• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.185-190
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• 2022

The aim of this article is to define fuzzy maximal open cover and discuss its few properties. we also defined and study fuzzy m-compact space and discussed its properties. Also we obtain few more results on fuzzy minimal c-regular and fuzzy minimal c-normal spaces. We have proved that a fuzzy Haussdorff m-compact space is fuzzy minimal c-normal.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.559-562
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• 1998

We prove the $C^r$ Closing Lemma for chain recurrence in compact surfaces.

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.491-496
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• 2006

In the paper, we study an n-dimensional compact Riemannian manifold (M, g) with the property that the lengthes of the images $c({\mathbb{R}})$ in M of any geodesic curves $c({\mathbb{R}}){\mapsto}M$ are finite.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.629-633
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• 2010

In this paper we provide a sharp lower bound of the first Neumann eigenvalue of a compact hypersurface $\Sigma$ inside a convex set C in a Riemannian manifold under the assumption that ${\partial}{\Sigma}$ meets ${\partial}C$ orthogonally.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.683-687
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• 1998

Suppose X is a subspace of $(\sum_{n=1} ^{\infty} X_n)_{c_0}$, dim $X_n<{\infty}$, which has the metric compact approximation property. It is proved that if Y is a Banach space of cotype q for some $2{\leq}1<{\infty}$ then K(X,Y) is an M-ideal in L(X,Y).

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.1-8
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• 2018

In this paper, we study some topological structure of a compact domain in ${\mathbb{R}}^n$ in terms of the curvature conditions and develop a geometric inequality involving the volume and the integral of mean curvatures over the boundary of the compact domain.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.48 no.1
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• pp.27-33
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• 1999

Compact fluorescent lamps are very sensitive to the variation of ambient temperature. This paper investigates the temperature characteristics of a 15[W] compact fluorescent lamp, and compensates the variation of light output by frequency control of its electronic ballast. Circuit parameters for the inverter of the electronic ballast are obtained by analyzing the R-L-C equivalent circuit for the inverter and the lamp. The optimum ratio of the two capacitance($C_1$/$C_2$), which are connected with the lamp in series and in parallel, respectively, is determined which consideration of the temperature variation within a range of 10~35[$^{\circ}C$]. As a result a value of 10 for the ratio is obtained at an operating frequency of 57[kHz], and with this value the frequency control works well for temperature compensation. Its validity is verified by investigating light output stabilization characteristics resulting from frequency control of the lamp at various temperatures.

• Journal of Powder Materials
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• v.3 no.4
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• pp.266-270
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• 1996

The microstructure evolution during sintering of a compact being composed of three layers of (WC-15%Co)/Fe powder mixture with different Fe contents has been observed. The Fe contents in the respective (WC-15%Co)/Fe layers were varied by 20%. 50%, and 90% in sequence by volume from a top layer to a bot- tom layer. The sintering temperatures and times were varied from 110$0^{\circ}C$ to 125$0^{\circ}C$ and from 1 h to 4 h, The compact layer was not densified below 120$0^{\circ}C$ in 4 h. Appropriate sintering temperature and time conditions for making a multi-layered hard metal compact were determined as 125$0^{\circ}C$ and 3 h, respectively.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.243-256
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• 2023

We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin [54]. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism f of a compact smooth manifold M has the robustly pointwise inverse pseudoorbit tracing property, f is structurally stable. (ii) For a C1 generic diffeomorphism f of a compact smooth manifold M, if f has the pointwise inverse pseudo-orbit tracing property, f is structurally stable. (iii) If a diffeomorphism f has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set Λ, then Λ is hyperbolic for f. Finally, (iv) for C¹ generically, if a diffeomorphism f has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set Λ, then Λ is hyperbolic for f. In addition, we investigate cases of volume preserving diffeomorphisms.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.665-676
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• 2004

In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptotic stability.