• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.539-544
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• 1994

We [1] investigated the Hausdorff dimension and the packing dimension of a certain perturbed Cantor set whose ratios are unformly bounded. In this paper, we consider a specific Cantor set whose ratios are not necessarily uniformly bounded but satisfy some other conditions. In fact, in the hypothesis, only the condition of the unform boundedness of ratios on the set is substituted by a "*-condition". We use energy theory related to Hausdorff dimension in this study while we [1] used Hausdorff density theorem to find the Hausdorff dimension of some perturbed Cantor set. In the end, we given an example which explains aformentioned facts.ned facts.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1195-1205
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• 2011

Let $H(\mathbb{D})$ denote the class of all analytic functions on the open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$. Let n be a nonnegative integer, ${\varphi}$ be an analytic self-map of $\mathbb{D}$ and $u{\in}H(\mathbb{D})$. The generalized weighted composition operator is defined by $$D_{{\varphi},u}^nf=uf^{(n)}{\circ}{\varphi},\;f{\in}H(\mathbb{D})$$. The boundedness and compactness of the generalized weighted composition operator from area Nevanlinna spaces to weighted-type spaces and little weighted-type spaces are characterized in this paper.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.727-747
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• 2011

By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.705-714
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• 2017

Let $A^2_{{\alpha},{\beta}}(\mathbb{B}_n)$ denote the space of holomorphic functions that are $L^2$ with respect to a weight of form ${\omega}_{{\alpha},{\beta}}(z)=(1-{\mid}z{\mid}^{\alpha}e^{-{\frac{\beta}{1-{\mid}z{\mid}}}}$, where ${\alpha}{\in}\mathbb{R}$ and ${\beta}$ > 0 on the unit ball $\mathbb{B}_n$. We obtain some results for the boundedness and compactness of $Ces{\grave{a}}ro$ operator on $A^2_{{\alpha},{\beta}(\mathbb{B}_n)$.

• Proceedings of the KIEE Conference
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• 2000.11d
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• pp.679-681
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• 2000

This thesis presents a analysis method of hybrid synthesis petri net for automated manufacturing systems in discrete event dynamic system. There are many errors that can happen to petri net modeling of complex systems because petri net modeling process has so many steps. A new matrix analysis method presented in this thesis can confirm the property of petri net such as boundedness, liveness and reversibility, modify errors which can be occurred in modeling.

• Proceedings of the KIEE Conference
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• 2006.07d
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• pp.1848-1849
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• 2006

The new robust controller design method is proposed for the flight control systems with model uncertainties. The proposed control system is a combination of the adaptive dynamic surface control (DSC) technique and the self recurrent wavelet neural network (SRWNN). The adaptive DSC technique provides us with the ability to overcome the "explosion of complexity" problem of the backstepping controller. The SRWNNs are used to observe the arbitrary model uncertainties of flight systems and all their weights are trained on-line. From the Lyapunov stability analysis, their adaptation laws are induced and the uniformly ultimately boundedness of all signals in a closed-loop adaptive system is proved. Finally, simulation results for a high performance aircraft (F-16) are utilized to validate the good tracking performance and robustness of the proposed control system.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.31-39
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• 2009

Let $T_{\rho}$ be the generalized fractional integral operator associated to a function ${\rho}:(0,{\infty}){\rightarrow}(0,{\infty})$, as defined in [16]. For a function W on $\mathbb{R}^n$, we shall be interested in the boundedness of the multiplication operator $f{\mapsto}W{\cdot}T_{\rho}f$ on generalized Morrey spaces. Under some assumptions on ${\rho}$, we obtain an inequality for $W{\cdot}T_{\rho}$, which can be viewed as an extension of Olsen's and Kurata-Nishigaki-Sugano's results.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.265-285
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• 2017

In this article, a mathematical model is proposed and analyzed to study the delayed dynamics of a system having a predator and two preys with distinct growth rates and functional responses. The equilibrium points of proposed system are determined and the local stability at each of the possible equilibrium points is investigated by its corresponding characteristic equation. The boundedness of the system is established in the absence of delay and the condition for existence of persistence in the system is determined. The discrete type gestational delay of predator is also incorporated on the system. Further it is proved that the system undergoes Hopf bifurcation using delay as bifurcation parameter. This study refers that time delay may have an impact on the stability of the system. Finally Computer simulations illustrate the dynamics of the system.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.251-263
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• 2017

The aim of this paper is to investigate the dynamical behavior of the difference equation $$x_{n+1}={\frac{{\alpha}x_n}{{\beta}+{\gamma}x^p_{n-1}x^q_{n-2}}},\;n=0,1,{\ldots}$$, where the parameters ${\alpha}$, ${\beta}$, ${\gamma}$, p, q are non-negative numbers and the initial values $x_{-2}$, $x_{-1}$, $x_0$ are positive numbers. Also, some numerical examples are given to verify our theoretical results.

• Transactions on Control, Automation and Systems Engineering
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• v.3 no.2
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• pp.95-105
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• 2001

In this paper, in order to control uncertain chaotic system, an adaptive fuzzy control(AFC) scheme is developed for the multi-input/multi-output plants represented by the Takagi-Sugeno(T-S) fuzzy models. The proposed AFC scheme provides robust tracking of a desired signal for the T-S fuzzy systems with uncertain parameters. The developed control law and adaptive law guarantee the boundedness of all signals in the closed-loop system. In addition, the chaotic state tracks the state of the stable reference model(SRM) asymptotically with time for any bounded reference input signal. The suggested AFC design technique is applied for the control of an uncertain Lorenz system based on T-S fuzzy model such as stabilization, synchronization and chaotic model following control(CMFC).