• Korean Journal of Mathematics
• /
• v.29 no.2
• /
• pp.321-332
• /
• 2021

This paper is a further development of the recent results by the authors on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We investigate various relationships between the generalized sequential Fourier-Feynman transform and the generalized sequential convolution product of functionals. Parseval's relation for the generalized sequential Fourier-Feynman transform is also given.

• Journal of the Korean Institute of Gas
• /
• v.3 no.3 s.8
• /
• pp.29-33
• /
• 1999

ln this study, a computerized prototype program was developed with frequency analysis system as a main system and data base as sub-items to utilize data. Through use of gate-by-gate analysis and minimal cut set using boolean algebra, the frequency analysis program peformed the qualitative approach for the accident development path and a quantitative risk analysis. In conclusion, it is thought that the resulting installation will be effective for lessening the probability of accidents through use of this lower cost software.

• Journal for History of Mathematics
• /
• v.22 no.2
• /
• pp.1-12
• /
• 2009

Zhu Shi Jie's Suan Xue Qi Meng is one of the most important books which gave a great influence to the development of Chosun Mathematics. Investigating San Hak Gye Mong Ju Hae(算學啓蒙註解) published in the middle of the 19th century, we study the development of Chosun Mathematics in the century. The author studied western mathematics together with theory of equations in Gu Il Jib (九一集) written by Hong Jung Ha(洪正夏) and then wrote the commentary, which built up a foundation on the development of Algebra of Chosun in the century.

• Journal of the Korea Computer Graphics Society
• /
• v.6 no.1
• /
• pp.37-50
• /
• 2000

Using the complex formulation of plane curves which R. T. Farouki introduced, we can identify any plane polynomial curve with only a polynomial with complex coefficients. In this paper, using the well-known fundamental theorem of algebra, we completely factorize the polynomial over the complex number field C and from the completely factorized form of the polynomial, we find a new necessary and sufficient condition for a plane polynomial curve to be a Pythagorean-hodograph curve, obseving the set of all roots of the complex polynomial corresponding to the plane polynomial curve. Applying this method to space polynomial curves in the three dimensional Minkowski space $R^{2,1}$, we also find the necessary and sufficient condition for a polynomial curve in $R^{2,1}$ to be a PH curve in a new finer form and characterize all possible curves completely.

• Journal of Educational Research in Mathematics
• /
• v.17 no.2
• /
• pp.91-109
• /
• 2007

This study deals with the problem of transition from arithmetic to algebra and the relationship between elementary and secondary school mathematics for systems of linear equations. In elementary school, activity for solving word problems related to systems of linear equations in two variables falls broadly into using two strategies: Guess and check and making a table. In secondary school, those problems are solved algebraically, for example, by solving systems of equations using the technique of elimination. The analysis of mathematics textbooks shows that there is no link between strategies of elementary school mathematics and secondary school mathematics. We devised an alternative way to reinforce link between elementary and secondary school mathematics for systems of linear equations. Drawing a diagram can be introduced as a strategy solving word problems related to systems of linear equations in two variables in elementary school. Moreover it is closely related to the idea of the technique of elimination of secondary school mathematics. It may be a critical juncture of elementary-secondary school mathematics in the case of systems of linear equations in two variables.

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

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.223-245
• /
• 2011

In this paper, we de ne an $L_p$ analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra $\cal{F}$($C_{a,b}$[0, T]) which is called the Fresnel type class, and in more general class $\cal{F}_{A_1;A_2}$ of functionals de ned on general functio space $C_{a,b}$[0, T] rather than on classical Wiener space. Also we obtain some relationships between the $L_p$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $\cal{F}$($C_{a,b}$[0, T]) and in $\cal{F}_{A_1,A_2}$.

• Communications of the Korean Mathematical Society
• /
• v.22 no.1
• /
• pp.75-90
• /
• 2007

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 S introduced by Cameron and Strovic. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class F(B) which corresponds to S. Recently Kim, Song and Yoo investigated more generalized relationships between the Fourier-Feynman transform and the convolution product for functionals in a generalized Fresnel class $F_{A_1,A'_2}$ containing F(B). In this paper, we establish various interesting relationships and expressions involving the first variation and one or two of the concepts of the Fourier-Feynman transform and the convolution product for functionals in $F_{A_1,A_2}$.

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

• Korean Journal of Mathematics
• /
• v.23 no.1
• /
• pp.47-64
• /
• 2015

We express generalized Fourier-Feynman transform and convolution product of functionals in a Banach algebra $\mathcal{S}(L^2_{a,b}[0,T])$ as limits of function space integrals on $C_{a,b}[0,T]$. Moreover we obtain change of scale formulas for function space integrals related with generalized Fourier-Feynman transform and convolution product of these functionals.