• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.3
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• pp.625-631
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• 2011

This paper presents a discrete-time output feedback consensus algorithm for Multi-Agent Systems (MAS). Under the assumption that an agent is aware of the relative state information about its neighbors, a state feedback consensus algorithm is designed based on Linear Matrix Inequality (LMI) method. In general, however, it is possible to obtain its relative output information rather than the relative state information. To reconcile this problem, an Unknown Input Observer (UIO) is employed in this paper. To this end, first it is shown that the relative state information can be estimated using the UIO and the measured relative output information. Then a certainty-equivalence type output feedback consensus algorithm is proposed by combining the LMI-based state feedback consensus algorithm with the UIO. Finally, simulation results are given to illustrate that the proposed method successfully achieves the state consensus.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.13 no.5
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• pp.432-435
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• 2020

The elasticity tensor for water may be employed to model the fully saturated porous material. Mostly water is assumed to be incompressible with a bulk modulus, however, the upper and lower bounds of off-diagonal components of the elasticity tensor of porous materials filled with water are violated when the bulk modulus is relatively high. In many cases, the generalized Hill inequality describes the general bounds of Voigt and Reuss for eigenvalues, but the bounds for the component of elasticity tensor are more realistic because the principal axis of eigenvalues of two phases, matrix and water, are not coincident. Thus in this paper, for anisotropic material containing pores filled with water, the bounds for the component of elasticity tensor are expressed by the rule of mixture and the upper and lower bounds of fully saturated porous materials are violated for low porosity and high bulk modulus of water.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.11a
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• pp.293-296
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• 2006

This paper presents new sufficient conditions to an intelligent digital redesign (IDR). The purpose of the IDR is to effectively convert an existing continuous-time fuzzy controller to an equivalent sampled-data fuzzy controller in the sense of the state-matching. The state-matching error between the closed-loop trajectories is carefully analyzed using the integral quadratic functional approach. The problem of designing the sampled-data fuzzy controller to minimize the state-matching error as well as to guarantee the stability is formulated and solved as the convex optimization problem with linear matrix inequality (LMI) constraints.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1211-1217
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• 2019

Let $0<{\alpha}<{\infty}$ be fixed, and let $X=(X_t)_{t{\geq}0}$ be a Bessel process with dimension $0<{\theta}{\leq}1$ starting at $x{\geq}0$. In this paper, it is proved that there are positive constants A and D depending only on ${\theta}$ and ${\alpha}$ such that $$E_x\({\exp}[{\alpha}\;\max_{0{\leq}t{\leq}{\tau}}\;X_t]\){\leq}AE_x\({\exp}[D_{\tau}]\)$$ for any stopping time ${\tau}$ of X. This inequality is also shown to be sharp.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.109-120
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• 2023

The Berezin symbol à of an operator A on the reproducing kernel Hilbert space 𝓗 (Ω) over some set Ω with the reproducing kernel k_λ is defined by $${\tilde{A}}(\lambda)=\,\;{\lambda}{\in}{\Omega}$$. The Berezin number of an operator A is defined by $$ber(A):=\sup_{{\lambda}{\in}{\Omega}}{\mid}{\tilde{A}}({\lambda}){\mid}$$. We study some problems of operator theory by using this bounded function Ã, including estimates for Berezin numbers of some operators, including truncated Toeplitz operators. We also prove an operator analog of some Young inequality and use it in proving of some inequalities for Berezin number of operators including the inequality ber (AB) ≤ ber (A) ber (B), for some operators A and B on 𝓗 (Ω). Moreover, we give in terms of the Berezin number a necessary condition for hyponormality of some operators.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.527-529
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• 2012

It is proved that the fractional Sobolev spaces $W^s_p(\mathbb{R}^n)$ 0 < $s$ < $n$, are compactly embedded into Lebesgue spaces $L^q(\Omega)$ for some bounded set $\Omega$­.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.515-523
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• 2007

In this paper, we investigate the Hyers-Ulam-Rassias stability of generalized Jensen type quadratic functional equations in Banach spaces.

• East Asian mathematical journal
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• v.36 no.5
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• pp.571-581
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• 2020

In this paper, an equilibrium problems involving a finite family of maximal monotone operators and inverse-strongly monotone operators are introduced and investigated. A strong convergence theorem of common solutions is obtained in Hilbert spaces.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.793-799
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• 1996

Let $A_1, A_2, \cdots, A_m$ be a sequence of events on a given probability space and let $X_m(A)$ be the number of those A's which occur.

• 대한예방의학회:학술대회논문집
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• 2005.10a
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• pp.342-342
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• 2005