• Kyungpook Mathematical Journal
• /
• v.52 no.3
• /
• pp.271-278
• /
• 2012

We study some functions defined on the unit tangent space, which are formed with the second fundamental form of submanifolds of a real space form. These give an exact expression of isotropy of submanifolds in a real space form and a relationship between intrinsic invariants and extrinsic ones.

• East Asian mathematical journal
• /
• v.19 no.1
• /
• pp.49-61
• /
• 2003

We study the asymptotic boundary behavior of the Bergman kernel function on the diagonal, the Bergman metric and the holomorphic sectional curvatures of the Bergman metric in bounded strongly pseudoconvex domains.

• Journal of the Chungcheong Mathematical Society
• /
• v.1 no.1
• /
• pp.85-90
• /
• 1988

We develope a signature invariant for odd higher dimensional links. This signature has an advantage that it is defined as a G-signature for a non-abelian group G so that it can distinguish two links whose different were not detected by other invariants defined on commutative set-ups.

• Honam Mathematical Journal
• /
• v.1 no.1
• /
• pp.77-81
• /
• 1979

Almost mathematicians wish to study on the classification of the objects within isomorphism and determination of effective and computable invariants to distinguish the isomorphism classes. In topology, the concepts of homotopy and homeomorphism are such examples. In this lecture I shall speak of with respect to (i) Thom's cobordism group (ii) Cobordism category (iii) finally, the semigroup in cobordism category is isomorphic to the Thom's cobordism group.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1097-1107
• /
• 2021

In this paper, we focus on the Hopf invariant and give an alternative proof for the unboundedness of stabilization heights of fiber surfaces, which was firstly proved by Baader and Misev.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.307-313
• /
• 2023

In this paper, we study the n-dimensional Möbius transformation. We obtain several conjugacy invariants and give a conjugacy classification for n-dimensional Möbius transformation.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.515-528
• /
• 2023

In this paper, we formulate the set of all saturated numerical semigroups with prime multiplicity. We characterize the catenary degrees of elements of the semigroups we obtained which are important invariants in factorization theory. We also give the proper characterizations of the semigroups under consideration.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.6
• /
• pp.1539-1553
• /
• 2023

We show the asymptotics of the volume density function in the class of central harmonic manifolds can be specified arbitrarily and do not determine the geometry.

• Honam Mathematical Journal
• /
• v.46 no.2
• /
• pp.181-197
• /
• 2024

In this study, we investigate Smarandache curves with Frenet-type frame in Myller configuration for Euclidean 3-space E₃. Also, we introduce some characterizations and invariants of them. Then, we construct a numerical example with respect to these special Smarandache curves in order to understand the obtained materials.

• Geomechanics and Engineering
• /
• v.22 no.1
• /
• pp.11-23
• /
• 2020

In this study, a new analytical-numerical procedure is developed to give the stresses and strains around a circular tunnel in rock masses exhibiting different stress-strain behavior. The calculation starts from the tunnel wall and continues toward the unknown elastic-plastic boundary by a finite difference method in the annular discretized plastic zone. From the known stresses in the tunnel boundary, the strains are calculated using the elastic-plastic stiffness matrix in which three dimensional Hoek-Brown failure criterion (Jiang and Zhao 2015) and Mohr-Coulomb potential function with proper dilation angle (i.e., non-associated flow rule) are employed in terms of stress invariants. The illustrative examples give ground response curve and show correctness of the proposed approach. Finally, from the results of a great number of analyses, a simple relationship is presented to find out the closure of circular tunnel in terms of rock mass strength and tunnel depth. It can be valuable for the preliminary decision of tunnel support and for prediction of tunnel problems.