• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.309-322
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• 2021

A conservative scheme for solving scalar hyperbolic equations is presented using a quadrature rule and an ODE solver. This numerical scheme consists of an upwind part, plus a correction part which is derived by introducing a new variable for the given hyperbolic equation. Furthermore, the stability and accuracy of the derived algorithm is shown with numerous computations.

• Journal of Advanced Navigation Technology
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• v.21 no.6
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• pp.608-613
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• 2017

In this paper, we consider the stability bound for uncertainty of delayed state variables in the linear discrete interval time-varying systems with time-varying delay time. The considered system has an interval time-varying system matrix for non-delayed states and is perturbed by the unstructured time-varying uncertainty in delayed states with time-varying delay time within fixed interval. Compared to the previous results which are derived for time-invariant cases and can not be extended to time-varying cases, the new stability bound in this paper is applicable to time-varying systems in which every factors are considered as time-varying variables. The proposed result has no limitation in applicable systems and is very powerful in the aspects of feasibility compared to the previous. Furthermore. the new bound needs no complex numerical algorithms such as LMI(Linear Matrix Inequality) equation or upper solution bound of Lyapunov equation. By numerical examples, it is shown that the proposed bound is able to include the many existing results in the previous literatures and has better performances in the aspects of expandability and effectiveness.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.1
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• pp.89-96
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• 2005

This paper is concerned with a balancing motion formulation and control of the ZMP (Zero Moment Point) for a biped-walking robot that has a prismatic balancing weight or a revolute balancing weight. The dynamic stability equation of a walking robot which have a prismatic balancing weight is conditionally linear but a walking robot's stability equation with a revolute balancing weight is nonlinear. For a stable gait, stabilization equations of a biped-walking robot are modeled as non-homogeneous second order differential equations for each balancing weight type, and a trajectory of balancing weight can be directly calculated with the FDM (Finite Difference Method) solution of the linearized differential equation. In this paper, the 3dimensional graphic simulator is developed to get and calculate the desired ZMP and the actual ZMP. The operating program is developed for a real biped-walking robot IWRⅢ. Walking of 4 steps will be simulated and experimented with a real biped-walking robot. This balancing system will be applied to a biped humanoid robot, which consist legs and upper body, as a future work.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.617-630
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• 2011

Let X, Y be vector spaces, and let r be 2 or 4. It is shown that if an odd mapping $f:X{\rightarrow}Y$ satisfies the functional equation $${\hspace{50}}rf(\frac{\sum_{j=1}^{d}\;x_j} {r})+\;{\sum\limits_{\iota(j)=0,1 \atop {\sum_{j=1}^{d}}\;{\iota}(j)=l}}\;rf(\frac{\sum_{j=1}^{d}{(-1)^{\iota(j)}x_j}}{r}) \\({\ddag}){\hspace{160}}=(_{d-1}C_l-_{d-1}C_{l-1}+1)\;{\sum\limits_{j=1}^{d}\;f(x_j)}$$ then the odd mapping $f:X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation in Banach modules over a unital $C^*$-algebra. As an application, we show that every almost linear bijection $h:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ of a unital $C^*$-algebra ${\mathcal{A}}$ onto a unital $C^*$-algebra ${\mathcal{B}}$ is a $C^*$-algebra isomorphism when $h(2^nuy)=h(2^nu)h(y)$ for all unitaries $u{\in}{\mathcal{A}}$, all $y{\in}{\mathcal{A}}$, and $n=0,1,2,{\cdots}$.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.455-466
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• 1999

In this note we present a numerical scheme for finding an approxximate solution of an equation which can be viewed as a model for spatial diffusion of age-depednent biological populations. Discretization of the model yields a linear system with a block tridi-agonal matrix. Our main concern will be discussion of stability for this scheme by examining the eigenvalues of the block tridiagonal matrix. Numerical results are presented.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.127-147
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• 2019

In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.253-259
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• 2011

Let A and B be Banach algebras with unit. Here we prove that an approximate algebra homomorphism f : A ${\rightarrow}$ B, in the sense of Rassias, is an algebra homomorphism.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.401-413
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• 2020

In this article we consider the following system of piecewise linear difference equations: x_n+1 = |x_n| - y_n - 1 and y_n+1 = x_n + |y_n| - 1. We show that when the initial condition is an element of the closed second or fourth quadrant the solution to the system is either a prime period-3 solution or one of two prime period-4 solutions.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.5-16
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• 2009

In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability for a following functional equation $$\sum\limits_{i=1}^mf(x_i+\frac{1}{m}\sum\limits_{{i=1\atop j{\neq}i}\.}^mx_j)+f(\frac{1}{m}\sum\limits_{i=1}^mx_i)=2f(\sum\limits_{i=1}^mx_i)$$ for a fixed positive integer m with $m\;{\geq}\;2$. This is applied to investigate derivations and their stability on proper Lie $CQ^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.953-955
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• 1993

In this paper we propose a new stability theorem and a robust stability condition for linguistic fuzzy model systems in state space. First we define a stability in linear sense. After representing the fuzzy model by a system with disturbances, A necessary and sufficient condition for the stability is derived. This condition is proved to be a sufficient condition of the fuzzy model. The Q in the Lyapunov equation is iteratively adjusted by an gradient-based algorithm to improve its stability test. Finally, stability robustness bounds of a system having modeling error is derived. An example is also included to show that the stability test is powerful.