyclopinidae) is described from Korea, as the third species of the genus. Specimens were collected by washing the subtidal sediments off Dokdo Island in the East Sea and the intertidal sands at Baegripo beach, Taean Peninsula on the Yellow Sea coast. Cyclopinopsis deformata n. sp. is characteristic and distinguished from its two congeneric species currently recognized, C. curticauda Smirnov, 1935 and C. brasiliensis Herbst, 1955 in having a deformed seta at the outer distal corner of the third exopodal segment of leg 4. The seta is supposed to be deformed from an outer spine on the third exopodal segment of leg 4, which has been known as completely lost in the genus until now. A character comparison table of the three species and a key to species of the genus Cyclopinopsis are provided herein.

• Animal cells and systems
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• v.5 no.1
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• pp.11-15
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• 2001

The first zoeal stage of Enosteoides ornata (Stimpson, 1858) is described and illustrated in detail. Its morphological characteristics are compared with those of other known species of the family Porcellanidae. In the family Porcellanidae its diagnostic characteristics are the exopod of an antenna armed with a seta and five spinules and the coxa of the first maxilliped having two setae. The former characteristic can be seen in most of the genus Petrolisthes zoeas, while the latter usually in the genus Pachycheles zoea. The Enosteoides ornata seems to be p1aced intermediately between the genus Pachycheles and the genus Petrolisthes based on the zoeal morphology.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.413-424
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• 2003

L. H Encinas, A. J. Menezes and J. M. Masque in [3] proposed a classification of isomorphism classes of hyperelliptic curve of genus 2 over finite fields with characteristic different from 2 and 5. Y. Choie and D. Yun in [2] obtained the number of isomorphic classes of hyperelliptic curves of genus 2 over $F_{2-}$ using direct counting method. We have obtained isomorphism classes of hyperelliptic curves of genus 2 over $F_{2n}$ for odd n, represented by an equation of the form $y^2$ + $a_{5}$ y = $x^{5}$ + $a_{8}$ x + $a_{10}$ ( $a_{5}$ $\neq$0) [1]. In this paper we characterize hyperelliptic curves of genus 2 over $F_{2n}$ for even n, represented by an equation of the form $y^2$ + $a_{5}$ y = $x^{5}$ + $a_{5}$ x + $a_{10}$ ( $a_{5}$ $\neq$0).>0).

• Animal cells and systems
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• v.5 no.1
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• pp.1-9
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• 2001

Terebelliphilus simplex n. gen., n. sp. and Myxomolgus invulgus n. sp. are described from the tubicolous polychaetes found in the intertidal shores in the Yellow Sea. The new genus Terebelliphilus belongs to the family Sabelliphilidae but is characteristic in bearing the reduced segmentations In legs 1-4, an unusual sexual dimorphism in antennule, and the ventral location of genital areas. Myxomolgus invulgus is readily distinguishable from its congeners by the morphological features of rostrum, antennule, mandible, maxilla, leg 4 and female leg 5.