• Journal of the Optical Society of Korea
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• 제14권4호
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• pp.438-443
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• 2010

In this paper, behaviors of photonic crystal (PC) radiative structures and antenna arrays have been compared for two types of uniform and binomial excitations. Appropriate duality has been shown between them. These results can be generalized to other types of excitation and arrangement of photonic crystal radiative arrays such as linear, planar and circular arrays of three dimensional (3D) photonic crystal termination resonators. Using these results in designing photonic circuits has some advantages for shaping a particular radiative beam at the photonic crystal exit, for instance reducing the divergence angle of the main lobe in order to enhance the directivity, for better coupling, or for splitting the emitted beam, for dividing the output beam to the next devices in photonic integrated circuits (PIC). For analysis and simulation of the photonic crystal structures, the finite difference time domain (FDTD) method has been employed.

• 충청수학회지
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• 제23권3호
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• pp.523-534
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• 2010

In this paper, we consider the weighted Bloch spaces ${\mathcal{B}}_q$(q > 0) on the open unit ball in ${\mathbb{C}}^n$. We prove a certain integral representation theorem that is used to determine the degree of growth of the functions in the space ${\mathcal{B}}_q$ for q > 0. This means that for each q > 0, the Banach dual of $L_a^1$ is ${\mathcal{B}}_q$ and the Banach dual of ${\mathcal{B}}_{q,0}$ is $L_a^1$ for each $q{\geq}1$.

• 대한수학회지
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• 제45권2호
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• pp.575-585
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• 2008

Suppose that D is a $C^*$-discrete quantum group and $D_0$ a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a D-module algebra, and if the inner product on the Hilbert space H is D-invariant, there is a unique $C^*$-representation $\theta$ of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of $\theta$(D) in L(H).

• 대한수학회보
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• 제25권2호
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• pp.167-170
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• 1988

Versions of Tannaka duality in operator algebraic context have been obtained in [6], [8] etc. Suppose .sigma.is an automorphism of a von Neumann algebra M, on which there is an action .alpha. of a compact group G such that .sigma. vertical bar $M^{\alpha}$=id, where $M^{\tau}$is the fixed point algebra under the action .alpha.. Then it is shown that if there is an action .tau. of a group H which commutes with .alpha., and which is ergodic in the sense that the fixed point algebra $M^{\tau}$ is trivial, then there exists g.mem.G such that .sigma.=.alpha.(g). Recently Evans and Kishimoto ([4]) showed the versions of Tannaka duality in $C^{*}$-settings under some conditions.s.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.475-489
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• 2022

This paper focuses on a robust semi-infinite interval-valued optimization problem with uncertain inequality constraints (RSIIVP). By employing the concept of LU-optimal solution and Extended Mangasarian-Fromovitz Constraint Qualification (EMFCQ), necessary optimality conditions are established for (RSIIVP) and then sufficient optimality conditions for (RSIIVP) are derived, by using the tools of convexity. Moreover, a Wolfe type dual problem for (RSIIVP) is formulated and usual duality results are discussed between the primal (RSIIVP) and its dual (RSIWD) problem. The presented results are demonstrated by non-trivial examples.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.235-246
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• 2015

In this paper, a vector optimization problem over cones is considered, where the functions involved are $\eta$-semidifferentiable. Necessary and sufficient optimality conditions are obtained. A dual is formulated and duality results are proved using the concepts of cone $\rho$-semilocally preinvex, cone $\rho$-semilocally quasi-preinvex and cone $\rho$-semilocally pseudo-preinvex functions.

• Bulletin of the Korean Chemical Society
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• 제20권4호
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• pp.466-468
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• 1999

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 1996년도 추계학술대회발표논문집; 고려대학교, 서울; 26 Oct. 1996
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• pp.239-240
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• 1996

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 1991년도 춘계공동학술대회 발표논문 및 초록집; 전북대학교, 전주; 26-27 Apr. 1991
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• pp.3-3
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• 1991

• 한국정밀공학회지
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• 제13권2호
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• pp.76-83
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• 1996

We have developed the unconventional robot arm which is composed of the two main parts, one is a ball screw and the other is a robot arm. The dynamic systems of the robot arm and ball screw are unstable systems coupled with each other. The ball screw mechanism is unstable system but controllable system. The robot arm's dynamics is quasi stable system when ball screw's angular position is zero, else, unstable system. Our system has the duality between stability and controllability at the view point of control. This duality causes difficulty to control of the robot arm using normal control law. We have investigated the location of the characteristic roots of the dynamic equation. And we have found out that the best condition for the control of the arm is quasi stable state. In this paper, we have proposed multiple control laws which are consist of three components to guarantee the stability and controllability simultaneously. The computer simulations were carried out based on VSC about the angular position control of the robot arm, and it is confirmed that the good performances could be obtained by using new controller.