• 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 Internet Computing and Services
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• v.12 no.6
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• pp.149-159
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• 2011

The current applications can be characterized as consisting of complex objects related by complex relationship. Therefore the relational database has been extended to object-relational database because of the complex objects. Accordingly, we need database design methodology for object-relational database. In this pager, we develop an integrated design methodology based on a extended UML class diagram for object-relational database. We make the extend UML class diagram by adding new stereotypes for object-relational database. Also we propose a guideline for transforming the extended UML class diagram to object-relational database schema. We use SQL:1999 as a object-relational data model and Oracle11g as a target object-relational database. We can build more easily and efficiently object-relational database for Oracle11g by using our methodology. Finally we applied our methodology on a computer classroom reservation system for evaluation the methodology.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.23 no.12
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• pp.1588-1595
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• 2019

This paper presents the technique on structuring information of the diagram repository for UML diagrams. Because object interactions are the body of object-oriented programming, this paper handles especially the sequence diagrams and class diagrams among UML diagrams. Based on class diagrams, sequence diagrams represent the procedure of object interactions in run-time and then the corresponding codes are generated from the contents of those sequence diagrams. To do this work, this paper presents a method to construct the information repository for generating code from the contents of sequence diagrams. This paper classifies the five message types of sequence diagrams and then extracts the needed information including items and values on the corresponding message types for constructing message repositories. Because sequence diagram is composed of messages included, the final repository is constructed by collecting each of structured repositories on messages sequentially.

• The Transactions of the Korea Information Processing Society
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• v.7 no.3
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• pp.818-830
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• 2000

Automation tools for program analysis are needed in order to program understand and maintain, extract the characteristics of object-oriented program such as class name, member function and data member. In this paper, we carried out design and implementation of the automation tool for effective maintenance of object-oriented software. Being based on Reverse Engineering, this approach extracts class relationship information from C++ source code and generates object-oriented model of class diagram using UML as the standard object-oriented methodology. Therefore, this paper provides developers visualized including class information, definitions of classes, inheritance relationships, set relationships, and simple reference relationships. Finally in this paper, we propose a method that construct class relationship information to table in analysis state and make form of table construction to link form so tat developers can perform understanding and maintaining program efficiently. And this method enable to restructure and reuse in object-oriented model.

• Journal of the Korea Society of Computer and Information
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• v.16 no.11
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• pp.25-34
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• 2011

In this paper we present an integrated design methodology for relational database based on object-oriented analysis and design. The integrated design methodology is based on business profile and has six phases. In the first phase, business use cases are identified and described by macroactivity diagrams and then the macroactivity diagrams are transformed to detailed business activity diagrams by using objects, object flows and business worker's responsibilities. In the third phase, the detailed business activity diagrams are transformed to business class diagrams that describe the static structure of the entire business system based on detailed business activity diagrams. In the four phase, the business class diagrams are transformed to class diagrams that represent the initial conceptual model of the target relational database. In the five phase, we add additional transformations on the class diagrams with generalization and specialization of associations, roles, activities, additional classes and redundant associations. Eventually, the final class diagrams are transformed to relational database schema. The methodology presented in this paper by applying that proposal for organic connection between object-oriented analysis and design methodology and relational database design methodology. And it will be able to deal with integration management. By the integrated design methodology, we can make more easily software systems based on relational database. In the case study, proposal integrated design methodology applied for a visa issuing system.

• Journal of Korea Water Resources Association
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• v.35 no.5
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• pp.597-609
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• 2002

This study suggests a methodology of hydrologic decision making for the establishment of a standard of drought management from the drought analysis by the past drought history and for the drought monitoring and management according to drought processing. The construction and analysis of a decision tree diagram are performed and the step by step plan according to drought severity is suggested. Say, the decision tree diagram is constructed by the transition probability and quantity of monthly precipitation. Then the drought processing is investigated by the analysis of diagram and the 3-step of drought notice, drought warning, and emergency plan are established. The suggested methology in this study can be used for the other area and the decision tree diagram be used by changing the diagram according to the utilization purposes. Also, the choice of monthly PDSI class and precipitation analysis can be performed by the continuous data supplement. And so, a new standard value by the modified diagram is provided and the continuous drought management will be possible.

• The KIPS Transactions:PartD
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• v.19D no.1
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• pp.39-48
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• 2012

In order to quickly understand which changes of source codes have been made and to perform effective maintenance of a system, it is important to visualize the changed parts. Although there are many works for analyzing software changes, there are few works for visualizing both of the change types and change quantifications for Java based systems. In this paper, we propose a change analysis technique based on class diagram and provide a change visualization technique by using change quantification information. In order to check the structural changes in source codes, source codes are transformed to class diagrams by reverse engineering methods. On the class diagrams, the changes are analyzed and quantified by numbers. Based on the change quantification, the changes are visualized on the class diagram by color spectrum. By using visualization techniques, maintainers can easily recognize the code changes to reduce the cost and time of maintenance.

• Proceedings of the Korea Multimedia Society Conference
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• 2002.11b
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• pp.368-372
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• 2002

XML 문서의 구조를 파악하기 위하여 현재 많은 연구가 진행 되고 있으며, 대부분 XML 문서의 구조를 찾아 DTD나 스키마로 표현하는데 중점을 두고 있다. 본 논문에서는 XML 문서에서 구조를 추출하여 이를 UML 클래스 다이어그램으로 자동 변환하는 시스템을 제안한다. 제안된 시스템에서는 XML 문서로부터 요소-속성 트리를 구성하고, 이를 활용하여 문서 구조를 UML 클래스 다이어그램으로 쉽게 변환하도록 한다.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.119.4-119
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• 2002

$\textbullet$ Intoduction : Control architecture of PSR $\textbullet$ Layered functionality diagrams $\textbullet$ Class diagrams $\textbullet$ Petri-net based configuration diagram $\textbullet$ Experiments $\textbullet$ Conclusions

• The Mathematical Education
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• v.22 no.1
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• pp.21-23
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• 1983

(1) Let f : XlongrightarrowX' be a homomorphism of BCK-algebras and let A,B be ideals of X and X' respectively such that f(A)⊂B. Then there is a unique homomorphism h : X/AlongrightarrowX'/B such that the diagram(equation omitted) commutes. (2) The class of all complexes of BCK-algebras becomes a category.