• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.61-71
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• 2001

We introduce a new class of ${\sigma}$-coherent frames and show that HA is a ${\sigma}$-coherent frame if A is a ${\sigma}$-frame. Based on this, it is shown that a frame is ${\sigma}$-coherent iff it is isomorphic to the frame of ${\sigma}$-ideals of a ${\sigma}$-frame. Finally we show that ${\sigma}$-COhFrm and ${\sigma}$Frm are equivalent.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.295-308
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• 2002

Using the Countably way below relation, we show that the category $\sigma$-CFrm of $\sigma$-coherent frames and $\sigma$-coherent homomorphisms is coreflective n the category Frm of frames and frame homomorphisms. Introducting the concept of stably countably approximating frames which are exactly retracts of $\sigma$-coherent frames, it is shown that the category SCAFrm of stably countably approximating frames and $\sigma$-proper frame homomorphisms is coreflective in Frm. Finally we introduce strongly Lindelof frames and show that they are precisely lax retracts of $\sigma$-coherent frames.

• Journal for History of Mathematics
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• v.16 no.1
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• pp.63-72
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• 2003

This paper is a sequel to [11]. We introduce $\sigma$-coherent frames, stably countably approximating frames and strongly Lindelof frames, and show that a stably countably approximating frame is a strongly Lindelof frame. We also show that a complete chain in a Lindelof frame if and only if it is a strongly Lindelof frame by using the concept of strong convergence of filters. Finally, using the concepts of super compact frames and filter compact frames, we introduce an example of a strongly Lindelof frame which is not a stably countably approximating frame.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.87-100
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• 2007

We introduce a concept of countably strong inclusions ${\triangleleft}$ and that of ${\triangleleft}-{\sigma}$-ideals and prove that the subframe $S({\triangleleft})$ of the frame ${\sigma}IdL$ of ${\sigma}$-ideals is a Lindel$\ddot{o}$fication of a frame L. We also deal with conditions for which the converse holds. We show that any countably approximating regular $D({\aleph}_1)$ frame has the smallest countably strong inclusion and any frame which has the smallest $D({\aleph}_1)$ Lindel$\ddot{o}$fication is countably approximating regular $D({\aleph}_1)$.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.195-206
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• 2008

The purpose of this note is to compare the rings of continuous functions, integer-valued or real-valued, in pointfree topology with those in classical topology. To this end, it first characterizes the Boolean frames (= complete Boolean algebras) whose function rings are isomorphic to a classical one and then employs this to exhibit a large class of frames for which the functions rings are not of this kind. An interesting feature of the considerations involved here is the use made of nonmeasurable cardinals. In addition, the integer-valued function rings for Boolean frames are described in terms of internal lattice-ordered ring properties.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.571-583
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• 2012

Let $G$ be a metrizable, ${\sigma}$-compact locally compact abelian group with a compact open subgroup. In this paper we define the Gramian and the dual Gramian operators for shift invariant subspaces of $L^2(G)$ and we use them to characterize shift generated dual frames for shift in- variant spaces, which forms a frame for a subspace of $L^2(G)$. We present necessary and sufficient conditions for which standard dual is a unique SG-dual frame of type I and type II.

• Journal of Korean Society of Steel Construction
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• v.15 no.4 s.65
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• pp.379-388
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• 2003

The response of single story buildings and other case studies were investigated to observe trends and develop a better understanding of the impact of some design parameters on the seismic response of Concentrically Braced Frames (CBF). While many parameters are known to influence the behavior of braced frames, the focus of this study was mostly on quantifying energy dissipation in compression and its effectiveness on seismic performance. Based on dynamic analyses of single story braced frame and case studies, a bracing member designed with bigger R and larger KL/r was found to result in lower normalized cumulative energy ratio in both cases.

• Journal of the Institute of Convergence Signal Processing
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• v.11 no.3
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• pp.189-196
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• 2010

In this paper, we proposed the adaptive local sigma filter reducing noises generated by an image sensor. The small noises generated by the image sensor are amplified by increased an analog gain and an exposure time of the image sensor together with information. And the goal of this work was the system design that is reduce the these amplified noises. Edge data are extracted by Flatness Index Map algorithm. We made the threshold adaptively changeable by the luminance average in this algorithm that extracts the edge data not in high luminance, but just low luminance. The Local Sigma Filter performed only about the edge pixel that were extracted by Flatness Index Map algorithm. To verify the performance of the designed filter, we made the Window test program. The hardware was designed with HDL language. We verified the hardware performance of Local Sigma Filter system using FPGA Demonstration board and HD image sensor, $1280{\times}720$ image size and 30 frames per second.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.195-200
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• 2003

An expert system for estimation of fatigue properties from simple tensile data of material is developed, considering nearly all important estimation methods proposed so far, i.e., 7 estimation methods. The expert system is developed using an expert system shell, UNIK, and the knowledge base is constructed with production rules and frames. Forward chaining is employed as a reasoning method. The expert system has three major functions including the function to update the knowledge base. The performance of the expert system is tested using the 54 ${\sigma}-N$ curves consisting of 381 ${\sigma}-N$ data points obtained for 22 materials. It is found that the expert system developed has excellent performance especially for steel materials, and reasonably good for titanium alloys.

• Bulletin of the Society of Naval Architects of Korea
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• v.6 no.2
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• pp.1-4
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• 1969

The added mass coefficients $K_2$ of two-dimensional cylinders of straightline-element sections for vertical viblation are presented as functions of parameters such as the beam-draf ratio B/H and the sectional area coefficient $\sigma$. The results are compared with those of Lewis forms and curvilinear-elements sections with single chine.