• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2071-2093
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• 2015

In this paper, we investigate the similarity transformations in the Minkowski n-space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion of ${\mathbb{E}}_1^n$. We determine the parametrizations of non-null self-similar curves in ${\mathbb{E}}_1^n$.

• East Asian mathematical journal
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• v.23 no.2
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• pp.207-212
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• 2007

We describe the class of invertible matrices T such that $TAT^{-1}$ is EPr, for a given EPr matrix A of order n. Necessary and sufficient condition is determined for $TAT^{-1}$ to be EP for an arbitrary matrix A of order n.

• KIEE International Transaction on Systems and Control
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• v.12D no.1
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• pp.7-11
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• 2002

In this study, fur the shape-based image retrieval, a method using local differential invariants is proposed. This method calculates the differential invariant feature vector at every feature point extracted by Harris comer point detector. Then through vector quantization using LBG algorithm, all feature vectors are represented by a codebook index. All images are indexed by the histogram of codebook index, and by comparing the histograms the similarity between images is obtained. The proposed method is compared with the existing method by performing experiments for image database including various 1100 trademarks.

• The KIPS Transactions:PartB
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• v.14B no.4
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• pp.263-272
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• 2007

This paper proposes a skeleton-based hierarchical shape description scheme, called a skeleton tree, for accurate shape-based image retrieval. A skeleton tree represents an object shape as a hierarchical tree where high-level nodes describe parts of coarse trunk regions and low-level nodes describe fine details of boundary regions. Each node refines the shape of its parent node. Most of the noise disturbances are limited to bottom level nodes and the boundary noise is reduced by decreasing weights on the bottom levels. The similarity of two skeleton trees is computed by considering the best match of a skeleton tree to a sub-tree of another skeleton tree. The proposed method uses a hybrid similarity measure by employing both Fourier descriptors and moment invariants in computing the similarity of two skeleton trees. Several experimental results are presented demonstrating the validity of the skeleton tree scheme for the shape description and indexing.

• Journal for History of Mathematics
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• v.34 no.2
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• pp.39-54
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• 2021

One of the topics in school mathematics is the relation between the roots and the coefficients of equations. It deals with the way to find the roots out of the coefficients of equations. One of the concepts derived from the theory of equations is symmetric functions. Symmetry is a kind of functionality of human cognition. It is, in mathematics, geometrically related to the congruence and the similarity of figures, and algebraically a kind of invariants. We look at stories on the appearance of symmetric functions through the development of the theory of equations.