• East Asian mathematical journal
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• v.37 no.4
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• pp.401-426
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• 2021

In order to propose ways to implement mathematical connection between algebra and geometry, this study reinterpreted and visualized the Khayyam's geometric method solving the cubic equations using two conic sections and the Al-Kāshi's method of constructing of angle trisection using a cubic equation. Khayyam's method is an example of a geometric solution to an algebraic problem, while Al-Kāshi's method is an example of an algebraic a solution to a geometric problem. The construction and property of conics were presented deductively by the theorem of "Stoicheia" and the Apollonius' symptoms contained in "Conics". In addition, I consider connections that emerged in the alternating process of algebra and geometry and present meaningful Implications for instruction method on mathematical connection.

• School Mathematics
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• v.10 no.2
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• pp.297-317
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• 2008

This study was designed to gain insight to adopt CAS into secondary level algebra education in Korea. Most inactive usage of calculators in math and most negative effects of calculators on their achievements of Korean students were shown in International studies such as TIMSS-R. A comparative study was carried out with consideration of mathematical backgrounds and technological environments. 8 Korean students and 26 US students in Grade 11 were participated in this study. Subjects' Problem solving process and their strategies of CAS usage in classical Box-problem with CAS were analyzed. CAS helped modeling by providing symbolic manipulation commands and graphs with students' mathematical knowledge. Results indicates that CAS requires shifts focus in algebraic contents: recognition of decimal & algebraic presentations of numbers; linking various presentations, etc. The extent of instrumentation effects on the selection of problem solving strategies among Korea and US students. Instrumentation

• Journal of KIISE
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• v.43 no.3
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• pp.314-326
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• 2016

Some process algebras were applied to enterprise business modelling for formal specification and verification. ${\pi}$-calculus and mobile ambient can be considered for the distributed and mobile, especially to represent the movements of distributed real-time business processes. However there are some limitations to model the movements: 1) ${\pi}$-calculus passes the name of port for indirect movements, and 2) mobile ambient uses ambient to synchronize asynchronous movements forcefully. As a solution to the limitations, this paper presents a new process algebra, called ${\delta}$-calculus, to specify direct and synchronous movements of business processes over geo-temporal space. Any violation of safety or security of the systems caused by the movements can be indicated by the properties of the movements: synchrony, priority and deadline. A tool, called SAVE, was developed on ADOxx metamodelling platform to demonstrate the concept.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.3
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• pp.648-654
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• 2010

Request operations and release operations occur repeatedly in resource allocation systems. The process requesting a resource acquires one by any priority-based mechanism, and returns the resource after some periods. In this system, resource failures lead to delay of resource allocation, or to termination of process holding the failed resource. To analyze this process effectively, this paper designs a probabilistic ACSR, a process algebra that extends ACSR with the probabilistic choice operation. The ability to express/analyze both request-release rates and failure-recovery rates is illustrated using probabilistic ACSR.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.599-624
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• 2009

The purpose of this study was to investigate the relationship between error types and Polya's problem solving process. For doing this, we selected 106 sophomore students in a middle school and gave them algebra word problem test. With this test, we analyzed the students' error types in solving algebra word problems. First, We analyzed students' errors in solving algebra word problems into the following six error types. The result showed that the rate of student's errors in each type is as follows: "misinterpreted language"(39.7%), "distorted theorem or solution"(38.2%), "technical error"(11.8%), "unverified solution"(7.4%), "misused data"(2.9%) and "logically invalid inference"(0%). Therefore, we found that the most of student's errors occur in "misinterpreted language" and "distorted theorem or solution" types. According to the analysis of the relationship between students' error types and Polya's problem-solving process, we found that students who made errors of "misinterpreted language" and "distorted theorem or solution" types had some problems in the stage of "understanding", "planning" and "looking back". Also those who made errors of "unverified solution" type showed some problems in "planing" and "looking back" steps. Finally, errors of "misused data" and "technical error" types were related in "carrying out" and "looking back" steps, respectively.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.2
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• pp.659-679
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• 2015

Distributed applications are composed of multiple nodes, which exchange information with individual nodes through message passing. Compared with traditional applications, distributed applications have more complex behavior patterns because a large number of interactions and concurrent behaviors exist among their distributed nodes. Thus, it is difficult to detect anomalous behaviors and determine the location and scope of abnormal nodes, and some attacks and misuse cannot be detected. To address this problem, we introduce a method for detecting anomalous behaviors based on process algebra. We specify the architecture of the behavior detection model and the detection algorithm. The anomalous behavior detection and analysis demonstrate that our method is a good discriminator between normal and anomalous behavior characteristics of distributed applications. Performance evaluation shows that the proposed method enhances efficiency without security degradation.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.93-111
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• 2004

In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $C_{a,\;b}[0,\;T]$. We then verify the existence of the multiple $L_{p}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $S({L_{a,\;b}}^{2}[0, T])$. Finally we establish some relationships between the multiple $L_{p}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $S({L_{a,\;b}}^{2}[0, T])$.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.720-723
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• 2005

There has been significant progress in the development of timed process algebra for the specification and analysis of real-time systems in recent years. ACSR is a timed process algebra, which supports synchronous timed actions and asynchronous instantaneous events. Timed actions model the usage of shared resources and the passage of time, whereas events allow synchronization between processes. To be able to specify real-time systems more effectively, this paper suggests the notion of probabilities. This paper also illustrates extended PACSR with a typical resource allocation system and its deadlock specification and analysis.

• Journal of KIISE:Databases
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• v.27 no.2
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• pp.185-198
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• 2000

Recently the technological advance in the hardware dealing with multimedia data as well as the explosive increase of the volume of multimedia data bring about new interest in the use of multimedia presentations in many application domains. To use multimedia presentations efficiently, the integration of multimedia presentations into DBMS is necessary. This paper presents a multimedia presentatation query language based on contents and query processing techniques. Presently, multimedia presentation authoring tools denote a multimedia presentation using a presentation graph which is a DAG. A Node in the graph is a same type of media stream and edges denote a play-out order and a synchronization way among nodes. The contents of presentations graphs are the information of each stream, the sequential order of the information inside each stream and the play-out order among the streams. GCalculus/S is a calculus-based query language and can deal with the contents of a presentation graph and physical characteristics of multimedia data. It expresses the sequential order of information inside each stream and the play-out order of streams of a presentation graph using temporal operators Next, Connected and Until. O-Algebra, which is object algebra, is extended to process GCalculus/S queries.

• Communications of Mathematical Education
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• v.31 no.3
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• pp.241-255
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• 2017

The 4th industrial revolution is coming. In order to prepare for the new learning environment with it, we may need digital mathematics textbooks that fully utilize all possible technologies. So various attempts have been made in elementary and middle school mathematics education. However, despite the importance of higher mathematics, we haven't seen a best possible math digital textbooks yet in Korea. In this paper, we introduce our new model of interactive math digital textbook about Linear Algebra/ Calculus/ Differential Equations/ Statistics/ Engineering Math. Especially, this manuscript focuses on our experience of using digital contents and interactive labs for developing a new model for linear algebra digital textbook. We introduce our works on linear algebra digital textbooks which include pdf e-book, web contents, video clips of lectures, interactive lab. Using this linear algebra digital textbook, students can freely use any mobile devices to access diverse learning materials, lessons, and hands-on exercises without any limitations. Also, times saved in the computation, coding, and typing process can be used to have more discussions for deeper understanding of mathematical concepts. This type of linear algebra digital textbook, which contains all interactive free cyber-lab with codes and all lectures for each sections, can be considered as a new model for the next generation of math digital textbook.