• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.437-456
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• 2003

In this paper we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish a Fubini theorem for the function space integral and generalized analytic Feynman integral of a functional F belonging to Banach algebra $S(L^2_{a,b}[0,T])$ and we proceed to obtain several integration formulas. Finally, we use this Fubini theorem to obtain several Feynman integration formulas involving analytic generalized Fourier-Feynman transforms. These results subsume similar known results obtained by Huffman, Skoug and Storvick for the standard Wiener process.

• Journal for History of Mathematics
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• v.26 no.4
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• pp.245-257
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• 2013

Hermann Grassmann classified mathematics and extended the dimension of vector spaces by using dialectics of contrasts. In this paper, we investigate his mathematical idea and its background, and the process of the classification of mathematics. He made a synthetic concept of mathematics based on his idea of 'equal' and 'inequal', 'discrete' and 'indiscrete' mathematics. Also, he showed a creation of new mathematics and a process of generalization using a dialectic of contrast of 'special' and 'general', 'real' and 'formal'. In addition, we examine his unique development in using 'real' and 'formal' in a process of generalization of basis and dimension of a vector space. This research on Grassmann will give meaningful suggestion to an effective teaching and learning of linear algebra.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.459-469
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• 2008

We give a mathematical approach using Linear Algebra, especially largest eigenvalue and eigenvector on decision making support system. We find a mathematical modeling on decision making problem which could be solved by AHP(Analytic Hierarchy Process) method. Especially, we give a new approach to change evaluation indicator weight on assessing research proposals.

• The Journal of the Korea Contents Association
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• v.11 no.9
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• pp.63-75
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• 2011

A number of process algebras have been proposed to develop distributed mobile real-time systems: pi-Calculus, Mobile Ambients Calculus, Bigraph, etc. However, as the systems get large and complex, the algebras become less suitable for understanding the interactions and mobility of the processes of the systems due to the size and complexity. Therefore it is necessary to handle the size and complexity for systematic understanding of the systems. This paper handles the size and complexity with a method of abstraction on sequences of interactions and movements of processes in the systems, which can be further organized in the form of hierarchically structured lattices, namely, Prism. The theoretical principle of the abstraction is based on a new concept of Behavior Ontology, which is extended from Active ontology. Prism allows the systems to be analyzed in the perspective of the lattices in Prism, which are characterized by the hierarchically organized behavioral properties of the developing systems, for systematic understanding the systems. In this way, the complexity of the interactions and the movements can be handled systematically in the semantically and hierarchically organized structure of the behavior.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.12B
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• pp.2249-2261
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• 1999

In this paper, we describe the design and implementation of the Label Distribution Protocol (LDP) for Multiprotocol Label Switching System. We review the implementation issues of LDP that is required to make a gigabit switched router, and propose a detail design of it. We present the data structures and procedures for the LDP as a result, which are based on IETF standard. We present design issues for applying this to carrier class products. The implemented protocol could afford 40,000 entries of the IP routing table that is required for deploying this system to commercialized data network. Furthermore this system implemented using the standard API of Unix, as a result, it has portability. By implementing LDP based on the international standard and these implementation issues, we expect that the implemented LDP will be interoperable with other commercialized products. We prove the validity of the design of the LDP through prototyping, and also verify the prototype with the specification using the process algebra and the performance analysis.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.5_6
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• pp.335-346
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• 2004

PtolemyII is an environment that supports heterogeneous modeling and design of concurrent systems such as embedded system. PtolemyII has several Domains which are physical rules to determine the way of communicating between components. PtolemyII has 11 domains such as PetriNet, Timed Multitasking, SR etc. Components of System can be specified using appropriate domains for their properties. Communicating Sequential Processes(CSP) is implemented as formally designed CSP domain, in PtolemyII. But CCS didn't be implemented as a domain. It is a kind of Process Algebra language which can be used for specifying and verifying concurrent systems formally. Thus, in this paper we implemented CCS domain. And that permitted developers using PtolemyII to use the same modeling pattern used in PtolemyII and to make system specifications in the base of the formal semantics of CCS. This caused the diversity of PtolemyII domains and the power of expression was improved. This paper will explain the structure of CCS domain implemented in PtolemyII and the way of implementing it.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.323-340
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• 2021

