• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.1-17
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• 2004

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton method to a solution of an equation in connection with the Lipschitz continuity of the Frechet-derivative of the operator involved. Using Lipschitz and center-Lipschitz conditions we show that the Newton-Kantorovich hypothesis is weakened. The error bounds obtained under our semilocal convergence result are finer and the information on the location of the solution more precise than the corresponding ones given by the dominating Newton-Kantorovich theorem, and under the same hypotheses/computational cost, since the evaluation of the Lipschitz also requires the evaluation of the center-Lipschitz constant. In the case of local convergence we obtain a larger convergence radius than before. This observation is important in computational mathematics and can be used in connection to projection methods and in the construction of optimum mesh independence refinement strategies.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.469-473
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• 1996

In this paper, it is proposed a new approach to the development of the automatic vision system to e famine and repair the steam generator tubes at remote distance. In nuclear power plants, workers are reluctant of works in steam generator because of the high radiation environment and limited working space. It is strongly recommended that the examination and maintenance works be done by an automatic system for the protection of the operator from the radiation exposure. Digital signal processors are used it, implementing real time recognition and examination of steam generator tubes in the proposed vision system. Performance of proposed digital vision system is illustrated by experiment for similar steam generator model.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.534-537
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• 1996

As consumer electronics, information, and aero-space industry grow, the demand for aspheric lens increases higher. To enhance the precision and productivity of aspheric surface, a CAM system for ultra-precision aspheric surface needs to be realized. In this study, the developed CAM system can generate NC code for various aspheric surfaces fast and precisely by Tri-arc interpolation method that the location of maximum error is fixed. The cutting condition input module and the NC code verification module are adequate to ultra-precision machining, so that a operator can obtain products fast and easily.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.6
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• pp.5-14
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• 1998

In this paper we propose a new approach to the development of the automatic vision system to examine and repair the steam generator tubes at remote distance. In nuclear power plants, workers are reluctant of works in steam generator because of the high radiation environment and limited working space. It is strongly recommended that the examination and maintenance works be done by an automatic system for the protection of the operator from the radiation exposure. Digital signal processors are used in implementing real time recognition and examination of steam generator tubes in the proposed vision system. Performance of proposed digital vision system is illustrated by simulation and experiment for similar steam generator model.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.04a
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• pp.308-315
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• 1997

In this study, the effect of modal filter error on the vibration control characteristics of flexible structures is analyzed for IMSC(Independent Modal Space Control), and optimal sensor placement in the structural vibration control with consideration of performance of modal filter has been studied. An Lyapunov asymptotic stability condition has been derived, which depends on the magnitude of the modal filter errors. The extent of the response deviation of the closed-loop system is also derived and evaluated using operator techniques. A sensor placement technique has also been suggested to maximize the performance of the modal filter. It has been found by a series of simulation that the suggested sensor placement technique is very effective on the determination of the number and placement of sensors of modal filter in the structural vibration control.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.41-53
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• 2008

Polynomials are one of most important and widely used numerical tools in dealing with a smooth function on a bounded domain and trigonometric functions work for smooth periodic functions. However, they are not the best choice if a function has a bounded support in space and in frequency domain. The Prolate Spheroidal wave function (PSWF) of order zero has been known as a best candidate as a basis for band-limited functions. In this paper, we review some basic properties of PSWFs defined as eigenfunctions of bounded Fourier transformation. We also propose numerical inversion schemes based on PSWF and present some numerical examples to show their feasibilities as signal processing tools.

• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.71-78
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• 2001

In 1984, Johnson[A bounded convergence theorem for the Feynman in-tegral, J, Math. Phys, 25(1984), 1323-1326] proved a bounded convergence theorem for hte Feynman integral. This is the first stability theorem of the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory. Johnson and Lapidus [Generalized Dyson series, generalized Feynman digrams, the Feynman integral and Feynmans operational calculus. Mem, Amer, Math, Soc. 62(1986), no 351] studied stability theorems for the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory for the functional with arbitrary Borel measure. These papers treat functionals which involve only a single integral. In this paper, we obtain the stability theorems for the Feynman integral as an $L(L_1 (\mathbb{R}^N), L_{\infty}(\mathbb{R}^{N}))$theory for the functionals which involve double integral with some Borel measures.

• The Pure and Applied Mathematics
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• v.20 no.3
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• pp.149-158
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• 2013

In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS's) in the 3-dimensional Euclidean space $\mathbb{E}^3$. Surfaces of revolution, cylindrical surfaces and tubes along a plane curve are special cases of GSCS's. Our main results state that the only GSCS's with Gauss map G satisfying ${\Delta}G=AG$ for some $3{\times}3$ matrix A are the planes, the spheres and the circular cylinders.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.531-540
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• 2015

If T is an unbounded hyponormal operator on an infinite dimensional complex Hilbert space H with ${\rho}(T){\neq}{\phi}$, then it is shown that T satisfies Weyl's theorem, generalized Weyl's theorem, Browder's theorem and generalized Browder's theorem. The equivalence of generalized Weyl's theorem with generalized Browder's theorem, property (gw) with property (gb) and property (w) with property (b) have also been established. It is also shown that a-Browder's theorem holds for T as well as its adjoint $T^*$.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.479-487
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• 2009

Let $S(z_1,z_2),\;S_1(z_1,z_2)$ and $S_2(z_1,z_2)$ be power series with operator coefficients such that $S_(z_1,\;z_2)=S_1(z_1,z_2)S_2(z_1,z_2)$. Assume that the multiplications by $S_1(z_1,z_2)$ and $S_2(z_1,z_2)$ are contractive transformations in H($\mathbb{D}^2,\;\mathcal{C}$). Then the factorizations of spaces $\mathcal{D}(\mathbb{D},\;\tilde{S})$ and $\mathcal{D}(\mathbb{D}^2,\mathcal{S})$ are well-behaved.