• International Journal of Control, Automation, and Systems
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• 제5권1호
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• pp.8-14
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• 2007

This paper describes a robust and non-fragile $H_{\infty}$ controller design method for descriptor systems with parameter uncertainties and time delay, as well as a static state feedback controller with multiplicative uncertainty. The controller existence condition, as well as its design method, and the measure of non-fragility in the controller are proposed using linear matrix inequality(LMI) technique, which can be solved efficiently by convex optimization. Therefore, the presented robust and non-fragile $H_{\infty}$ controller guarantees the asymptotic stability and disturbance attenuation of the closed loop systems within a prescribed degree in spite of parameter uncertainties, time delay, disturbance input and controller fragility.

• International Journal of Control, Automation, and Systems
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• 제1권4호
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• pp.503-510
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• 2003

This paper describes the synthesis of robust and non-fragile $H^{i~}$state feedback controllers for linear varying systems with time delay and affine parameter uncertainties, as well as static state feedback controller with structural uncertainty. The sufficient condition of controller existence, the design method of robust and non-fragile $H^{i~}$static state feedback controller, and the region of controllers satisfying non-fragility are presented. Also, using some change of variables and Schur complements, the obtained conditions can be rewritten as parameterized Linear Matrix Inequalities (PLMIs), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. We show that the resulting controller guarantees the asymptotic stability and disturbance attenuation of the closed loop system in spite of time delay and controller gain variations within a resulted polytopic region.

• 대한수학회지
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• 제42권5호
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• pp.1057-1069
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• 2005

In this article, we prove the existence of two embedded minimal annuli in a slab which are all bounded by a Jordan convex curve and a straight line.

• 대한수학회논문집
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• 제20권3호
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• pp.511-520
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• 2005

In this article, we prove the existence of a minimal annulus bounded by a Jordan curve and a straight line.

• 대한수학회보
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• 제44권1호
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• pp.173-176
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• 2007

The non-existence is proved of four-dimensional mod 2 semisimple representations of Gal ($\=\mathbb{Q}/\mathbb{Q}$) which are unramified outside 2.

• 대한수학회지
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• 제55권1호
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• pp.59-71
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• 2018

In the present paper, we study and classify factorable surfaces in a 3-dimensional isotropic space with constant isotropic Gaussian (K) and mean curvature (H). We provide a non-existence result relating to such surfaces satisfying ${\frac{H}{K}}=const$. Several examples are also illustrated.

• 대한수학회논문집
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• 제28권2호
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• pp.353-360
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• 2013

We study lightlike hypersurfaces of indefinite Kenmotsu manifolds. The purpose of this paper is to prove that there do not exist totally geodesic screen distributions on semi-symmetric lightlike hypersurfaces of indefinite Kenmotsu manifolds with flat transversal connection.

• 대한수학회보
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• 제45권2호
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• pp.269-271
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• 2008

We prove that a full jack field does not exist on the sum of a trivial bundle and the canonical bundle on $G_{2,4}$, the Grassmanian of 2-planes in 4-space.

• 대한수학회보
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• 제45권2호
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• pp.273-275
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• 2008

We will give a short and elementary proof of the existence of infinitely many primes p such that a given positive integer a congruent 3 modulo 4 is a quadratic non-residue modulo p.

• 대한수학회보
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• 제51권4호
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• pp.1211-1216
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• 2014

In this paper, we study the structure of m-quasi Einstein manifolds when there exists another distinct solution to the (${\lambda}$, n + m)-Einstein equation. In particular, we derive sufficient conditions for the non-existence of such solutions.