• Honam Mathematical Journal
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• v.32 no.1
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• pp.1-16
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• 2010

By using the generalized operator method given by Burchnall and Chaundy in 1940, the authors present one-dimensional inverse pairs of symbolic operators. Many operator identities involving these pairs of symbolic operators are rst constructed. By means of these operator identities, 11 decomposition formulas for the generalized hypergeometric $_4F_3$ function are then given. Furthermore, the integral representations associated with generalized hypergeometric functions are also presented.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.499-506
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• 2013

The half-inverse spectral problem for an impulsive Sturm-Liouville operator consists in reconstruction of this operator from its spectrum and half of the potential. In this study, the spectrum of the impulsive Sturm-Liouville problem is given and by using the Hochstadt and Lieberman's method we show that if $q(x)$ is prescribed on (0, ${\frac{\pi}{2}}$), then only one spectrum is sufficient to determine $q(x)$ on the interval (0, ${\pi}$) for this problem.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2183-2187
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• 2005

In this paper we propose a new fault detection and isolation (FDI) method for those faults of parameter change type. First, we design a residual generator based on the ${\delta}$-operator model of the plant by using the stable pseudo inverse system. Second, the parameter change is estimated by using the property of the block Hankel operator. Third, reliability with respect to stability is quantified. Fourth, the limitations for the meaningful diagnosis in our method are given. The numerical examples demonstrate the effectiveness of the proposed method.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.175-184
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• 1999

Along with the computation and analysis for nonlinear system being more and more involved in the fields such as automation control electronic technique and electrical power system the nonlin-ear theory has become quite a attractive field for academic research. In this paper we derives the solutions for state equation of nonlinear system by using the inverse operator expression of the so-lutions is obtained. An actual computation example is given giving a comparison between IOM and Runge-kutta method. It has been proved by our investigation that IOM has some distinct advantages over usual approximation methods in that it is computationally con-venient rapidly convergent provides accurate solutions not requiring perturbation linearization or the massive computation inherent in discrietization methods such as finite differences. So the IOM pro-vides an effective method for the solution of nonlinear system is of potential application valuable in nonlinear computation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.1C
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• pp.8-13
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• 2006

A new RS(Reed Solomon) Decoder design method, using Galois Subfield GF($2^4$) Multiplier, is described. The Decoder is designed using Normalized error position stored ROM. Here New Inverse Calculator in GF($2^8$) is designed, which is simpler and faster than the classical GF($2^8$) direct inverse calculator, using the Galois Subfield GF($2^4$) Arithmatic operator.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.603-611
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• 2003

In this paper we extend the definition of K-positive definite operators from linear to Frechet differentiable operators. Under this setting, we derive from the inverse function theorem a local existence and approximation results corresponding to those of Theorems land 2 of the authors [8], in an arbitrary real Banach space. Furthermore, an asymptotically K-positive definite operator is introduced and a simplified iteration sequence which converges to the unique solution of an asymptotically K-positive definite operator equation is constructed.

• Proceedings of the KIEE Conference
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• 1989.07a
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• pp.101-105
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• 1989

The iterative learning controller makes the system output follow the desired output over a finite time interval through iterating trials. In this paper, first we discuss that the design problem of learning controller is originally the design problem of the inverse model. Then we show that the tracking error which is the difference between the desired output and the system output is reduced monotonically by properly modeled inverse system if the magnitude of the learning operator being introduced is bounded within the unit circle in complex domain. Also it would be shown that the conventional learning control method is a kind of extremely simplified inverse model learning control method of the objective controlled system. Hence this control method can be considered as a generalization of the conventional learning control method. The more a designer model the objective controlled system precisely, the better the performance of the approximated inverse model learning controller would be. Finally we compare the performance of the conventional learning control method with that of the approximated inverse model learning control method by computer simulation.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.219-231
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• 2009

We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.29-40
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• 2000

We provide semilocal convergence theorems for Newton-like methods in Banach space using outer and generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Frechet-derivative. This way our Newton-Kantorovich hypotheses differ from earlier ones. Our results can be used to solve undetermined systems, nonlinear least square problems and ill-posed nonlinear operator equations.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.909-920
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• 2011

A regularized Newton method for nonlinear ill-posed problems is considered. In each Newton step an implicit iterative method with an appropriate stopping rule is proposed and analyzed. Under certain assumptions on the nonlinear operator, the convergence of the algorithm is proved and the algorithm is stable if the discrepancy principle is used to terminate the outer iteration. Numerical experiment shows the effectiveness of the method.