The purpose of this case study is to explore the similarities revealed in the process of solving and generalizing word problems related to systems of linear equations in two variables according to covariational reasoning. As a result, student S, who reasoned with coordination of value level, had a static image of the quantities given in the situation. student D, who reasoned with smooth continuous covariation level, had a dynamic image of the quantities in the problem situation and constructed an invariant relationship between the quantities. The results of this study suggest that the activity that constructs the relationship between the quantities in solving word problems helps to strengthen the mathematical problem solving ability, and that teaching methods should be prepared to strengthen students' covariational reasoning in algebra learning.

• KIPS Transactions on Computer and Communication Systems
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• v.11 no.9
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• pp.289-304
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• 2022

It is necessary to apply process algebra and logic in order to analyze and verify safety requirements for Smart IoT Systems due to distributivity and mobility of the systems over some predefined geo-temporal space. However the analysis and verification cannot be fully intuitive over the space due to the fact that the existing process algebra and logic are very limited to express the distributivity and the mobility. In order to overcome the limitations, the paper presents a new logic, namely for GTS-VL (Geo-Temporal Space-Visual Logic), visualization of the analysis and verification over the space. GTS-VL is the first order logic that deals with relations among the different types of blocks over the space, which is the graph that visualizes the system behaviors specified with the existing dTP-Calculus. A tool, called SAVE, was developed over the ADOxx Meta-Modeling Platform in order to demonstrate the feasibility of the approach, and the advantages and practicality of the approach was shown with the comparative analysis of PBC (Producer-Buffer-Consumer) example between the graphical analysis and verification method over the textual method with SAVE tool.

• Journal of the Korean Operations Research and Management Science Society
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• v.30 no.2
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• pp.73-80
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• 2005

In this paper, we consider characteristics of waiting times in s1n91e-server 3-node tandem queues with finite buffers, a Poisson arrival process and deterministic service times at all nodes. There are three buffers : one at the first node is infinite and the others are finite. We obtain the fact that sojourn time or departure process is independent of the capacities of the finite buffers and does not depend on the order of service times, which are the same results in the literature. Moreover, the explicit expressions of stationary waiting times in all areas of the systems can be derived as functions of the finite buffer capacities. We also disclose a relationship of waiting times in subareas of the systems between two blocking policies communication and manufacturing. Some numerical examples are also provided.

• Proceedings of the Korean Information Science Society Conference
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• 2000.10a
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• pp.474-476
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• 2000

소프트웨어 프로젝트의 비용의 대부분이 구현(implementation) 단계나 테스트 단계에서의 에러 수정에 소모되고 있으며, 이러한 에러들의 대부분은 프로젝트 개발 초기 단계에서의 부정확(imprecision)에 기안한 것이다. 정형 명세 기법은 명세 단계에서 기인하는 에러들을 줄이기 위해 Z나 VDM과 같은 정형 표기법에 의해 쓰여진다. 그러나, Z 표기법의 병행성 표현 능력의 부족으로 병행성을 요구하는 시스템의 명세에서 사용할 수 없거나, Process Algebra의 CSP(Communicating Sequence Processes)등과 같은 다른 정형 언어와 함께 명세해야 하는 단점이 있다. 본 연구에서는 Z와 같은 범용 목적의 명세 언어가 병행성(concurrency)을 표현할 수 있도록 하기 위해서, 병행 프로세서(concurrent process) 개념을 도입하며, 이를 나타내는 표기를 정의하고 사용한다. 또한, 병행성의 제어를 위해서 프로시듀어 기술부(procedure description)의 도입 및 관련 스키마(schema)들을 정의한다.