• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.157-162
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• 1998

This paper provides some properties of positive real systems in time domain. It is well-known that a positive real system and a bounded real system are closely related by bilinear transform in a frequency domain. By using supply rate and storage function, we show that a positive real system can be transformed into a bounded real system, and that a positive real system can be transformed into another positive real system with in a time domain. Also, we show that an ESPR(extended strictly positive real) system can be decomposed into a feedback system of lossless positive real system and another ESPR system. These results may be used to design an output feedback controller for mixed H$H_2$ESPR problem.

• International Journal of Control, Automation, and Systems
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• v.6 no.1
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• pp.76-85
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• 2008

Motivated by the fact that in many industrial robots the joint velocity is estimated from position measurements, the trajectory tracking of robot manipulators with output feedback is addressed in this paper. The fact that robot actuators have limited power is also taken into account. Let us notice that few solutions for the torque-bounded output feedback tracking control problem have been proposed. In this paper we contribute to this subject by presenting a theoretical reexamination of a known controller, by using the theory of singularly perturbed systems. Motivated by this analysis, a redesign of that controller is introduced. As another contribution, we present an experimental evaluation in a two degrees-of-freedom revolute-joint direct-drive robot, confirming the practical feasibility of the proposed approach.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.457-471
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• 2017

A necessary and sufficient condition for the product AB of a selfadjoint operator A and a bounded selfadjoint operator B to be normal is given. Various properties of the factors of the unitary polar decompositions of A and B are obtained in the case when the product AB is normal. A block operator model for pairs (A, B) of selfadjoint operators such that B is bounded and AB is normal is established. The case when both operators A and B are bounded is discussed. In addition, the example due to Rehder is reexamined from this point of view.

• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.35-56
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• 2015

In this paper, we classify all nonconstant smooth CR maps from a sphere $S_{n,1}{\subset}\mathbb{C}^n$ with n > 3 to the Shilov boundary $S_{p,q}{\subset}\mathbb{C}^{p{\times}q}$ of a bounded symmetric domain of Cartan type I under the condition that p - q < 3n - 4. We show that they are either linear maps up to automorphisms of $S_{n,1}$ and $S_{p,q}$ or D'Angelo maps. This is the first classification of CR maps into the Shilov boundary of bounded symmetric domains other than sphere that includes nonlinear maps.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.12
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• pp.2626-2634
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• 1997

The purpose of multicasting is to reduce the network costs for transmitting the same traffic to multiple destinations. In this paper, an efficient delay-bounded multicasting routing algorithm is proposed, which satistifies the network conditions of cost minimization and can adjust the dynamic events, such as 'leave and/or join ones' from the multicast group. Also, our algorithm is designed for various network requirements such as the efficiet dynamic group support, high-quality data distribution, and adaptability to variable situation. After the delay tolerance and the maximum group size are determined according to network state and requirements for delay and cost, the dynamic delay-bounded multicast tree is constructed using partial multicast routing. We evaluate the performance of the proposed algorithm by running simulations on randomly generated test networks using a Sun Sparc 20 workstation. We were able to obtain good simulation resutls, which means solutions that lies between the minimum cost solution and the minimum delay one.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.715-720
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• 2004

Suppose X is a closed subspace of Z = ${({{\Sigma}^{\infty}}_{n=1}Z_{n})}_{p}$ (1 < p < ${\infty}$, dim $Z_{n}$ < ${\infty}$). We investigate an isometrically isomorphic embedding of L(X)/K(X) into L(X, Z)/K(X, Z), where L(X, Z) (resp. L(X)) is the space of the bounded linear operators from X to Z (resp. from X to X) and K(X, Z) (resp. K(X)) is the space of the compact linear operators from X to Z (resp. from X to X).

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.1-20
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• 2004

Let A be a uniform algebra, and let $\phi$ be a self-map of the spectrum $M_A$ of A that induces a composition operator $C_{\phi}$, on A. It is shown that the image of $M_A$ under some iterate ${\phi}^n$ of \phi is hyperbolically bounded if and only if \phi has a finite number of attracting cycles to which the iterates of $\phi$ converge. On the other hand, the image of the spectrum of A under $\phi$ is not hyperbolically bounded if and only if there is a subspace of $A^{**}$ "almost" isometric to ${\ell}_{\infty}$ on which ${C_{\phi}}^{**}$ "almost" an isometry. A corollary of these characterizations is that if $C_{\phi}$ is weakly compact, and if the spectrum of A is connected, then $\phi$ has a unique fixed point, to which the iterates of $\phi$ converge. The corresponding theorem for compact composition operators was proved in 1980 by H. Kamowitz [17].

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.235-251
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• 2021

We consider the Schrödinger type operator ��k = (-∆)k+Vk on ℝn(n ≥ 2k + 1), where k = 1, 2 and the nonnegative potential V belongs to the reverse Hölder class RHs with n/2 < s < n. In this paper, we establish the (Lp, Lq)-boundedness of the higher order Riesz transform T��,�� = V2��∇2��-��2 (0 ≤ �� ≤ 1/2 < �� ≤ 1, �� - �� ≥ 1/2) and its adjoint operator T∗��,�� respectively. We show that T��,�� is bounded from Hardy type space $H^1_{\mathcal{L}_2}({\mathbb{R}}_n)$ into Lp2 (ℝn) and T∗��,�� is bounded from ��p1 (ℝn) into BMO type space $BMO_{\mathcal{L}_1}$ (ℝn) when �� - �� > 1/2, where $p_1={\frac{n}{4({\beta}-{\alpha})-2}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})+2}}$. Moreover, we prove that T��,�� is bounded from $BMO_{\mathcal{L}_1}({\mathbb{R}}_n)$ to itself when �� - �� = 1/2.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1101-1110
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• 2023

At the present paper, we investigate bounded approximately local derivations of ℓ¹-Munn algebra 𝕄_I(𝒜), where I is an arbitrary non-empty set and 𝒜 is an approximately locally unital Banach algebra. Indeed, we show that if _𝒜B(𝒜, 𝒜^*) and B_𝒜(𝒜, 𝒜^*) are reflexive, then every bounded approximately local derivation from 𝕄_I(𝒜) into any Banach 𝕄_I(𝒜)-bimodule X is a derivation. Finally, we apply this result to study bounded approximately local derivations of the semigroup algebra ℓ¹(S), where S is a uniformly locally finite inverse semigroup.

• Journal of the Korean Mathematical Society
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• v.61 no.5
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• pp.1035-1050
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• 2024

The Cameron-Martin translation theorem describes how Wiener measure changes under translation by elements of the Cameron-Martin space in an abstract Wiener space (AWS). Translation theorems for the analytic Feynman integrals also have been established in the literature. In this article, we derive a more general translation theorem for the analytic Feynman integral associated with bounded linear operators (B.L.OP.) on AWSs. To do this, we use a certain behavior which exists between the analytic Fourier-Feynman transform (FFT) and the convolution product (CP) of functionals on AWS. As an interesting application, we apply this translation theorem to evaluate the analytic Feynman integral of the functional $$F(x)={\exp}\left(-iq\int_{0}^{T}x(t)y(t)dt\right),\,y{\in}C_0[0,\,T],\;q{\in}{\mathbb{R}}\,{\backslash}\,\{0\}$$ defined on the classical Wiener space C₀[0, T].