• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.529-540
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• 2024

In this paper, using the Fourier transform, inverse Fourier transform and Littlewood-Paley decomposition technique, we prove the boundedness of bilinear pseudodifferential operators with symbols in the bilinear Hörmander class $BS^{m}_{1,1}$ in variable Triebel-Lizorkin spaces and variable Besov spaces.

• Kyungpook Mathematical Journal
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• v.11 no.1
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• pp.101-115
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• 1971

• Journal of the Korean Mathematical Society
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• v.15 no.2
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• pp.149-153
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• 1979

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.183-190
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• 1996

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.297-308
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• 2002

• Kyungpook Mathematical Journal
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• v.25 no.2
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• pp.113-117
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• 1985

• Kyungpook Mathematical Journal
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• v.23 no.1
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• pp.43-47
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• 1983

• East Asian mathematical journal
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• v.11 no.2
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• pp.223-228
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• 1995

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.2
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• pp.96-101
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• 2007

Neural networks are known as kinds of intelligent strategies since they have learning capability. There are various their applications from intelligent control fields; however, their applications have limits from the point that the stability of the intelligent control systems is not usually guaranteed. In this paper we propose an adaptive tracking control for robot manipulators using the radial basis function network (RBFN) that is e. kind of neural networks. Adaptation laws for parameters of the RBFN are developed based on the Lyapunov stability theory to guarantee the stability of the overall control scheme. Filtered tracking errors between actual outputs and desired outputs are discussed in the sense of the uniformly ultimately boundedness(UUB). Additionally, it is also shown that parameters of the RBFN are bounded. Experimental results for a SCARA-type robot manipulator show that the proposed adaptive tracking controller is adaptable to the environment changes and is more robust than the conventional PID controller and the neuro-controller based on the multilayer perceptron.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1383-1399
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• 2015

Let ${\mathbb{D}}=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$ be the open unit disk in the complex plane $\mathbb{C}$, ${\varphi}$ an analytic self-map of $\mathbb{D}$ and ${\psi}$ an analytic function in $\mathbb{D}$. Let D be the differentiation operator and $W_{{\varphi},{\psi}}$ the weighted composition operator. The boundedness and compactness of the product-type operator $W_{{\varphi},{\psi}}D$ from the weighted Bergman-Orlicz space to the weighted Zygmund space on $\mathbb{D}$ are characterized.