• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.473-498
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• 2015

The purpose of this study is to examine thinking process of the mathematically gifted students and how invariants affect the construction and discovery of curve when carry out activities that produce and reproduce the algebraic curves, mathematician explored from the ancient Greek era enduring the trouble of making handcrafted complex apparatus, not using apparatus but dynamic geometry software. Specially by trying research that collect empirical data on the role and meaning of invariants in a dynamic geometry environment and research that subdivide the process of utilizing invariants that appears during the mathematically gifted students creating a new curve, this study presents the educational application method of invariants and check the possibility of enlarging the scope of its appliance.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.799-814
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• 2009

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of some class invariants from the generalized Weber functions $\mathfrak{g}_0,\mathfrak{g}_1,\mathfrak{g}_2$ and $\mathfrak{g}_3$ over quadratic number fields with discriminant $D{\equiv}1$ (mod 12).

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.515-536
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• 2014

In the present study, we analyze four seventh grade students' recognition of geometric properties and the following justification processes while their adopting different construction approaches in GSP(Geometer's Sketchpad). As the students recognized dependency and level-1 invariants by dragging activities, they determined their own construction approaches. Two students, who preferred robust construction, immediately recognized the path of a draggable point and provided step-1 justification. The other students attempted soft construction followed by their recognition of level-2 invariants and the path, and came to step-2 justification.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.363-447
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• 2009

The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.

• Journal of Korea Multimedia Society
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• v.1 no.2
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• pp.173-182
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• 1998

As a result of remarkable developments in multimedia technology, the image database system that can efficiently retrieve image data becomes a core technology of information-oriented society. In this paper, we proposed the 2-phase Image Retrieval System considering both color and shape information as the method of image features extraction for content-based image data retrieval. At the first level, to get color information, with improving and extending the indexing method using color distribution characteristic suggested by Striker et al., i.e. the indexing method considering local color distribution characteristics, the system roughly classifies images through the improved method. At the second level, the system finally retrieves the most similar image from the image queried by the user using the shape information about the image groups classified at the first level. To extract the shape information, we use the Improved Moment Invariants (IMI) that manipulates only the pixels on the edges of objects in order to overcome two main problems of the existing Moment Invariant methods large amount of processing and rotation sensitiveness which can frequently be seen in the Directive Histogram Intersection technique suggested by Jain et al. Experiments have been conducted on 300 automobile images. And we could obtain the more improved results through the comparative test with other methods.

• Journal of the Korea Society of Computer and Information
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• v.5 no.2
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• pp.60-70
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• 2000

As a result of remarkable developments in computer technology, the image retrieval system that can efficiently retrieve image data becomes a core technology of information-oriented society. In this paper, we implemented the Hierarchical Image Retrieval System for content-based image data retrieval. At the first level, to get color information, with improving the indexing method using color distribution characteristic suggested by Striker et al., i.e. the indexing method considering local color distribution characteristics, the system roughly classifies images through the improved method. At the second level, the system finally retrieves the most similar image from the image queried by the user using the shape information about the image groups classified at the first level. To extract the shape information, we use the Improved Moment Invariants(IMI) that manipulates only the pixels on the edges of objects in order to overcome two main problems of the existing Moment Invariant methods large amount of processing and rotation sensitiveness which can frequently be seen in the Directive Histogram Intersection technique suggested by Jain et al. Experiments have been conducted on 300 automobile images And we could obtain the more improved results through the comparative test with other methods.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.921-925
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• 2011

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}21$ (mod 36).

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.853-860
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• 2010

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}-3$ (mod 36).

• The Journal of Information Technology and Database
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• v.5 no.1
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• pp.85-96
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• 1998

최근 멀티미디어 기술의 발전으로 인해 영상을 효율적으로 검색할 수 있는 영상 데이터베이스 시스템이 정보화 사회의 중요한 핵심 기술로 대두되고 있다. 본 논문에서는 내용기반 영상 데이터 검색을 위한 영상 특징 추출 방법으로 색상 정보와 모양 정보를 고려하는 다단계 영상 검색 시스템을 제안하였다. 제안된 시스템에서는 2단계로 이루어진다. 1단계에서는 색상 정보를 위해서 Striker 등이 제시한 색상 분포 특성을 이용한 색인 방법의 문제점을 보완하고 확장하여 지역 색상 분포 특성을 고려한 색인 방법을 사용하여 1차로 영상을 대 분류한다. 2단계에서는 1단계에서 대 분류된 집단 영상들에 대하여 2차로 모양 정보를 이용하여 사용자가 질의한 영상과 유사한 영상을 최종적으로 검색한다. 모양 정보를 위해서는 기존 불변 모멘트의 문제점인 많은 연산량과, Jain 등이 제시한 방향 히스토그램 인터섹션 방법에서 제기된 회전에 민감하다는 문제점을 해결하기 위해 물체의 윤곽선에 해당하는 화소들만을 대상으로 연산을 수행하는 향상된 불변 모멘트(Improved Moment Invariants: IMI)를 이용한다. 실험 영상으로 300개의 상표 영상을 사용하여 기존 방법들과의 비교 실험을 통해 향상된 검색 결과를 얻을 수 있었다.

• Proceedings of the Korea Database Society Conference
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• 1998.09a
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• pp.395-405
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• 1998

최근 멀티미디어 기술의 발전으로 인해 영상을 효율적으로 검색할 수 있는 영상 데이터베이스 시스템이 정보화 사회의 중요한 핵심 기술로 대두되고 있다. 본 논문에서는 내용기반 영상 데이터 검색을 위한 영상 특징 추출 방법으로 색상 정보와 모양 정보를 고려하는 다단계 영상 검색 시스템을 제안하였다. 1단계에서는 색상 정보론 얻기 위해서는 Striker 등이 제시한 색상 분포 특성을 이용한 색인 방법의 문제점을 보완하고 확장해서 지역 색상 분포 특성을 고려한 색인 방법을 사용하여 1차로 영상을 대분류한다. 2단계에서는 1단계에서 대분류된 집단 영상들에 대하여 2차로 모양 정보를 이용하여 사용자가 질의한 영상과 유사한 영상을 최종적으로 검색한다. 모양 정보를 얻기 위해서는 기존 불변 모멘트의 문제점인 많은 연산량과, Jain 등이 제시한 방향 히스토그램 인터섹션 방법에서 제기된 회전에 민감하다는 문제점을 해결하기 위해 물체의 윤곽선에 해당하는 화소들만을 대상으로 연산을 수행하는 향상된 불변 모멘트(Improved Moment Invariants : IMI)를 이용한다. 실험 영상으로 300개의 자동차 영상을 사용하여 기존 방법들과의 비교 실험을 통해 향상된 검색 결과를 얻을 수 있었다.