• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2007.04a
• /
• pp.259-264
• /
• 2007

In this paper, to analyze the initial valued non-homogeneous elastic half space by the scaled boundary analysis, the infinite element approach was introduced. The free surface of the initial valued non-homogeneous elastic half space was mode1ed as a circumferential direction of boundary scaled boundary coordinate. The infinite element was used to represent the infinite length of the free surface. The initial value of material property(elastic modulus) was considered by the combination of the position of the sealing center and the power function of the radial direction. By use of the mapping type infinite element, the consistent e1ements formulation could be available. The performance and the feasibility of proposed approach are examined by two numerical examples.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.459-468
• /
• 1997

The purpose of this paper is to give some characterizations of homogeneous real hypersurfaces of type A in complex space forms $M_n(c), c \neq 0$, in terms of Lie derivatives.

• Communications of the Korean Mathematical Society
• /
• v.17 no.1
• /
• pp.31-36
• /
• 2002

In this paper we first introduce a space of homogeneous type X, and we consider a kind of generalized upper half-space X $\times$ (0, $\infty$). We are mainly concerned with some inequalities in terms of Carleson measures or in terms of certain maximal operators with respect to general approach regions in X $\times$ (0, $\infty$). The main tool of the proof is the Whitney decomposition.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.3
• /
• pp.453-461
• /
• 2010

We first introduce a space of homogeneous type X, and develop the theory of the tent spaces on the generalized upper half-space $X{\times}(0,{\infty})$. The goal of this paper is to study that every element of the tent spaces $T_{\Omega}^{p}$($X{\times}(0,{\infty})$, $0, can be decomposed into elementary particles which are called "atoms."

• East Asian mathematical journal
• /
• v.23 no.1
• /
• pp.37-43
• /
• 2007

We study a maximal operator defined on spaces of homogeneous type, and we prove that this operator is of weak type (1,1). As a consequence we show that the maximal operator belongs to the Muckenhoupt's class $A_1$.

• East Asian mathematical journal
• /
• v.21 no.1
• /
• pp.41-48
• /
• 2005

In this paper we first introduce a space of homogeneous type X, and then consider a kind of generalized upper half-space $X{\times}(0,\;\infty)$. We are mainly considered with inequalities for the $L^p$ norms of area functions associated with approach regions in $X{\times}(0,\;\infty)$.

• East Asian mathematical journal
• /
• v.35 no.3
• /
• pp.319-329
• /
• 2019

In this paper, we provide sufficient conditions of a pair of weights (u, v) and a function b so that the dyadic paraproduct is bounded from $L^2_u(X)$ into $L^2_v(X)$, where X is a space of homegeneous type. In order to prove the main result we use the honest dyadic system introduced in [10].

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.1
• /
• pp.35-42
• /
• 2012

In this paper we first introduce a Carleson inequality and study the generalized form of Carleson inequality in the context of spaces of homogeneous type. The previous inequality is known to play important roles in harmonic analysis.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.6
• /
• pp.1607-1620
• /
• 2023

In this paper, we mainly study the problem of the existence of homogeneous geodesics in sub-Finsler manifolds. Firstly, we obtain a characterization of a homogeneous curve to be a geodesic. Then we show that every compact connected homogeneous sub-Finsler manifold and Carnot group admits at least one homogeneous geodesic through each point. Finally, we study a special class of ℓ^p-type bi-invariant metrics on compact semi-simple Lie groups. We show that every homogeneous curve in such a metric space is a geodesic. Moreover, we prove that the Alexandrov curvature of the metric space is neither non-positive nor non-negative.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.21 no.2
• /
• pp.199-208
• /
• 2008

In this paper, to analyze the initial valued non-homogeneous elastic half space by the scaled boundary analysis, the infinite element approach was introduced. The free surface of the initial valued non-homogeneous elastic half space was modeled as a circumferential direction of boundary scaled boundary coordinate. The infinite element was used to represent the infinite length of the free surface. The initial value of material property(elastic modulus) was considered by the combination of the position of the scaling center and the power function of the radial direction. By use of the mapping type infinite element, the consistent elements formulation could be available. The performance and the feasibility of proposed approach are examined by two numerical examples.