• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.799-814
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• 2009

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of some class invariants from the generalized Weber functions $\mathfrak{g}_0,\mathfrak{g}_1,\mathfrak{g}_2$ and $\mathfrak{g}_3$ over quadratic number fields with discriminant $D{\equiv}1$ (mod 12).

• Honam Mathematical Journal
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• v.40 no.1
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• pp.187-198
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• 2018

In this paper, we study the instantaneous geometric properties of motion of rigid bodies in the Lorentzian plane. For this purpose we define Lorentzian form of Bottemas instantaneous invariants. In these regards, we obtain the necessary and sufficient condition of a Lorentzian plane to be at Cardan position with respect to these invariants.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.521-530
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• 2000

We find the values of numerical invariants col(R) and row (R) for R=k[te, te+1, t(e-1)e-1] where k is a field and e$\geq$4. We also show that col(R) = crs (R) and row (R) = drs(R), but they are strictly less than the reduction number of R plus 1.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.623-639
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• 2021

We define a new algebraic structure called Legendrian racks or racks with Legendrian structure, motivated by the front-projection Reidemeister moves for Legendrian knots. We provide examples of Legendrian racks and use these algebraic structures to define invariants of Legendrian knots with explicit computational examples. We classify Legendrian structures on racks with 3 and 4 elements. We use Legendrian racks to distinguish certain Legendrian knots which are equivalent as smooth knots.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.247-257
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• 2024

We use the structure of skew braces to enhance the biquandle counting invariant for virtual knots and links for finite biquandles defined from skew braces. We introduce two new invariants: a single-variable polynomial using skew brace ideals and a two-variable polynomial using the skew brace group structures. We provide examples to show that the new invariants are not determined by the counting invariant and hence are proper enhancements.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1095-1103
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• 2016

B. Y. Chen introduced a series of curvature invariants, known as Chen invariants, and proved sharp estimates for these intrinsic invariants in terms of the main extrinsic invariant, the squared mean curvature, for submanifolds in Riemannian space forms. Special classes of submanifolds in Sasakian manifolds play an important role in contact geometry. F. Defever, I. Mihai and L. Verstraelen [8] established Chen first inequality for C-totally real submanifolds in Sasakian space forms. Also, the differential geometry of slant submanifolds has shown an increasing development since B. Y. Chen defined slant submanifolds in complex manifolds as a generalization of both holomorphic and totally real submanifolds. The slant submanifolds of an almost contact metric manifolds were defined and studied by A. Lotta, J. L. Cabrerizo et al. A Chen first inequality for slant submanifolds in Sasakian space forms was established by A. Carriazo [4]. In this article, we improve this Chen first inequality for special contact slant submanifolds in Sasakian space forms.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.463-469
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• 1996

We construct closed orientable four-manifolds which have nontrivial Seiberg-Witten invariants, but do not admit any symplectic structure.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.331-334
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• 2016

We give an explicit formula for the computation of Iwa-sawa ${\lambda}$-invariants and an example of the computation using our method.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.437-468
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• 2001

This paper is an exposition of the relationship between Witten's functional integral and Vassiliev invariants.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.479-501
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• 2023

We study the rationality and symmetry of the Gromov-Witten invariants of the projective line twisted by certain line bundles.