• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.583-595
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• 2020

Let HE_I, HE_II, HE_III and HE_IV be the first, second, third and fourth type Loo-Keng Hua domain respectively, 𝜑 a holomorphic self-map of HE_I, HE_II, HE_III, or HE_IV and u ∈ H(𝓜) the space of all holomorphic functions on 𝓜 ∈ {HE_I, HE_II, HE_III, HE_IV}. In this paper, motivated by the well known Hua's matrix inequality, first some inequalities for the points in the Bers-type spaces of the Loo-Keng Hua domains are obtained, and then the boundedness and compactness of the weighted composition operators W_𝜑,u : f ↦ u · f ◦ 𝜑 on Bers-type spaces of these domains are characterized.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.295-303
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• 2007

In this paper we investigate the boundedness character of the positive solutions of the rational difference equation of the form $$x_{n+1}=\frac{a_0+{{\sum}^k_{j=1}}a_jx_{n-j+1}}{b_0+{{\sum}^k_{j=1}}b_jx_{n-j+1}},\;\;n=0,\;1,...$$ where $k{\in}N,\;and\;a_j,b_j,\;j=0,\;1,...,\;k $, are nonnegative numbers such that $b_0+{{\sum}^k_{j=1}}b_jx_{n-j+1}>0$ for every $n{\in}N{\cup}\{0\}$. In passing we confirm several conjectures recently posed in the paper: E. Camouzis, G. Ladas and E. P. Quinn, On third order rational difference equations(part 6), J. Differ. Equations Appl. 11(8)(2005), 759-777.

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.54-57
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• 2002

In this paper model reference adaptive control (MRAC) of linear time-varying(LTV) systems is considered. MRAC for a linear time invariant(LTI) system does not assure the boundedness of the output and parameter estimation errors in the presence of time variations of the parameters. However, changing the adaptive laws such as use of $\sigma$-modification can result in the boundedness of the output and parameter estimation errors[5]. Together with the $\sigma$-modification in the adaptive law, we also modify the control law by adding an additional term to the standard control law. The additional term leads to smaller bounds of the output and parameter estimation errors when compared to the case where only the standard control law is applied.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.9
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• pp.944-955
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• 1990

A high-performance robotic controller is proposed for uncertain robots by using an adaptive control method, which guarantees the boundedness of uncertain systems with partially known uncertainty bounds. In order to improve the tracking performance of the robotic controller, a linear compensator is introduced to the robotic system which has been linearized via a nonlinear feedback. The above adaptive method is then utilized to guarantee the ultimate boundedness of the tracking errors. The performance of the robotic controller is compared with that of the computed torque method by computer simulations under uncertain environments. The simulation results show that the proposed method gives better performance than the computed torque method. Since the proposed method has a small number of parameters to be estimated, the controller is simpler to implement than other existing adaptive controller for robots. Hence, the proposed robotic control method is expected to be well suited for high-performance operation of robots under uncertain environment.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.1
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• pp.1-11
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• 1988

In this paper, the boundedness of adjustable parameters for the model reference adaptive control(MRAC) system using a constant reference signal is discussed. This analysis is motivated by that it is possibel to verify the existence, boundedness and bounded range of the parameter as well as the stability of the adaptive system with an alternative propoerty of Lyapunov function. For two adaptive laws; a general gradient mothod(GGM) and a least square method(LSM), unique solution set in parameter space can be estabilished by a new approach suggeste here. Computer simulation results to show the effect of parameter space analysis are also examined.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.5
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• pp.838-847
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• 1994

Although there is an analytical proof of modeling capability of the neural network, the convergency error in nonlinearity modeling is inevitable, since the steepest descent based practical larning algorithms do not guarantee the convergency of modeling error. Therefore, it is difficult to apply the neural network to control system in critical environments under an on-line learning scheme. Although the convergency of modeling error of a neural network is not guatranteed in the practical learning algorithms, the convergency, or boundedness of tracking error of the control system can be achieved if a proper feedback control law is combined with the neural network model to solve the problem of modeling error. In this paper, the neural network is introduced for compensating a system uncertainty to control a nonlinear dynamic system. And for suppressing inevitable modeling error of the neural network, an iterative neural network learning control algorithm is proposed as a virtual on-line realization of the Adaptive Variable Structure Controller. The efficiency of the proposed control scheme is verified from computer simulation on dynamics control of a 2 link robot manipulator.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.259-275
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• 2019

The aim of this paper is to prove that Marcinkiewicz integral operators are bounded from ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ to ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ when the parameters ${\alpha}({\cdot})$, $p({\cdot})$ and $q({\cdot})$ satisfies some conditions. Also, we prove the boundedness of ${\mu}$ on variable Herz-type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$.

• Journal of Contemporary Eastern Asia
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• v.21 no.2
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• pp.13-26
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• 2022

This study explores the following research question to address issues linked to emotions, identity, and institutions: how has the cult (institution) of the three Kims affected North Koreans' strong sense of nationalism (emotion), which is based on their Juche ideology (identity)? This paper investigates four fundamental elements of historical institutionalism: time boundedness, path dependency, institutional changes, and the shadow of the past. First, time boundedness illustrates how culture and education have been used to build trust and loyalty in the general public to construct individual and family cults. Second, path dependence reveals how the Songbun system has resulted in strong nationalism throughout Rodongdang's institutionalization. Third, institutional changes highlight the significance of age divides, as different age groups do not always support the three Kims' cult. Finally, the shadow of the past helps us understand the primary processes for generating mass ardent nationalism in the form of powerful impulses for self-sacrifice.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.277-303
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• 2021

Under the rough kernels Ω belonging to the block spaces B0,qr (Sn-1) or the radial Grafakos-Stefanov kernels W����(Sn-1) for some r, �� > 1 and q ≤ 0, the boundedness and continuity were proved for two classes of rough maximal singular integrals and maximal operators associated to polynomial mappings on the Triebel-Lizorkin spaces and Besov spaces, complementing some recent boundedness and continuity results in [27, 28], in which the authors established the corresponding results under the conditions that the rough kernels belong to the function class L(log L)α(Sn-1) or the Grafakos-Stefanov class ����(Sn-1) for some α ∈ [0, 1] and �� ∈ (2, ∞).

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.465-483
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• 2021

Let 𝓗(𝔻) be the space of analytic functions on the unit disc 𝔻. Let 𝜓 = (𝜓_j)ⁿ_j=0 and 𝚽 = (𝚽_j)ⁿ_j=0 be such that 𝜓_j, 𝚽_j ∈ 𝓗(𝔻). The linear differential operator is defined by T_𝜓(f) = ∑ⁿ_j=0 𝜓_jf^(j), f ∈ 𝓗(𝔻). We characterize the boundedness and compactness of the difference operator (T_𝜓 - T_𝚽)(f) = ∑ⁿ_j=0 (𝜓_j - 𝚽_j) f^(j) between weighted-type spaces of analytic functions. As applications, we obtained boundedness and compactness of the difference of multiplication operators between weighted-type and Bloch-type spaces. Also, we give examples of unbounded (non compact) differential operators such that their difference is bounded (compact).