• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1123-1132
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• 2020

In the present paper, we define new class of functions T_α,β(λ; z) which is an extension of the classical Wright function and the Mittag-Leffler function. We show some mean value inequalities for the this function, such as Turán-type inequalities, Lazarević-type inequalities and Wilker-type inequalities. Moreover, integrals formula and integral inequality for the function T_α,β(λ; z) are presented.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.163-177
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• 2012

This paper presents a LMI(linear matrix inequality)-based fuzzy approach of modeling and active vibration control of geometrically nonlinear flexible plates with piezoelectric materials as actuators and sensors. The large-amplitude vibration characteristics and dynamic partial differential equation of a piezoelectric flexible rectangular thin plate structure are obtained by using generalized Fourier series and numerical integral. Takagi-Sugeno (T-S) fuzzy model is employed to approximate the nonlinear structural system, which combines the fuzzy inference rule with the local linear state space model. A robust fuzzy dynamic output feedback control law based on the T-S fuzzy model is designed by the parallel distributed compensation (PDC) technique, and stability analysis and disturbance rejection problems are guaranteed by LMI method. The simulation result shows that the fuzzy dynamic output feedback controller based on a two-rule T-S fuzzy model performs well, and the vibration of plate structure with geometrical nonlinearity is suppressed, which is less complex in computation and can be practically implemented.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.1
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• pp.1-5
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• 2006

This paper deals with a fault detection system design for uncertain nonlinear systems modelled as T-S fuzzy systems with the integral quadratic constraints. In order to generate a residual signal, we used a left coprime factorization of the T-S fuzzy system. From the filtered signal of the residual generator, the fault occurence can be detected effectively. A simulation study with nuclear steam generator level control system shows that the suggested method can be applied to detect the fault in actual applications.

• English Language & Literature Teaching
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• v.11 no.2
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• pp.91-110
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• 2005

Many Korean EFL (English as a Foreign Language) students do not have sufficient opportunity to develop cultural knowledge and information in their classrooms. EFL teachers also tend to ignore the teaching of culture. Even though culture is taught, it simply tends to deliver "fact-only" information from the viewpoint of a "tourist level rather than cultural awareness by comparing native with target cultural references. Teaching target cultural knowledge and information should be delivered within the native cultural frame, and teaching of culture must be an integral part of teaching and learning English. The research methodology was quantitative. Quantitative data was gathered from 83 Korean EFL teachers and 286 EFL students by questionnaire. Findings indicated that three of these independent variables (cultural inequality, English-only instruction, and Unoism) were significantly and inversely related to integration of culture.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.130-140
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• 2021

In this paper, we introduce and study the concept of trigonometrically quasi-convex function. We prove Hermite-Hadamard type inequalities for the newly introduced class of functions and obtain some new Hermite-Hadamard inequalities for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is trigonometrically quasi-convex convex. We also extend our initial results to functions of several variables. Next, we point out some applications of our results to give estimates for the approximation error of the integral the function in the trapezoidal formula.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.229-242
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• 2022

In this paper, we introduce a new subclass of k-uniformly close-to-convex functions with respect to conjugate points. We study characterization, coefficient estimates, distortion bounds, extreme points and radii problems for this class. We also discuss integral means inequality with the extremal functions. Our findings may be related with the previously known results.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.9-26
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• 2022

The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter $H{\in}({\frac{1}{2}},\;1)$. We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.923-935
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• 2023

In this paper, we will discuss existence of solution of square-mean pseudo almost automorphic solution for fractional stochastic evolution equations driven by G-Brownian motion which is given as ^c₀D^𝛼_𝜌 Ψ_𝜌 = 𝒜(𝜌)Ψ_𝜌d𝜌 + 𝚽(𝜌, Ψ_𝜌)d𝜌 + ϒ(𝜌, Ψ_𝜌)d ⟨ℵ⟩_𝜌 + χ(𝜌, Ψ_𝜌)dℵ_𝜌, 𝜌 ∈ R. Furthermore, we also prove that solution of the above equation is unique by using Lipschitz conditions and Cauchy-Schwartz inequality. Moreover, examples demonstrate the validity of the obtained main result and we obtain the solution for an equation, and proved that this solution is unique.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.823-855
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• 1996

We study Dirichlet forms and the associated diffusion processes for the Gibbs measures related to the quantum unbounded spin systems (lattice boson systems) interacting via superstable and regular potentials. This work is a continuation of the author's previous study on the classical systems [LPY] to the quantum cases. In [LPY], we constructed Dirichlet forms and the associated diffusion processes for the Gibbs measures of classical unbounded spin systems. Furthermore, we also showed the essential self-adjointness of the Dirichlet operator and the log-Sobolev inequality for any Gibbs measure under appropriate conditions on the potentials. In this atudy we try to extend the results of the classical systems to the quantum cases. Because of some technical difficulties, we are only able to construct a Dirichlet form and the associated diffusion process for any Gibbs measure of the quantum systems. We utilize the general scheme of the previous work on the theory in infinite dimensional spaces [AH-K1-2, AKR, AR1-2, Kus, MR, Ro, Sch] and the ideas we employed in our study of the calssical systems ]LPY].

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.7
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• pp.976-986
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• 2014

In this paper, the problem of reliable control of linear systems with time-varying delays, randomly occurring disturbances, and actuator failures is investigated. It is assumed that actuator failures occur when disturbances affect to the systems. Firstly, by using a suitable Lyapunov-Krasovskii functional and some recent techniques such as Wirtinger-based integral inequality and reciprocally convex approach, stabilization criterion for nominal systems with time-varying delays is derived. Secondly, the proposed method is extended to the reliable $H_{\infty}$ controller design for linear dynamic systems with time-varying delays, randomly occurring disturbances, and actuator failures. Since nonlinear matrix inequalities (NLMIs) are involved in proposed results, the cone complementarity algorithm will be introduced. Finally, two numerical examples are included to show the effectiveness of the proposed criteria.