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

• Transactions of the Korean Society of Automotive Engineers
• /
• v.3 no.2
• /
• pp.42-50
• /
• 1995

This paper proposes a new method to investigate combustion phenomena using the variation of crankshaft speed, From the idea that the variation of crankshaft speed contains the information of combustion, the energy method is applied as a single degree of freedom. Through the comparison of measured and calculated crankshaft speed, the proposed energy model is proved to be effective. When the crankshaft speed is used in the energy equation, filtering of the speed is required. The frequency components of cylinder pressure are analyzed and the coefficients of Fourier series above the twelfth frequency of engine speed are considered as a noise. As an example of application of this research, some combustion analyses like mean effective pressure, heat release rate, and misfire detection were carried out.

• Journal of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.309-318
• /
• 1996

The Gross Laplacian $\Delta_G$ was introduced by Groww for a function defined on an abstract Wiener space (H,B) [1,7]. Suppose $\varphi$ is a twice H-differentiable function defined on B such that $\varphi"(x)$ is a trace class operator of H for every x \in B.in B.

• Journal of Korea Multimedia Society
• /
• v.21 no.3
• /
• pp.391-399
• /
• 2018

In this paper, we construct and compare various guitar chord classification systems using perceptron neural network and convolutional neural network without pre-processing other than Fourier transform to identify the optimal chord classification system. Conventional guitar chord classification schemes use, for better feature extraction, computationally demanding pre-processing techniques such as stochastic analysis employing a hidden markov model or an acoustic data filtering and hence are burdensome for real-time chord classifications. For this reason, we construct various perceptron neural networks and convolutional neural networks that use only Fourier tranform for data pre-processing and compare them with dataset obtained by playing an electric guitar. According to our comparison, convolutional neural networks provide optimal performance considering both chord classification acurracy and fast processing time. In particular, convolutional neural networks exhibit robust performance even when only small fraction of low frequency components of the data are used.

• The Journal of the Korea Contents Association
• /
• v.17 no.2
• /
• pp.439-448
• /
• 2017

Facial expression is important factor on social interaction. Facial muscle movement provides emotion information to develop social network. However, facial movement has less determined to recognize social emotion. This study is to analyze facial micro-movements and to recognize the social emotion such as intimacy, empathy, and valence. 76 university students were presented to the stimuli for social emotions and was measure their facial expression using camera. As a results, facial micro-movement. showed significant difference of social emotion. After extracting the movement amount of 3 unconscious muscles and 18 conscious muscles, Dominant Frequency band was confirmed. While muscle around the nose and cheek showed significant difference in the intimacy, one around mouth did in the empathy and one around jaw in the valence. The results proposed new facial movement to express social emotion in virtual avatars and to recognize social emotion.

• Journal of Environmental Science International
• /
• v.18 no.11
• /
• pp.1215-1224
• /
• 2009

This study evaluated the applicability of visible-light-driven N- and S-doped titanium dioxide($TiO_2$) for the control of low-level dimethyl sulfide(DMS) and dimethyl disulfide(DMDS). In addition, a photocatalytic unit(PU)-adsorption hybrid was evaluated in order to examine the removal of DMS and DMDS which exited the PU and a gaseous photocatalytic byproduct($SO_2$) which was generated during the photocatalytic processes. Fourier-Tranform-Infrared(FTIR) spectrum exhibited different surface characteristics among the three-types of catalysts. For the N- and S-doped $TiO_2$ powders, a shift of the absorbance spectrum towards the visible-light region was observed. The absorption edge for both the N- and S-doped $TiO_2$ was shifted to $\lambda$ 720 nm. The N-doped $TiO_2$ was superior to the S-doped $TiO_2$ in regards to DMS degradation. Under low input concentration(IC) conditions(0.039 and 0.027 ppm for DMS and DMDS, respectively), the N-doped $TiO_2$ revealed a high DMS removal efficiency(above 95%), but a gradual decreasing removal efficiency under high IC conditions(7.8 and 5.4 ppm for DMS and DMDS, respectively). Although the hybrid system exhibited a superior characteristic to PU alone regarding the removal efficiencies of both DMS and DMDS, this capability decreased during the course of a photocatalytic process under the high IC conditions. The present study identified the generation of sulfate ion on the catalyst surface and sulfur dioxide(maximum concentrations of 0.0019 and 0.0074 ppm for the photocatalytic processes of DMS and DMDS, respectively) in effluent gas of PU. However, this generation of $TiO_2$ would be an insignificant addition to indoor air quality levels.