• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1635-1646
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• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.293-302
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• 2001

We improve the greedy algorithm which is one of the general convergence criterion for certain iterative sequence in a given space by building a constructive greedy algorithm on a normed linear space using an arithmetic average of elements. We also show the degree of approximation order is still $Ο(1\sqrt{\n}$) by a bounded linear functional defined on a bounded subset of a normed linear space which offers a good approximation method for neural networks.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1421-1441
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• 2017

We compute explicitly the matrix represented by the Toeplitz operator on the Hardy space over a smoothly finitely connected bounded domain in the plane with respect to special orthonormal bases consisting of the classical kernel functions for the space of square integrable functions and for the Hardy space. The Fourier coefficients of the symbol of the Toeplitz operator are obtained from zeroth row vectors and zeroth column vectors of the matrix. And we also find some condition for the product of two Toeplitz operators to be a Toeplitz operator in terms of matrices.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.4
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• pp.207-211
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• 2004

We consider a class of uncertain nonlinear systems containing the uncertainties without a priori information except that they are bounded. For such systems, we assume that the upper bound of the uncertainties is represented as a Fredholm integral equation of the first kind and we propose an adaptation law that is capable of estimating the upper bound. Using this adaptive upper bound, a continuous robust control which renders uncertain nonlinear systems uniformly ultimately bounded is designed.

• Journal of Integrative Natural Science
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• v.6 no.3
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• pp.181-182
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• 2013

In this note, we are concerned with a class of semi-linear elliptic pdes with exponential nonlinearity in a bounded domain. Here, the nonlinearity is more or less growing exponentially with power p. We consider the problem under two types of Dirichlet boundary condition. We give existence and non-existence of solutions for those problems and some asymptotics.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.889-894
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• 1993

This paper presents a robust adaptive control scheme based on the Lyapunov design for robot manipulators subjected to inertial parameter uncertainties and bounded torque disturbances. The scheme is a modified version of the adaptive computed torque method which adopts a dead zone into the adaptation mechanism so as to avoid parameter drifts by disturbances. It is shown via stability analysis and computer simulations that all the signals in the overall adaptive system are bounded and tracking errors lie within a prespecified bound.

• Transactions on Control, Automation and Systems Engineering
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• v.3 no.2
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• pp.83-88
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• 2001

The robust linear H(sub)$\infty$ FIR filter, which guarantees a prescribed H(sub)$\infty$ performance, is designed for continuous time-varying systems with unknown cone-bounded nonlinearity. The infinite horizon filtering for time-varying systems is systems is investigated in therms of two Riccati equations by the finite moving horizon.

• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.273-275
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• 1992

A dynamic system containing uncertain elements is considered. The upper bound of the values of these uncertainties is estimated. Using the estimated value a bounded error state feedback control is proposed based on Corless and Leitmann's result [1].

• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.901-908
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• 1988

In machining die cavities or mechanical parts, we often encounter the needs to remove a material within a given boundary. Even though this pocket cutting capability has been implemented in many NC packages, most of them can handle convex shaped pockets bounded by curves of limited types and numbers. In this work, a procedure has been developed to machine pockets of a free surface bounded by lines, circular arcs and free curves. Also, the cutter location data is computed directly without using iterative method for better computational efficiency.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.483-488
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• 1989

In this paper, the concept of persistent excitation(PE) is examed and the model reference adaptive control of a linear plant subjected to bounded disturbances is considered. Computer simulation reasults of nonlinear differential equations shows that the global behavior of the adaptive system depends upon the PE of the reference input as well as the amplitude of the external disturbances. The sufficient conditions on the PE of the reference input for the signals in the adaptive system to be globally bounded has been derived.