• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.41-47
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• 2000

Johnson and Skoug [Pacific J. Math. 83(1979), 157-176] introduced the concept of scale-invariant measurability in Wiener space. And the applied their results in the theory of the Feynman integral. A converse measurability theorem for Wiener space due to the $K{\ddot{o}}ehler$ and Yeh-Wiener space due to Skoug[Proc. Amer. Math. Soc 57(1976), 304-310] is one of the key concept to their discussion. In this paper, we will extend the results on converse measurability in Wiener space which Chang and Ryu[Proc. Amer. Math, Soc. 104(1998), 835-839] obtained to abstract Wiener space.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.481-495
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• 2009

Huffman, Park and Skoug introduced various results for the $L_{p}$ analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra $\mathcal{S}$ introduced by Cameron and Storvick. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class $\mathcal{F}(B)$ which corresponds to $\mathcal{S}$. Moreover they introduced the $L_{p}$ analytic Fourier-Feynman transform for functionals on a product abstract Wiener space and then established the above results for functionals in the generalized Fresnel class $\mathcal{F}_{A1,A2}$ containing $\mathcal{F}(B)$. In this paper, we investigate more generalized relationships, between the Fourier-Feynman transform and the convolution product for functionals in $\mathcal{F}_{A1,A2}$, than the above results.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.4 s.97
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• pp.85-94
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• 1999

Reconfiguration, expansion, or new establishment of FMS requires the availability of a shop floor control (SFC) system relevant to the FMS since it is closely related with the hardware component of FMS. Due to the expensive cost of its development, significant research efforts have been made to develop an SFC system that is reusable. This paper presents Abstract Machine Tool (AMT) approach applied to develop an SFC sytem that is reusable without additional programming. The AMT model enables us to design the SFC system independently of the hardware-dependent attributes of euqipment; an AMT models a workstation by abstraction and presents an equipment-independent interface to machining cell controller. Specifically, we describe how we formalize the interfaces among equipment in order to build an AMT and how we design the machining cell control software based on AMT models. We also present MACHINIST the machining cell control system for IAE-FMS plant as an implementation example.

• ETRI Journal
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• v.19 no.4
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• pp.363-388
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• 1997

This paper describes a research result on automatic generation of abstract test cases from formal specifications by applying many related algorithms and techniques such as the testing framework, rural Chinese postman tour and unique input output sequence concepts. In addition, an efficient algorithm for verifying the strong connectivity of the reference finite state machine and the concept of unique event sequence are explained. We made use of several techniques to from an integrated framework for abstract test case generation from LOTOS and SDL specifications. A prototype of the proposed framework has been built with special attention to real protocol in order to generate the executable test cases in an automatic way. The abstract test cases in tree and tabular combined notation (TTCN) language will be applied to the TTCN compiler in order to obtain the executable test cases which re relevant to the industrial application.

• KIPS Transactions on Software and Data Engineering
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• v.3 no.1
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• pp.37-42
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• 2014

The abstract should concisely state what was done, how it was done, principal results, and their significance. It should be less than 300 words for all forms of publication. The abstract should be written as one paragraph and should not contain tabular material or numbered references. At the end of abstract, keywords should be given in 3 to 5 words or phrases.

• Journal of the Korean Chemical Society
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• v.57 no.2
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• pp.176-203
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• 2013

In this work is induced a new topology of solutions of chemical equations by virtue of point-set topology in an abstract stoichiometrical space. Subgenerators of this topology are the coefficients of chemical reaction. Complex chemical reactions, as those of direct reduction of hematite with a carbon, often exhibit distinct properties which can be interpreted as higher level mathematical structures. Here we used a mathematical model that exploits the stoichiometric structure, which can be seen as a topology too, to derive an algebraic picture of chemical equations. This abstract expression suggests exploring the chemical meaning of topological concept. Topological models at different levels of realism can be used to generate a large number of reaction modifications, with a particular aim to determine their general properties. The more abstract the theory is, the stronger the cognitive power is.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.99-117
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• 1998

Let $(B, H, p_1)$ be an abstract Wiener space and $F(B)$ the Fresnel class on $(B, H, p_1)$ which consists of functionals F of the form : $$ F(x) = \int_{H} exp{i(h,x)^\sim} df(h), x \in B, $$ where $(\cdot, \cdot)^\sim$ is a stochastic inner product between H and B, and f is in $M(H)$, the space of complex Borel measures on H. We introduce an $L_1$ analytic Fourier-Feynman transforms for functionls in $F(B)$. Furthermore, we introduce a convolution on $F(B)$, and then verify the existence of the $L_1$ analytic Fourier-Feynman transform for the convolution product of two functionals in $F(B)$, and we establish the relationships between the $L_1$ analytic Fourier-Feynman tranform of the convolution product for two functionals in $F(B)$ and the $L_1$ analytic Fourier-Feynman transforms for each functional. Finally, we show that most results in [7] follows from our results in Section 3.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.1131-1148
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• 2009

Algebra is one of the important subjects that not only mathematics but many science major students should know at least at the elementary level. Unfortunately abstract algebra, specially, is seen as an extremely difficult course to learn. One reason of difficulties is because of its very abstract nature, and the other is due to the lecture method that simply telling students about mathematical contents. In this paper we study about the teaching and learning abstract algebra in universities in corporation of a programming language such as ISETL. ISETL is a language whose syntax closely imitates that of mathematics. In asking students to read and write code in ISETL before they learn in class, we observe that students can much understand and construct formal statements that express a precise idea. We discuss about the classroom activities that may help students to construct and internalize mathematical ideas, and also discuss about some barriers we might overcome.

• Research in Mathematical Education
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• v.25 no.3
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• pp.227-244
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• 2022

The concrete-representational-abstract integrated (CRA-I) sequence is an explicit approach for teaching students who struggle in mathematics. This approach is beneficial because it assists students in the development of conceptual understanding. This article describes how the approach is used in general as well as its use with a specific geometry concept, area of a rectangle. The author will describe why one might choose CRA-I and the steps needed for implementation. Finally, the CRA-I steps will be shown with a lesson series related to teaching the concept of area. The article will describe lesson activities, methods, materials, and procedures.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1093-1103
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• 2022

In this paper, we establish an evaluation formula to calculate the Wiener integral of polynomials in terms of natural dual pairings on abstract Wiener spaces (H, B, 𝜈). To do this we first derive a translation theorem for the Wiener integral of functionals associated with operators in 𝓛(B), the Banach space of bounded linear operators from B to itself. We then apply the translation theorem to establish an integration by parts formula for the Wiener integral of functionals combined with operators in 𝓛(B). We finally apply this parts formula to evaluate the Wiener integral of certain polynomials in terms of natural dual pairings.