• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.287-307
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• 2016

Using the fixed point method, we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in matrix fuzzy normed spaces.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.6
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• pp.869-876
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• 1994

This paper presents an efficient method to calculate voltage collapse point and to avoid voltage instability. To evaluate voltage stability in power systems, it is necessary to get critical loading points. For this purpose, this paper uses linear programming to calculate efficiently voltage collapse point. Also, if index value becomes larger than given threshold value, voltage stability is improved by compensation of reactive power at selected bus. This algorithm is verified by simulation on the IEEE 14-bus sample system.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.77-87
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• 2020

In this paper, we investigate the stability of a functional equation f(x + 3y) - 5f(x + 2y) + 10f(x + y) - 8f(x) + 5f(x - y) - f(x - 2y) - 2f(-x) - f(2x) + f(-2x) = 0 by using the fixed point theory in the sense of L. Cǎdariu and V. Radu.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.873-887
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• 2007

In this paper cellular neutral networks with time-varying delays and continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results.

• East Asian mathematical journal
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• v.35 no.5
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• pp.559-568
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• 2019

In this paper, we investigate the stability problems for a functional equation f(x + 2y)+f(x - 2y) - 4f(x + y) - 4f(x - y) + 6f(x) - 2f(2y) + 12f(y) - 4f(-y) = 0 by using the fixed point theory in the sense of L. C˘adariu and V. Radu.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.801-812
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• 2022

In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers-Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.571-592
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• 2022

By established a Banach space with the Hausdorff distance, we introduce the alternative fixed-point theorem to explore the existence and uniqueness of a fixed subset of Y and investigate the stability of set-valued Euler-Lagrange functional equations in this space. Some properties of the Hausdorff distance are furthermore explored by a short and simple way.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.6
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• pp.554-557
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• 2008

We analyze the stability property of a class of nonlinear time-delay systems with time-varying delays. We present a time-delay independent sufficient condition for the global asymptotic stability. In order to prove the sufficient condition, we exploit the inherent property of the considered systems instead of applying the Krasovskii or Razumikhin stability theory that may cause the mathematical difficulty of analysis. We prove the sufficient condition by constructing two sequences that represent the lower and upper bound variations of system state in time, and showing the two sequences converge to an identical point, which is the equilibrium point of the system. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.6 s.171
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• pp.118-126
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• 2005

There are many types of walking robots in the world. For dynamic walking of the robots it is necessary to keep its dynamic stability. The dynamic stability is influenced by the position of ZMP (zero moment point). In this paper we study the control of the ZMP position of walking robot. For experiment we developed a quadruped robot and analyzed the dynamic stability of the robot. Developed robot has 2 joints at each leg and WBO (weight balancing oscillator) on the body of the robot. The WBO is designed to move linearly from side to side when the robot walks dynamically. Walking test was performed to verify the validity of the proposed methods. Especially we showed that the dynamic stability of the robot can be improved without sacrifice of the walking speed by control the WBO.

• Transactions of the Korean Society of Automotive Engineers
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• v.15 no.3
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• pp.91-98
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• 2007

This paper presents the induced mathematical modeling equations for evaluating the operation stability with automatic transmission of heavy duty vehicle. This theoretical approach indicates that linearized governing equations of system can be converted into eigen-value problems. if the eigen-value has positive number, we can predict the engine operating point locates an unstable operating region. To be a stable state, the unstable operating point diverges toward a stable point which is able to maintain uniform velocity. Based on the previous theoretical analysis, we carry out dynamic simulation to show the behavior of engine operating point and torque converter in transient state. As a result of the dynamic simulation, the suggested theoretical method is found to be reasonable for evaluating the operation stability of a torque converter. In addition, the numerical results explain the engine stops and fluctuating phenomenon in reality.