• 충청수학회지
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• 제25권2호
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• pp.283-289
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• 2012

In this paper, we define the Ono invariants of imaginary quadratic function fields and obtained several results concerning the relations between the Ono invariants and the class numbers.

• 충청수학회지
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• 제34권4호
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• pp.335-343
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• 2021

In this article, we investigate the finiteness of Auslander Index when a ring A has not necessarily a canonical module, or a Gorenstein module. We also study the relations between column invariants and row invariants.

• 대한수학교육학회지:수학교육학연구
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• 제25권4호
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• pp.473-498
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• 2015

본 연구의 목적은 고대 그리스 시대부터 수학자들이 복잡한 기구를 손수 제작하는 수고를 감내하면서 탐구하였던 대수곡선을 기구가 아닌 공학을 사용해 재현하고 생성하는 활동을 수행할 때, 수학영재들은 곡선의 자취를 어떻게 작도하며 불변량(Invariants)은 곡선의 작도와 생성에 어떤 영향을 주는지를 구체적으로 살펴보는데 있다. 특히, 역동적 기하 환경에서 불변량(Invariants)의 역할과 의미에 관한 실증적인 자료를 확보해보는 연구와 수학영재들이 새로운 곡선을 창출하는 과정에서 나타나는 불변량의 활용 유형을 세분해보는 연구를 시도해 봄으로써, 불변량에 대한 교육적 활용 방안을 제시하고 그 활용 범위의 확대 가능성을 확인하고자 하였다.

• 대한수학회지
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• 제34권4호
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• pp.771-790
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• 1997

By using the method of equivalence of E. Cartan we calculate the local scalar invariants for Riemannian 2-maniolds. We define also a notion of local invariants for submanifolds in $R^{n + d}, n \geq 2, d \geq 1$, in terms of the symmetry of the local isometric embedding equations of Riemannian n-manifolds into $R^{n + d}$. We show that the local invariants obtained by the Cartan's method are the intrinsic expressions of the local invariants in our sense in the casees of surfaces in $R^3$.

• 대한수학회지
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• 제38권5호
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• pp.1061-1068
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• 2001

We write down explicity a recursive formula of one-pointed gravitational Gromov-Witten invariants and reduce the computation of them to a combinatoric problem which is not solved yet. The one-pointed invariants were played important role in Givental’s program in mirror symmetry. In section 3, we describe the combinatoric problem which can be read independently.

• 대한수학회지
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• 제39권1호
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• pp.103-117
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• 2002

We consider the situation that ${\mathbb{Z}_p}\;=\;{\mathbb{Z}/p\mathbb{Z}}$ acts freely on a closed oriented 4-manifold X with ${b_2}^{+}\;{\geq}\;2$. In this situation, we study the relation between the Seiberg-Witten invariants of X and those of the quotient manifold $X/{\mathbb{Z}}_p$. We prove that the invariants of X are equal to those of $X/{\mathbb{Z}}_p$ modulo p.

• Korean Journal of Mathematics
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• 제11권1호
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• pp.45-49
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• 2003

We introduce the $k_0$-proximity space as a generalization of the Efremovi$\check{c}$-proximity space. We try to show that $k_0$-proximity structure lies between topological structures and uniform structure in the sense that all topological invariants are $k_0$-proximity invariants and all $k_0$-proximity invariants are uniform invariants.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.535-539
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• 2006

The ring of invariants of two 2 by 2 matrices C(2, 2) is a polynomial ring with 5 variables [1]. In this paper we find the system of parameters of C(3, 2) by Groebner bases.

• 대한수학회지
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• 제37권2호
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• pp.177-191
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• 2000

All scalar CR invariants of weight $\leq$ 6 are explicitly given for 3-dimensional strictly pseudoconvex CR structures, as an application of Fefferman's ambient metric construction and its generalization by he author.

• East Asian mathematical journal
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• 제35권1호
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• pp.31-40
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• 2019

We introduce a family of polynomial invariants by using intersection index defined from a Gauss diagram of a long virtual knot, and we give some properties for long virtual knots. We extend these polynomials so that we give two-variable polynomial invariants and some example.