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REMARKS ON CENTERED-LINDELÖF SPACES
Song, Yan-Kui Korean Mathematical Society 2006 대한수학회논문집 Vol.21 No.3
In this paper, we construct an example of a normal centered-Lindelof space X such that $St-l(X){\geq}{\omega}1\;under\;2^{\aleph_0}=2^{\aleph_1}$
REMARKS ON ABSOLUTELY STAR-LINDELOF SPACES
Song, Yan-Kui Korean Mathematical Society 2004 대한수학회보 Vol.41 No.2
Vaughan proved that if X is countably compact, then the Alexandroff duplicate A(X) is acc. In this note, we give an example to show that the result can not be generalized to star-Lindelof spaces. Moreover, we give a positive result.
Remarks on absolutely star-Lindelof spaces
Yan-Kui Song 대한수학회 2004 대한수학회보 Vol.41 No.2
Vaughan proved that if X is countably compact, thenthe Alexandroff duplicate A(X) is acc.In this note, we give an example to show that the result can notbe generalized to star-Lindel{"o}f spaces. Moreover, we give apositive result.
REMARKS ON CS-STARCOMPACT SPACES
Song, Yan-Kui Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.1
A space X is cs-starcompact if for every open cover $\mathcal{U}$ of X, there exists a convergent sequence S of X such that St(S, $\mathcal{U}$) = X, where $St(S,\mathcal{U})\;=\; \cup\{U{\in}\mathcal{U}:U{\cap}S{\neq}\phi\}$. In this paper, we prove the following statements: (1) There exists a Tychonoff cs-starcompact space having a regular-closed subset which is not cs-starcompact; (2) There exists a Hausdorff cs-starcompact space with arbitrary large extent; (3) Every Hausdorff centered-Lindel$\ddot{o}$f space can be embedded in a Hausdorff cs-starcompact space as a closed subspace.
REMARKS ON K-STARCOMPACT SPACES
Song, Yan-Kui Korean Mathematical Society 2007 대한수학회논문집 Vol.22 No.4
In this note, we construct an example of a Hausdorff K-starcompact (hence, $1\frac{1}{2}$-star-compact) space X having a regular closed $G_{\delta}-subset$ which is not $1\frac{1}{2}$-starcompact (hence, not K-starcompact).
SOME REMARKS ON CENTERED-LINDELÖF SPACES
Song, Yan-Kui Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.2
In this paper, we prove the following two statements: (1) There exists a Hausdorff locally $Lindel{\ddot{o}}f$ centered-$Lindel{\ddot{o}}f$ space that is not star-$Lindel{\ddot{o}}f$. (2) There exists a $T_1$ locally compact centered-$Lindel{\ddot{o}}f$ space that is not star-$Lindel{\ddot{o}}f$. The two statements give a partial answer to Bonanzinga and Matveev [2, Question 1].
Yu Xia,Jun-Yang Li,Yan-Kui Song,Jia-Xu Wang,Yan-Feng Han,Ke Xiao 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.3
Due to the complexity of modeling and the strong transmission coupling, the rich background of rigid actuator control has not been transferred to variable stiffness actuator (VSA). Therefore, most model-based control techniques developed for VSA require feedback linearization first. Alternatively, VSA can use non-model-based control techniques such as PD control, but it does not show strong robustness under disturbances. This paper is concerned with designing a novel adaptive neural network backstepping control scheme without using feedback linearization for a special VSA with saturation inputs, output constraints, and disturbances. Firstly, for ensuring the VSA with lower tracking error and higher security, the prescribed performance-tangent barrier Lyapunov function (PP-TBLF) is introduced to handle the prescribed output performance constraints. Subsequently, the Chebyshev neural network and the Nussbaum-type function are exploited to approximate the unknown nonlinearities and unknown gains. Meanwhile, the inverse hyperbolic sine function tracking differentiator is utilized to solve the “explosion of complexity” caused by the differentiation of virtual inputs and also approximate the complex partial derivatives caused by the auxiliary control signals. Finally, the stability of the whole scheme is proved by the Lyapunov criterion. The simulation results illustrate the raised control scheme’s feasibility and show a better closed-loop behavior relative to that obtained using a classic PD controller.