• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1519-1525
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• 2010

In this paper, we define property ($D_k$) and get the following strict implications. $$(UC){\Rightarrow}(D_2){\Rightarrow}(D_3){\Rightarrow}{\cdots}{\Rightarrow}(D_{\infty}){\Rightarrow}(BS)$$.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.865-868
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• 1997

Let R be a ring with a unity and let M be a unitary left R-module. In this paper, we establish [5, Proposition 2.8] by showing the proof of it. Moreover, from the above result, we obtain some properties of direct projective modules which have the summand sum property.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.91-101
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• 2005

In this paper, we give the notion of the D-shadowing property, D-inverse shadowing property for dynamical systems. and investigate the density of D-shadowing dynamical systems and the D-inverse shadowing dynamical systems. Moreover we study some relationships between the D-shadowing property and other dynamical properties such as expansivity and topological stability.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.161-168
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• 2006

In this paper, we study property (${\beta}$) and B-convexity in reflexive Banach spaces. It is shown that k-uniform convexity implies B-convexity and property (${\beta}$). We also show that there is a Banach space with property (${\beta}$) which cannot be equivalently renormed to be B-convex.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.11a
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• pp.252-255
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• 1997

In this paper, we will propose the methodology of data analysis using the fuzzy property set model. In real world, the data can be represented with the object. $\theta$. and the property, $\pi$, and its has-property relation, P. Then, the conceptual space can be defined with the chosen properties. Each object has a unique location in the conceptual space. In Fuzzy mode, the fuzzy property, and fuzzy conceptual space can be redefined. To analyze data using the fuzzy property set model, the rough set need to be defined in the fuzzy conceptual space.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.785-794
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• 2022

In this paper we show that if A ∈ L(X) and R ∈ L(X) is a quasinilpotent operator commuting with A then X_A(F) = X_A+R(F) for all subset F ⊆ ℂ and 𝜎_loc(A) = 𝜎_loc(A + R). Moreover, we show that A and A + R share many common local spectral properties such as SVEP, property (C), property (𝛿), property (𝛽) and decomposability. Finally, we show that quasisimility preserves local spectrum.

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.71-74
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• 1991

In this paper, we study the Bourgain property for real-valued functions, and give conditions for a family of real-valued functions to have the Bourgain property.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.35-47
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• 1992

In this paper we give a necessary condition for a homeomorphism restricted to its nonwandering set to have the shadowing property. Also, we consider a homeomorphism which cannot have the shadowing property.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.5
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• pp.103-111
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• 2008

This study proposes a technique to estimate the material property of a paper by using an experimental methods and commercial CAE software. Under gravitation, if one side of the paper is attached to the ground, the opposite side of paper is largely deformed, and vibrates freely. Since the paper has an orthotropic characteristic due to its treatment, the deformations in two orthogonal directions of the dry paper are different. An experimental method to measure the static deformation of the paper introduces this phenomenon. And dynamic behavior, frequency of free vibration is measured. And then. virtual prototypes that can represent the static and dynamic behavior are modeled by using the commercial CAE software $RecurDyn^{MT}$/MTT3D, which has been widely used by the printer makers. While comparing the deformation and frequency from the experiment and simulation, a design optimization technique in the commercial CAE software of R-INOPL, $RecurDyn^{TM}$/AutoDesign is used to estimate the material property such as Young's modulus, shear modulus and density of the paper.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.53-63
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• 2000

The inverse shadowing property of a dynamical system is an "inverse" form of the shadowing property of the system. Recently, Kloeden and Ombach proved that if an expansive system on a compact manifold has the shadowing property then it has the inverse shadowing property. In this paper, we study topological stability of the inverse shadowing dynamical systems. In particular, we show that if an expansive system on a compact manifold has the inverse shadowing property then it is topologically stable, and so it has the shadowing property.