• Management Science and Financial Engineering
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• v.14 no.1
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• pp.23-34
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• 2008

In this study, we consider stationary waiting times in a Poisson driven single-server m-node queues in series. We assume that service times at nodes are independent, and are either deterministic or non-overlapped. Each node excluding the first node has a finite waiting line and every node is operated under a FIFO service discipline and a communication blocking policy (blocking before service). By applying (max, +)-algebra to a corresponding stochastic event graph, a special case of timed Petri nets, we derive the explicit expressions for stationary waiting times at all areas, which are functions of finite buffer capacities. These expressions allow us to compute the performance measures of interest such as mean, higher moments, or tail probability of waiting time. Moreover, as applications of these results, we introduce optimization problems which determine either the biggest arrival rate or the smallest buffer capacities satisfying probabilistic constraints on waiting times. These results can be also applied to bounds of waiting times in more general systems. Numerical examples are also provided.

• The KIPS Transactions:PartD
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• v.16D no.3
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• pp.339-352
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• 2009

There are a number of formal methods for distributed real-time systems in ubiquitous computing to analyze and verify the behavioral, temporal and the spatial properties of the systems. However most of the methods reveal structural and fundamental limitations of complexity due to mixture of spatial and behavioral representations. Further temporal specification makes the complexity more complicate. In order to overcome the limitations, this paper presents a new formal method, called Timed Calculus of Abstract Real-Time Distribution, Mobility and Interaction(t-CARDMI). t-CARDMI separates spatial representation from behavioral representation to simplify the complexity. Further temporal specification is permitted only in the behavioral representation to make the complexity less complicate. The distinctive features of the temporal properties in t-CARDMI include waiting time, execution time, deadline, timeout action, periodic action, etc. both in movement and interaction behaviors. For analysis and verification of spatial and temporal properties of the systems in specification, t-CARDMI presents Timed Action Graph (TAG), where the spatial and temporal properties are visually represented in a two-dimensional diagram with the pictorial distribution of movements and interactions. t-CARDMI can be considered to be one of the most innovative formal methods in distributed real-time systems in ubiquitous computing to specify, analyze and verify the spatial, behavioral and the temporal properties of the systems very efficiently and effectively. The paper presents the formal syntax and semantics of t-CARDMI with a tool, called SAVE, for a ubiquitous healthcare application.

• Asia pacific journal of information systems
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• v.12 no.2
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• pp.99-118
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• 2002

In this paper, we propose a visual relational database query language, VRQL, by modifying and extending the recently proposed $VOQL^*$. Like $VOQL^*$, VRQL, based on ven Diagram and graph, naturally reflects the structure of schemas in queries and has recursive formal semantics. However, VRQL has relationally complete expressiveness, while $VOQL^*$ is only a conjunctive query language. In the logical definition part of VRQL, which is the relational version of $VOQL^*$, most features of $VOQL^*$ are retained, and the semantics of queries are based on the tuple relational calculus. In the procedural definition part of VRQL, by introducing the concept of VRQL view and set operations, the expressiveness of VRQL is increased to the level equivalent to that of the relational algebra. Due to the introduction of VRQL views, existing queries or temporary queries used in the process of creating queries can be represented with views, so that complex queries may be represented more conveniently. Set operations, used with VRQL views, enable us to represent various queries, beyond the expressiveness of conjunctive query languages.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.47
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• pp.219-232
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• 1998

A lot of difficulties exist in analyzing the structure of a system owing to the complex and organic relations in the systems we face in reality. Focuses have been put on the research of optimal solution in a defined structure, however, on the assumption that the structure of the system has been already defined. With the grasping of the structure as the most prior condition, ISM(Interpretive Structural Modeling) and FSM(Fuzzy Structural Modeling) are suggested as solutions in this paper. ISM uses the systematic application of some elementary notions of graph theory and boolean algebra, FSM uses Fuzzy conception for representing relationship between elements. In FSM, the entries in the relation matrix are taken to value on the interval [0,1] by virtue of a fuzzy binary relation. Numeric examples are used as the actual application as follows.

• Journal of Educational Research in Mathematics
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• v.20 no.2
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• pp.185-202
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• 2010

This study was designed to investigate the possibility that the optimization problem solving activities based on the instrumented CAS can have an influence on the sequence of mathematics curriculum in secondary mathematics education. Some optimization problem solving activities based on CAS were constructed and executed to eleventh grade(the penultimate year of Korean high school) 7 students for nine class hours. They have experienced using CAS in mathematics class for three months, but never learned calculus. The data which consists of classroom observations(audio and video taped) and post-unit interviews with students were analyzed. In the analysis, with CAS, students can highly deal with the applied optimization problems made up of calculus, cubic equation, solution of radical equation, and graph analysis which never learned. This result shows CAS may have an influence on the sequence of mathematics curriculum in secondary mathematics education.

• 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.

• 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.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.58 no.3
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• pp.316-322
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• 2009

This paper presents an analytical design method of a passive harmonic filter for a three-phase diode rectifier and uses a new transfer function approach in the analysis and design. The transfer function approach derives an analytical formulation of an utility system including passive filters with a basis of Laplace transform and provides a graphical formulation so that a visualized insight into an interaction between individual filter and system response can be attainted. Harmonic impedance, voltage division and current division transfer function are used as a design tool, which makes a calculated filter parameters to satisfy IEEE-519 distortion limits. A simple five-step design procedure is introduced in the filter design, which consists of system analysis, selection of PCC(Point of Common Coupling), filter specification calculation, appropriate filter design for system and filter implementation. Philosophy governing the design procedure is based on a numerical/graphical iterative solution, trial and error with visualization feed-back based on "algebra on the graph". Finally, performance of the designed passive harmonic filter is verified by experiment and shows that 5th, 7th, 9th, 11th and 13th harmonics are decreased within IEEE-519 distortion limits, respectively.

• The KIPS Transactions:PartD
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• v.11D no.4
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• pp.929-936
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• 2004

A major limitation of available component-based platforms Is that they do not provide suitable means for describing and reasoning on the concurrent behaviour of interacting component-based system. Indeed while these platforms provide convenient ways to describe the typed signatures of components, e.g. like CORBA's IDL, they offer a quite low-level support to describe the concurrent behaviour of component. The ability to describe and verify the concurrent behaviour of interacting components is key aspect In the development of large component-based software system. This study propose a component interface specification using process algebra and configuration's role which allows one to prove correctness of software architecture generated at design level as well as to define compatibility relations by our evolution rule and $\pi$-graph. Also, we shown on an appropriateness of a specification techniques and definitions proposed in this paper by case-study.

• The Mathematical Education
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• v.53 no.1
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• pp.25-40
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• 2014

Mathematical concept exists in the structural form, not in the independent form. The purpose of this study is to consider the network which students actually have for the mathematical concept structure related to the properties of derivatives. First, we analyzed the properties of derivatives in 'Mathematics II' and showed the mathematical concept structure of the relations among derivatives, functions, and primitive functions as a network. Also, we investigated the understanding of high school students for the mathematical concept structure between derivatives and functions, and the structure between functions and second order derivatives when the functional formula is not given, and only the graph is given. The results showed that students mainly focus on the relation of 'function-derivatives', the thinking process for direction of derivative and the thinking style for algebra. On this basis, we suggest the educational implication that is necessary for students to build the network properly.