• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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• pp.131-138
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• 2021

In this paper, we define a concept of weak T-fibration which is a generalization of weak H-fibration, and study some properties of weak T-fibration and relations between the weak T-fibration and the Postnikov system for a fibration.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.44 no.3
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• pp.9-13
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• 2007

This Paper deals with the synthesis of absolutely stabilizing fixed order controllers for Lure-Postnikov systems. Lure-Postnikov systems are frequently encountered in mechanical engineering applications. Analytical tools for synthesizing stabilizing fixed structure controllers, such as the PID controllers examining the absolute stability of Lure-Postnikov systems, have recently been studied in the literature. However, tools for synthesizing controllers of arbitrary order have not been studied yet. We propose a systematic method for synthesizing absolutely stabilizing controllers of arbitrary order for the Lure-Postnikov systems. Our approach is based on recent results in the literature on approximation of the set of stabilizing controller parameters that render a family of real and complex polynomials Hurwitz. We provide an example of a robotic system to illustrate the procedure developed.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.831-841
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• 2009

For a map f : A $\rightarrow$ X, we define and study a concept of $G^f$-space for a map, which is a generalized one of a G-space. Any G-space is a $G^f$-space, but the converse does not hold. In fact, $S^2$ is a $G^{\eta}$-space, but not G-space. We show that X is a $G^f$-space if and only if $G_n$(A, f,X) = $\pi_n(X)$ for all n. It is clear that any $H^f$-space is a $G^f$-space and any $G^f$-space is a $W^f$-space. We can also obtain some results about $G^f$-spaces in Postnikov systems for spaces, which are generalization of Haslam's results about G-spaces.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.603-614
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• 2015

For a map $p:X{\rightarrow}A$, we define and study a concept of $G^{\prime}_p$-space for a map, which is a generalized one of a G'-space. Any G'-space is a $G^{\prime}_p$-space, but the converse does not hold. In fact, $CP^2$ is a $G^{\prime}_{\delta}$-space, but not a G'-space. It is shown that X is a $G^{\prime}_p$-space if and only if $G^n(X,p,A)=H^n(X)$ for all n. We also obtain some results about $G^{\prime}_p$-spaces and homology decompositions for spaces. As a corollary, we can obtain a dual result of Haslam's result about G-spaces and Postnikov systems.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.177-186
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• 2016

For a map $f:A{\rightarrow}X$, there are concepts of $H^f$-spaces, $T^f$-spaces, which are generalized ones of H-spaces [17,18]. In general, Any H-space is an $H^f$-space, any $H^f$-space is a $T^f$-space. For a principal fibration $E_k{\rightarrow}X$ induced by $k:X{\rightarrow}X^{\prime}$ from ${\epsilon}:PX^{\prime}{\rightarrow}X^{\prime}$, we obtain some sufficient conditions to having liftings $H^{\bar{f}}$-structures and $T^{\bar{f}}$-structures on $E_k$ of $H^f$-structures and $T^f$-structures on X respectively. We can also obtain some results about $H^f$-spaces and $T^f$-spaces in Postnikov systems for spaces, which are generalizations of Kahn's result about H-spaces.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.4
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• pp.297-305
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• 2023

In this paper, we study some properties about C^f_k-structures and obtain a sufficient condition to be lifting C^f_k-structure, and using the above result, we can obtain a Stasheff's result about to be lifting H-structure as a corollary.