• Honam Mathematical Journal
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• v.29 no.4
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• pp.523-533
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• 2007

Let $\cal{B}$ be a reflexive Banach space of functions analytic on the open unit disc and M be an invariant subspace of the multiplication operator by the independent variable, $M_z$. Suppose that $\varphi\;\in\;\cal{H}^{\infty}$ and $M_{\varphi}$ : M ${\rightarrow}$ M, defined by $M_{\varphi}f={\varphi}f$, is the operator of multiplication by ${\varphi}$. We would like to investigate the spectrum and the essential spectrum of $M_{\varphi}$ and we are looking for the necessary and sufficient conditions for $M_{\varphi}$ to be a Fredholm operator. Also we give a sufficient condition for a sequence $\{w_n\}$ to be an interpolating sequence for $\cal{B}$. At last the commutant of $M_{\varphi}$ under certain conditions on M and ${\varphi}$ is determined.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.920-923
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• 1996

This paper presents a new algorithm for the self-localization of a mobile robot using perspective invariant(Cross Ratio). Most of conventional model-based self-localization methods have some problems that data structure building, map updating and matching processes are very complex. Use of the simple cross ratio can be effective to the above problems. The algorithm is based on two basic assumptions that the ground plane is flat and two parallel walls are available. Also it is assumed that an environmental map is available for matching between the scene and the model. To extract an accurate steering angle for a mobile robot, we take advantage of geometric features such as vanishing points(V.P). Point features for computing cross ratios are extracted robustly using a vanishing point and the intersection points between floor and the vertical lines of door frames. The robustness and feasibility of our algorithms have been demonstrated through experiments in indoor environments using an indoor mobile robot, KASIRI-II(KAist SImple Roving Intelligence).

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.7
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• pp.577-582
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• 2013

In this paper Legendre wavelets are used to approximate the solutions of linear time-invariant system. The Legendre wavelet and its integral operational matrix are presented and an efficient algorithm to solve the Sylvester matrix equation is proposed. The algorithm is based on the decomposition of the Sylvester matrix equation and the preorder traversal algorithm. Using the special structure of the Legendre wavelet's integral operational matrix, the full order Sylvester matrix equation can be solved in terms of the solutions of pure algebraic matrix equations, which reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• Korean Journal of Computational Design and Engineering
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• v.19 no.2
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• pp.119-128
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• 2014

Computing the natural-looking interpolation of different shapes is a fundamental problem of computer graphics. It is proved by some researchers that such an interpolation can be achieved by pursuing the isometry. In this paper, a novel coordinate system that is invariant under isometries is defined. The coordinate system can easily be converted from the global vertex coordinates. Furthermore, the global coordinates can be efficiently recovered from the new coordinates by simply solving two sparse least-squares problems. Since the proposed coordinate system is invariant under isometries, then transformations such as global rigid trans-formations, articulated posture deformations, or any other isometric deformations, do not change the coordinate values. Therefore, shape interpolation can be done in this framework without being affected by the distortions caused by the isometry.

• Proceedings of the IEEK Conference
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• 2008.06a
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• pp.959-960
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• 2008

Recently, biometric authentication mechanism has been used to provide high level of security in cryptographic systems. In this paper, we propose an efficient method of generating invariant iris key to be applied in cryptographic systems. In order to generate iris key and improve the performance at the stolen token scenario, multiple random projection technique was combined with multiple linear transformation methods. From the experimental results, we proved that invariant iris keys were generated and the proposed method was robust to stolen token scenario.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.2
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• pp.123-130
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• 1999

In discrete-time controlled system, sampling time is one of the critical parameters for control performance. It is useful to employ different sampling rates into the system considering the feasibility of measuring system or actuating system. The systems with the different sampling rates in their input and output channels are named multirate system. Even though the original continuous-time system is time-invariant, it is realized as time-varying state equation depending on multirate sampling mechanism. By means of the augmentation of the inputs and the outputs over one period, the time-varying system equation can be constructed into the time-invariant equation. The two multirate formulations have some trade-offs in the simplicity to construct the controller, the control performance. It is good issue to determine the suitable formulation in consideration of performance of them. In this paper, the two categories of multirate formulations will be compared in terms of the linear quadratic (LQ) cost function. The results are used to select the multirate formulation and the sampling rates suitable to the desired control performance.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.4
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• pp.967-976
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• 1994

A tensor invariant model equation for the turbulent energy dissipation rate is proposed in the present study, which is able to simulate secondary straining effects such as curvature effects without the introduction of additional empirical input. The source term in this model has a combined form of the generation term due to the mean vorticity with the conventional one due to the mean strain rate. An extended low-Reynolds-number $k-\epsilon$ turbulence model involving this new model equation is tested for a turbulent Coutte flow between coaxial cylinders with inner cylinder rotated, which is a well defined example of curved flows. The predicted results indicate that the present model works much better for this flow, compared with previous models.

• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.639-642
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• 1999

There exist geometrically invariant relations in single-view images under a specific geometrical structure. This invariance may be utilized for 3D object recognition. Two types of invariants are compared in terms of the robustness to the variation of the feature points. Deviation of the invariant relations are measured by adding random noise to the feature point location. Zhu’s invariant requires six points on adjacent planes having two sets of four coplanar points, whereas the Kaist method requires four coplanar points and two non-coplanar points. Experimental results show that the latter method has the advantage in choosing feature points while suffering from weak robustness to the noise.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.49 no.1
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• pp.26-30
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• 2012

In this paper, we propose a signal generation method of rectangular QAM for rotationally invariant I/Q TCM. The proposed method consists of only digital logic gates without look-up table so that we can implement the system compactly. Our scheme can be applied to every rectangular QAM with the level higher than 64.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.545-551
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• 1996

It is well known in the theory of distributions and proved in [GS, S] that $$ (i) (Bochner-Schwartz) Every positive definite (tempered) distribution is the Fourier transform of a positive tempered measure \mu. $$ $$ (ii) (Schwartz kernel theorem) Let B(\varphi, \psi) be a bilinear distribution. Then for some u \in D'(R^n \times R^n) B(\varphi, \psi) = u(\varphi(x)\bar{\psi}(y)) for every \varphi, \psi \in C_c^\infty. $$ $$ (iii) A translation invariant positive definite bilinear distribution B(\varphi, \psi) is of the form B(\varphi, \psi) = \smallint \varphi(x)\psi(x) d\mu(x) for every \varphi, \psi \in C_c^\infty (R^n), where \mu is a positive tempered measure.