• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.4
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• pp.53-61
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• 1998

This paper describes the stability analysis of TSK (Takagi-Sugeno-Kang) fuzzy systems which can represent a large class of nonlinear systems with good accuracy. A TSK fuzzy model consists of TSK fuzzy rules and the consequent of each fuzzy rule is a linear input-output equation with a constant term. There may exist equilibrium points more than one in the TSK fuzzy model and each equilibrium point rnay also have different nature of stability. The local stability of an equilibrium point is determined by eigenvalues of the Jacobian matrix of the linearized TSK fuzzy model around the equilibrium point. Stability of both the continuous-time and the discrete-time systems is analyzed in this paper.

• Journal of Korean Association for Spatial Structures
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• v.19 no.4
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• pp.69-76
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• 2019

A stadium roof that uses the pin-jointed spatial truss system has to be designed by taking into account the unstable phenomenon due to the geometrical non-linearity of the long span. This phenomenon is mainly studied in the single-free-node model (SFN) or double-free-node model (DFN). Unlike the simple SFN model, the more complex DFN model has a higher order of characteristic equations, making analysis of the system's stability complicated. However, various symmetric conditions can allow limited analysis of these problems. Thus, this research looks at the stability of the DFN model which is assumed to be symmetric in shape, and its load and equilibrium state. Its governing system is expressed by nonlinear differential equations to show the double Duffing effect. To investigate the dynamic behavior and characteristics, we normalize the system of the model in terms of space and time. The equilibrium points of the system unloaded or symmetrically loaded are calculated exactly. Furthermore, the stability of these points via the roots of the characteristic equation of a Jacobian matrix are classified.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.231-234
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• 1996

This paper considers the output regulation problems on uncertain systems. Using NR-estimator(on-line), a family of equilibrium points for the uncertain system is computed. The state variables of the closed loop system track the average value of the obtained equilibrium manifold by dynamic state feedback control.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.51-65
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• 2011

In this paper, a composite iterative process is introduced for a generalized equilibrium problem and a pair of nonexpansive mappings. It is proved that the sequence generated in the purposed composite iterative process converges strongly to a common element of the solution set of a generalized equilibrium problem and of the common xed point of a pair of nonexpansive mappings.

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.523-528
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• 2009

In this paper, we consider the existence of solutions to some generalized vector quasi-equilibrium-like problem under a c-diagonal quasi-convexity assumptions, but not monotone concepts. For an example, in the proof of Theorem 1, the c-diagonally quasi-convex concepts of a set-valued mapping was used but monotone condition was not used. Our problem is a new kind of equilibrium problems, which can be compared with those of Hou et al. [4].

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.3
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• pp.1028-1046
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• 2022

Genome-wide association studies (GWAS) aim to find the significant genetic variants for common complex disease. However, genotype data has privacy information such as disease status and identity, which make data sharing and research difficult. Differential privacy is widely used in the privacy protection of data sharing. The current differential privacy approach in GWAS pays no attention to raw data but to statistical data, and doesn't achieve equilibrium between utility and privacy, so that data sharing is hindered and it hampers the development of genomics. To share data more securely, we propose a differential privacy preserving approach of data sharing for GWAS, and achieve the equilibrium between privacy and data utility. Firstly, a reasonable disturbance interval for the genotype is calculated based on the expected utility. Secondly, based on the interval, we get the Nash equilibrium point between utility and privacy. Finally, based on the equilibrium point, the original genotype matrix is perturbed with differential privacy, and the corresponding random genotype matrix is obtained. We theoretically and experimentally show that the method satisfies expected privacy protection and utility. This method provides engineering guidance for protecting GWAS data privacy.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.533-555
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• 2022

In this paper, we introduce a new algorithm for finding a solution of an equilibrium problem in a real Hilbert space. Our paper extends the single projection method to pseudomonotone variational inequalities, from a 2018 paper of Shehu et. al., to pseudomonotone equilibrium problems in a real Hilbert space. On the basis of the given algorithm for the equilibrium problem, we develop a new algorithm for finding a common solution of a equilibrium problem and fixed point problem. The strong convergence of the algorithm is established under mild assumptions. Several of fundamental experiments in finite (infinite) spaces are provided to illustrate the numerical behavior of the algorithm for the equilibrium problem and to compare it with other algorithms.

• Journal of Korean Society of Transportation
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• v.28 no.5
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• pp.131-139
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• 2010

The transport mode choice problem is to determine which of the alternative transport modes connecting an origin and destination will be used by a traveler. Most of the research relating to transport mode choice have mainly been focused on modeling, properties, and applications of the model, but rarely were concerned with equilibrium among the modes. This paper proves the equilibrium among the modes by using a logit mode choice model, and then verifies it with the Korean Transport Database (KTDB). In order to obtain such an equilibrium, this paper also presents a solution algorithm based on the fixed point theorem. The algorithm was tested with an example and confirmed the equilibrium solution.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.363-374
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• 2007

In this paper, we consider the discrete nonlinear delay model which describe the control of a single population of cells. We establish a sufficient condition for oscillation of all positive solutions about the positive equilibrium point and give a sufficient condition for the global attractivity of the equilibrium point. The oscillation condition guarantees the prevalence of the population about the positive steady sate and the global attractivity condition guarantees the nonexistence of dynamical diseases on the population.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.465-472
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• 2015

In this paper, we study the existence and the stability of equilibria of predator-prey models with Ivlev's functional response. We give a simple proof for the uniqueness of limit cycles of the predator-prey system. The existence and the stability at the origin and a boundary equilibrium point(including the positive equilibrium point) are also investigated.