• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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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.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.473-498
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• 2015

The purpose of this study is to examine thinking process of the mathematically gifted students and how invariants affect the construction and discovery of curve when carry out activities that produce and reproduce the algebraic curves, mathematician explored from the ancient Greek era enduring the trouble of making handcrafted complex apparatus, not using apparatus but dynamic geometry software. Specially by trying research that collect empirical data on the role and meaning of invariants in a dynamic geometry environment and research that subdivide the process of utilizing invariants that appears during the mathematically gifted students creating a new curve, this study presents the educational application method of invariants and check the possibility of enlarging the scope of its appliance.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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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 $R^3$.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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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.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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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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• v.11 no.1
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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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• v.22 no.1_2
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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.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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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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• v.35 no.1
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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.