• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.1148-1153
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• 2004

This paper presents the mechanism to increase lateral stability of a mobile robot using an energy stability margin theory. Previous measure of stability used in a wheeled mobile robot has been based on a static stability margin. However, the static stability margin is independent of the height of the robot and does not provide sufficient measure for the amount of stability when the terrain is not a horizontal plane. In this work, the energy stability margin theory, which is dependent on robot's height is used to develop a 2 dof mechanism to increase lateral stability. This proposed mechanism shifts the center of gravity of the robot to the point where the energy stability margin is maximized and overall stability of the robot equipped with this mechanism will be increased.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.295-301
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• 2009

We prove the Hyers-Ulam stability of a Pexiderized exponential equation of mappings f, g, h : $G{\times}S{\rightarrow}{\mathbb{C}}$, where G is an abelian group and S is a commutative semigroup which is divisible by 2. As an application we obtain a stability theorem for Pexiderized exponential equation in Schwartz distributions.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1555-1565
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• 2013

In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90] and [S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859].

• IEMEK Journal of Embedded Systems and Applications
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• v.4 no.2
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• pp.97-102
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• 2009

In this paper, the problem of stability analysis for networked control systems with norm-bounded parameter uncertainties is investigated. By construction Lyapunov's functional, a new delay-dependent stability criterion for uncertain networked control system is established in terms of LMIs (linear matrix inequalities) which can be easily by various convex optimization algorithms. One numerical example is included to show the effectiveness of proposed criterion.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.53-61
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• 2003

We prove the generalized Hyers-Ulam-Rassias stability of the invertible mapping in a Banach module over a unital Banach algebra, and prove the generalized Hyers-Ulam-Rassias stability of the Jensen's functional equations in a Hilbert module over a unital $C^{*}$-algebra.

• The Pure and Applied Mathematics
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• v.20 no.3
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• pp.223-232
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• 2013

Alexseev's formula generalizes the variation of constants formula and permits the study of a nonlinear perturbation of a system with certain stability properties. In recent years M. Pinto introduced the notion of $h$-stability. S.K. Choi et al. investigated $h$-stability for the nonlinear differential systems using the notion of $t_{\infty}$-similarity. Applying these two notions, we study bounds for solutions of the perturbed differential systems.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.567-579
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• 2008

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

• The Journal of the Acoustical Society of Korea
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• v.4 no.1
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• pp.16-21
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• 1985

Both shifiting the input signal's frequencies by a fixed frequency and compressing the input signal's bandwidth have been known to be effective in improving the stability margin of public adress systems operating in reverberant spaces. This paper describes the effect of an alternative approach of improving the acoustic-feedback stability and yet maintaining speech inteligibility by bandwidth compression and expansion. Conditions are derived for this technizue to be realized and an experimental system has been made - up. A series of experiments has been performed in small spaces and the results have shown that more than 5dB improvement can be obtained in the stability margin.

• Earthquakes and Structures
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• v.21 no.6
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• pp.601-612
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• 2021

The paper concerns the selection of a design accelerograms used for the slope stability assessment under earthquake excitation. The aim is to experimentally verify the Arias Intensity as an indicator of the excitation threat to the slope stability. A simple dynamic system consisting of a rigid block on a rigid inclined plane subjected to horizontal excitation is adopted as a slope model. Strong ground motions recorded during earthquakes are reproduced on a shaking table. The permanent displacement of the block serves as a slope stability indicator. Original research stand allows us to analyse not only the relative displacement but also the acceleration time history of the block. The experiments demonstrate that the Arias Intensity of the accelerogram is a good indicator of excitation threat to the stability of the slope. The numerical analyses conducted using the experimentally verified extended Newmark's method indicate that both the Arias Intensity and the peak velocity of the excitation are good indicators of the impact of dynamic excitation on the dam's stability. The selection can be refined using complementary information, which is the dominant frequency and duration of the strong motion phase of the excitation, respectively.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.697-711
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• 2017

Let X, Y be real normed vector spaces. We exhibit all the solutions $f:X{\rightarrow}Y$ of the functional equation f(rx + sy) + rsf(x - y) = rf(x) + sf(y) for all $x,y{\in}X$, where r, s are nonzero real numbers satisfying r + s = 1. In particular, if Y is a Banach space, we investigate the Hyers-Ulam stability problem of the equation. We also investigate the Hyers-Ulam stability problem on a restricted domain of the following form ${\Omega}{\cap}\{(x,y){\in}X^2:{\parallel}x{\parallel}+{\parallel}y{\parallel}{\geq}d\}$, where ${\Omega}$ is a rotation of $H{\times}H{\subset}X^2$ and $H^c$ is of the first category. As a consequence, we obtain a measure zero Hyers-Ulam stability of the above equation when $f:\mathbb{R}{\rightarrow}Y$.