• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.243-246
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• 1988

Let M(z)=exp (-1+z/1-z) be the unit singular inner function. See [1] or [2] for the basic facts about inner functions. We define the iterations of M9z) as (Fig.) Since the composition M$_{2}$(z)=M.M(z) is known (see [5] for example) to be singular inner function it has the "cannonical" representation (Fig.) where .mu. is a finite, positive singular Borel measure on the unit circle T. In section 2, we have explicit cannonical representation of M$_{2}$(z) by determining the singular measure .mu. In section 3 we show that (Fig.) These facts might have been known but could not be found in the literature.iterature.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1669-1681
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• 2015

In this paper, we provide semi-convergence results of the parameterized inexact Uzawa method with singular preconditioners for solving singular saddle point problems. We also provide numerical experiments to examine the effectiveness of the parameterized inexact Uzawa method with singular preconditioners.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1173-1183
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• 2017

We give some sufficient conditions for the null and infinite derivatives of the $Riesz-N{\acute{a}}gy-Tak{\acute{a}}cs$ (RNT) singular function. Using these conditions, we show that the Hausdorff dimension of the set of the infinite derivative points of the RNT singular function coincides with its packing dimension which is positive and less than 1 while the Hausdorff dimension of the non-differentiability set of the RNT singular function does not coincide with its packing dimension 1.

• International Journal of Control, Automation, and Systems
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• v.5 no.1
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• pp.86-92
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• 2007

In this paper, we first establish $D_L$-admissibility and $D_R$-admissibility conditions for singular systems. The admissibility conditions expressed as Lyapunov type inequalities extend the existed results of normal systems to singular systems. As special cases the admissibility conditions of the continuous-time and the discrete-time singular systems can be obtained directly. The results established in this paper can be applied to solve the problems of eigenvalue assignment, regional pole-placement and robust control etc.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.1135-1143
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• 2007

The singular value decomposition and the spectral decomposition are the useful methods in the area of matrix computation for multivariate techniques such as principal component analysis and multidimensional scaling. These techniques aim to find a simpler geometric structure for the data points. The singular value decomposition and the spectral decomposition are the methods being used in these techniques for this purpose. In this paper, the singular value decomposition and the spectral decomposition are compared.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.6
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• pp.780-785
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• 1998

In this paper, it is shown that the conventional methods for dealing with the singularity problem of a manipulator can be generalized as a local minimization problem with differently weighted objective functions. A new damping method proposed in this article automatically determines the damping amounts for singular values, which are inversely proportional to the magnitude of the singular values. Furthermore, this can be done without explicitly computing the singular values. The proposed method can be applied to all the manipulators with revolute joints.

• Communications for Statistical Applications and Methods
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• v.17 no.6
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• pp.803-810
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• 2010

The singular value decomposition of a rectangular matrix is a basic tool to understand the structure of the data and particularly the relationship between row and column factors. However, conventional singular value decomposition used the least squares method and is not robust to outliers. We propose a simple robust singular value decomposition algorithm based on the weighted least absolute deviation which is not sensitive to leverage points. Its implementation is easy and the computation time is reasonably low. Numerical results give the data structure and the outlying information.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.657-661
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• 2010

We study a singular function which we call a generalized cylinder convex(concave) function induced from different generalized dyadic expansion systems on the unit interval. We show that the generalized cylinder convex(concave)function is a singular function and the length of its graph is 2. Using a local dimension set in the unit interval, we give some characterization of the distribution set using its derivative, which leads to that this singular function is nowhere differentiable in the sense of topological magnitude.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.482-485
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• 1993

This paper deals with structured singular value and mixed sensitivity problem for robust performance. We derive the sufficient condition that mixed sensitivity problem satisfies structured singular value in robust performance problem. And we show the bound of perturbation between structured singular value and norm of mixed sensitivity functions.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.191-202
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• 2022

In this paper, we obtain the quantitative weighted bounds of oscillatory singular integral with rough kernel. Moreover, the quantitative weighted bounds of maximally truncated oscillatory singular integral with rough kernel are also obtained.