• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.387-400
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• 2014

We prove that the set of k-type nonwandering points of a Z2-action T can be decomposed into a disjoint union of closed and T-invariant sets $B_1,{\ldots},B_l$ such that $T|B_i$ is topologically k-type transitive for each $i=1,2,{\ldots},l$, if T is expansive and has the shadowing property.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.3
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• pp.177-182
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• 2013

This paper proposes an input-constrained reference tracking control of a converter model. To this end, first it is shown that the bilinear converter model can be equivalently represented by a linear uncertain model belonging to a polytopic set. Then, an input-constrained tracking control scheme for the linear uncertain model is designed based on recently proposed tracking control scheme. The control scheme yields not only a stabilizing control gain but also a feasible and invariant set for the converter model. Finally, simulation results show that the state trajectory always stays in the feasible and invariant set and that the output tracks the given reference while satisfying the input constraint.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.163-191
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• 2002

We introduce Clapp-Puppe type generalized Lusternik-Schnirelmann (co)category in a Quillen model category. We establish some of their basic properties and give various characterizations of them. As the first application of these characterizations, we show that our generalized (co)category is invariant under Quillen modelization equivalences. In particular, generalized (co)category is invariant under Quillen modelization equivalences. In particular, generalized (co)category of spaces and simplicial sets coincide. Another application of these characterizations is to define and study rational cocategory. Various other applications are also given.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.17-39
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• 2013

The study of nonlinear discrete-time control dynamical systems with disturbance is an important topic in control theory. In this paper, we concentrate our efforts to multiple valued iterative dynamical systems, which model the nonlinear discrete-time control dynamical systems with disturbance. After establishing the validity of such modeling, we study the invariant set theory of the multiple valued iterative dynamical systems, including the controllability/reachablity problems of the maximal invariant sets.

• International Journal of Control, Automation, and Systems
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• v.6 no.6
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• pp.800-808
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• 2008

A fingerprint verification system based on a set of invariant moment features and a nonlinear Back Propagation Neural Network(BPNN) verifier is proposed. An image-based method with invariant moment features for fingerprint verification is used to overcome the demerits of traditional minutiae-based methods and other image-based methods. The proposed system contains two stages: an off-line stage for template processing and an on-line stage for testing with input fingerprints. The system preprocesses fingerprints and reliably detects a unique reference point to determine a Region-of-Interest(ROI). A total of four sets of seven invariant moment features are extracted from four partitioned sub-images of an ROI. Matching between the feature vectors of a test fingerprint and those of a template fingerprint in the database is evaluated by a nonlinear BPNN and its performance is compared with other methods in terms of absolute distance as a similarity measure. The experimental results show that the proposed method with BPNN matching has a higher matching accuracy, while the method with absolute distance has a faster matching speed. Comparison results with other famous methods also show that the proposed method outperforms them in verification accuracy.

• The Transactions of the Korea Information Processing Society
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• v.3 no.7
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• pp.1894-1905
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• 1996

Delauuany triangulation which is the dual of Dirichlet tessellation is not affine invariant. In other words, the triangulation is dependent upon the choice of the coordinate axes used to represent the vertices. In the same reason, Delahanty tetrahedrization does not have an affine iveariant transformation property. In this paper, we present a new type of tetrahedrization of spacial points sets which is unaffected by translations, scalings, shearings and rotations. An affine invariant tetrahedrization is discussed as a means of affine invariant 2 -D triangulation extended to three-dimensional tetrahedrization. A new associate norm between two points in 3-D space is defined. The visualization of the structure of tetrahedrization can discriminate between Delaunay tetrahedrization and affine invariant tetrahedrization.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.397-408
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• 1998

We often use the Hausdorff dimension as a tool of measuring how complicate the fractal is. But it is usually very difficult to calculate that value. So there have been many tries to find the dimension of the given set and most of these are related to the density theorem of invariant measure. The aims of this paper are to introduce the k-irreducible subsimilar sets as a generalization of the set defined by V.Drobot and J.Turner in ([1]) and calculate their Hausdorff dimensions by using algebraic methods.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.2
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• pp.157-160
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• 2003

In this paper, we describe how to represent lower case hand-written English alphabets by a sequence of two to seven fuzzy sets. Each fuzzy set represents an arc segment of the character and each arc segment is assumed to be a part of an ellipse. The part of an ellipse is defined by five quantities; its short and long radii, its orientation angle, whether it is a part of the lower half or the upper half, and whether it is the full half or a part of a half. Hence, we use the Cartesian product of five fuzzy sets to represent each arc segment. We show that this representation is a translation, rotation, and scaling invariant and that it can be used to generate the hand-written English alphabets. The representation we describe is different from the one proposed earlier by the author and when compared with the previous representation, the one described in this paper simulates more closely the behavior of how one writes English characters.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.371-381
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• 2021

In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet frame sets in locally compact abelian groups. The condition is generated by modulating a collection of characteristic functions that correspond to a generalized shift-invariant system via the Fourier transform. We present two approaches (for stationary and non-stationary wavelets) to construct the scaling function for L²(G) and, using the scaling function, we construct an orthonormal wavelet basis for L²(G). We propose an open problem related to the extension principle for Riesz wavelets in locally compact abelian groups.