• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1031-1056
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• 2005

In this paper, we define the conditional first variation over Wiener paths in abstract Wiener space and investigate its properties. Using these properties, we also investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transforms of functions in a Banach algebra which is equivalent to the Fresnel class. Finally, we provide another method evaluating the Fourier-Feynman transform for the product of a function in the Banach algebra with n linear factors.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.967-990
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• 2006

In this paper, we evaluate first variations, conditional first variations and conditional Fourier-Feynman transforms of cylinder type functions over Wiener paths in abstract Wiener space and then, investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of those functions. Finally, we derive the conditional Fourier-Feynman transform for the product of cylinder type function which defines the functions in a Banach algebra introduced by Yoo, with n linear factors.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.521-536
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• 2023

This paper is a further development of the recent results by the author and coworker on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We establish existence of the generalized first variation of these functionals. Also we investigate various relationships between the generalized sequential Fourier-Feynman transform, the generalized sequential convolution product and the generalized first variation of the functionals.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.207-221
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• 2011

We examine the various relationships that exist among the Fourier-Yeh-Feynman transform, convolution and the first variation for functionals on Yeh-Wiener space that belong to a Banach algebra S(Q).

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.485-501
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• 2001

In this paper we express analytic Feynman integral of the first variation of a functional F in terms of analytic Feynman integral of the product F with a linear factor and obtain an integration by parts formula of the analytic Feynman integral of functionals on abstract Wiener space. We find the Fourier-Feynman transform for the product of functionals in the Fresnel class F(B) with n linear factors.

• Proceedings of the KSRS Conference
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• 1999.11a
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• pp.140-143
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• 1999

SSH(Sea Surface Height) from TOPEX/Poseidon and SST data are analyzed to estimate characteristics of annual and inter-annual variations in the East Asian seas(110E - l80E, 20N - 50N) from November 1992 to May 1998. In EOF analysis of SSH and SST, 57% and 97% of the variance are represented by the first two modes. The first mode of SSH and SST shows strong annual variations expected for steric changes. The second mode of SSH shows a long-term variation, but that of SST shows 3 - 4month offset from annual variation. In the EOF analysis of the SSH and SST, 61% and 54% of the total variance are represented by the first three modes. The first mode represented a long-term variation, and the third mode reflected the bi-ennial variation. The first three mode were not strongly correlated with ENSO. We further apply Canonical Correlation Analysis(CCA) to find the dominant correlation patterns with ENSO.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.291-302
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• 2011

We first study the generalized Fourier-Gauss transforms of functionals defined on the complexification $\cal{B}_C$ of an abstract Wiener space ($\cal{H}$, $\cal{B}$, ${\nu}$). Secondly, we introduce a new class of convolution products of functionals defined on $\cal{B}_C$ and study several properties of the convolutions. Then we study various relations among the first variation the convolutions, and the generalized Fourier-Gauss transforms.

• Journal of the Korean Society of Earth Science Education
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• v.5 no.3
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• pp.245-255
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• 2012

The purposes of this research are to analyze preservice elementary teachers' degree of difficulty in classes of seasonal variation and suggest the measures of classes so that preservice elementary teachers can progress classes of seasonal variation effectively. To achieve them, the research was conducted for 90 first graders completing teaching method of elementary science in P university of education from Sep. to Dec. 2012. This research was conducted, based on the results of in-depth interview for 9 preservice elementary teachers who performed classes of seasonal variation, survey on the degree of class difficulty and evaluation of classes on 8 classes theme of Earth sector in elementary science. The results of this research are as follows. The first, preservice elementary teachers had relatively high class difficulty for teaching seasonal variation among the sector of the earth in elementary science. The second, in the evaluation of preservice elementary teachers' classes, the more the subject showed high class difficulty, the more the score of class evaluation was low. The reason is analyzed that high class difficulty reduces teacher's confidence. The third, preservice elementary teachers had insufficient knowledges and concepts which are basically necessary for the classes of seasonal variation. Especially, it was more serious for preservice elementary teachers who didn't learn Earth-science during their high school time. The fourth, it is necessery that concrete and systematical teaching method should be developed so as to improving preservice elementary teachers' teaching method for the classes of seasonal variation.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.1260-1264
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• 2009

Precipitation time series is a mixture of complicate fluctuation and changes. The monthly precipitation data of 61 stations during 36 years (1973-2008) in Korea are comprehensively analyzed using the EOFs technique and CSEOFs technique respectively. The main motivation for employing this technique in the present study is to investigate the physical processes associated with the evolution of the precipitation from observation data. The twenty-five leading EOF modes account for 98.05% of the total monthly variance, and the first two modes account for 83.68% of total variation. The first mode exhibits traditional spatial pattern with annual cycle of corresponding PC time series and second mode shows strong North South gradient. In CSEOF analysis, the twenty-five leading CSEOF modes account for 98.58% of the total monthly variance, and the first two modes account for 78.69% of total variation, these first two patterns' spatial distribution show monthly spatial variation. The corresponding mode's PC time series reveals the annual cycle on a monthly time scale and long-term fluctuation and first mode's PC time series shows increasing linear trend which represents that spatial and temporal variability of first mode pattern has strengthened. Compared with the EOFs analysis, the CSEOFs analysis preferably exhibits the spatial distribution and temporal evolution characteristics and variability of Korean historical precipitation.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1561-1577
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• 2014

In this paper, we define a conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation of functionals via the Gaussian process. We then examine various relationships of the conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation for functionals F in $S_{\alpha}$ [5, 8].