• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.635-647
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• 2014

In this paper, a generalized perturbed midpoint rule is established. Various error bounds for this generalization are also obtained.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.68-72
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• 1986

Upper bounds of the perturbed Co-semigroups of the infinite dimensional systems are investigated by using the algebraic Riccati equation(ARE). In the case that the solution P of the ARE is strictly positive, the perturbed semigroups are uniformly bounded. A sufficient condition for the solution P to be strictly positive is provided. The uniform boundedness plays an important role in extending approximately weak stability to weak stability on th whole space. Exponential Stability of the perturbed semigroups is studied by using the Young's inequlity. Some further discussions on the uniform boundedness of the perturbed semigroups are given.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.387-393
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• 2006

We study three conditions which seem similar but a little different on a perturbed Cantor set. Since they give different conditions on a perturbed Cantor set, we have another results corresponding to the conditions. We compare the conditions and give different examples which provide different results.

• Tribology and Lubricants
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• v.12 no.1
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• pp.47-55
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• 1996

In this study, steady state and perturbed pressures are experimentally measured under inherently compensated restrictors in externally pressurized air bearings. A piezo actuator is used for simulating small displacement perturbation in the air film. The pressures under the restrictors are measured by a miniature type pressure transducer and the height of the air film is measured by capacitance type gap sensors developed by Chapman's method. The perturbed pressure is obtained through Fourier transformation of the two signals. The measured perturbed pressures are in good agreement with the calculated values.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.205-212
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• 2014

This paper investigates mean square exponential dissipativity of singularly perturbed stochastic delay differential equations. The L-operator delay differential inequality and stochastic analysis technique are used to establish sufficient conditions ensuring the mean square exponential dissipativity of singularly perturbed stochastic delay differential equations for sufficiently small ${\varepsilon}$ > 0. An example is presented to illustrate the efficiency of the obtained results.

• Transactions on Control, Automation and Systems Engineering
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• v.3 no.3
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• pp.164-169
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• 2001

This paper considers the problem of robust stabilization and disturbance attenuation for a class of uncertain singularly perturbed systems with norm-bounded nonlinear uncertainties. It is shown that the state feedback gain matrices can be determined to guarantee the stability of the closed-loop system for all $\varepsilon$$\in$(0, $\infty$). Based on this key result and some standard Riccati inequality approaches for robust control of singularly perturbed systems, a constructive design procedure is developed.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.499-511
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• 2015

This paper shows that the solutions to the perturbed dierential system $$y^{\prime}=f(t,y)+{\int}_{t_o}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded property. To show this property, we impose conditions on the perturbed part ${\int}^{t}_{t_o}g(s,y(s))ds+h(t,y(t),Ty(t))$ and on the fundamental matrix of the unperturbed system y' = f(t, y).

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.593-605
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• 2002

Explicit hounds are obtained for the perturbed, or corrected, trapezoidal and midpoint rules in terms of the Lebesque norms of the second derivative of the function. It is demonstrated that the bounds obtained are the same for both rules although the perturbation or the correction term is different.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.447-454
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• 2004

We study the Hausdorff and packing dimensions of subsets composing multifractal spectrum generated by a quasi-self-similar probability measure on a perturbed Cantor set.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.489-496
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• 2004

We study the h- stability of nonlinear difference system x(n+1) =f(n, x(n)) and its perturbed system y(n+l) =f(n, y(n))+g(n, y(n), Sy(n)).