• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.413-431
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• 2012

Let $C^r[0,t]$ be the function space of the vector-valued continuous paths $x:[0,t]{\rightarrow}\mathbb{R}^r$ and define $X_t:C^r[0,t]{\rightarrow}\mathbb{R}^{(n+1)r}$ and $Y_t:C^r[0,t]{\rightarrow}\mathbb{R}^{nr}$ by $X_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}),\;x(t_n))$ and $Y_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}))$, respectively, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n=t$. In the present paper, using two simple formulas for the conditional expectations over $C^r[0,t]$ with the conditioning functions $X_t$ and $Y_t$, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form $${\exp}\{{\int_o}^t{\theta}(s,\;x(s))\;d{\eta}(s)\}{\psi}(x(t)),\;x{\in}C^r[0,t]$$ where ${\eta}$ is a complex Borel measure on [0, t] and both ${\theta}(s,{\cdot})$ and ${\psi}$ are the Fourier-Stieltjes transforms of the complex Borel measures on $\mathbb{R}^r$.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.10
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• pp.1207-1214
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• 1999

Many papers have recently been presented to develop energy functions for power systems. However, earlier studies adopted case-by-case approaches, which failed to give a general approach to deal with various kinds of generator models. In this paper, two useful theorems are developed regarding the integral relationships of the generator power versus its phasor current and voltage. By using the proposed theorems, an exact energy conservation law can be derived from the complex integral. The proposed energy conservation law, which is free of the generator model, can be utilized to develop energy functions for various kinds of generator models including the speed governors and exciters. An illustrative example is given for a multimachine system with the Eq' model of generator. This thesis also shows a possibility of more accurate and fast stability analysis by using the proposed Energy Conservation Law.

• Proceedings of the KIEE Conference
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• 1998.11a
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• pp.263-268
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• 1998

Many papers have recently been presented to develop energy functions for power systems. However, earlier studies adopted case-by-case approaches, which failed to give a general approach to deal with various kinds of generator models. In this paper, two useful theorems are developed regarding the integral relationships of the generator power versus its phasor current and voltage. By using the proposed theorems, an exact energy conservation law can be derived from the complex integral. The proposed energy conservation law, which is free of the generator model, can be utilized to develop energy functions for various kinds of generator models including the speed governors, and exciters. An illustrative example is given for a multimachine system with the Eq' model of generator. This thesis also shows a possibility of more accurate and fast stability analysis by using the proposed Energy Conservation Law.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.205-229
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• 2022

The aim of this paper is to obtain some results which belong to fixed point theory such as strong convergence, rate of convergence, stability, and data dependence by using the new Jungck-type iteration method for a mapping defined in complex-valued Banach spaces. In addition, some of these results are supported by nontrivial numerical examples. Finally, it is shown that the sequence obtained from the new iteration method converges to the solution of the functional integral equation in complex-valued Banach spaces. The results obtained in this paper may be interpreted as a generalization and improvement of the previously known results.

• The Journal of the Acoustical Society of Korea
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• v.7 no.4
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• pp.22-30
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• 1988

In this paper, the sound radiation from a clamped circular plate in an infinite baffle is calculated by using the FFT technique. The radiated sound fields are obtained by two-dimensional fast Fourier transform method is the spatial domain instead of a direct numerical evaluation of Rayleigh integral for economy of the computation time. The computation time is consumed at least by 1/200 times of the direct numerical evaluation on the Rayleigh integral in acoustic fields. The FFT method can be applicable to any shaped geometry as well as circular plate. The FFT solution could be very powerful in predicting the near and far fields of complex structures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.1016-1019
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• 2002

This paper deals with a fundamental and classical scattering problem by a finite strip. For the analysis of scattered acoustic field, a “single” integral equation is derived. Firstly, the complexity by considering the effect of the mean flow is alleviated by the introduction of Prandtl-Glauert coordinate and the new dependent variable. Secondly, the difficulty of solving the resultant strongly-coupled integral equations which always appear in this kind of 3-part mixed boundary value problem is solved by observing some good properties of the functions in complex domain and manipulating the equations and variables for the use of those properties. The solution can be obtained asymptotically in terms of gamma function and Whittaker function. One aim of this study is the improvement of methodology for the research using integral equations. The other is the basic understanding of scattering by a finite strip related to the linear cascade model of rotating fan blades.

• The Journal of Korea Robotics Society
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• v.9 no.1
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• pp.20-27
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• 2014

In this paper, an exact reshaping method for the motor dynamics of a flexible-joint robot is proposed using an integral manifold approach. Obtaining the exact model for both motor-side and link-side dynamics of a flexible-joint robot is difficult due to its under-actuated nature and complex dynamics. Despite the simple structure of the motor-side dynamics, they are difficult to model accurately for a flexible-joint robot due to motor disturbances, especially when speed reducers such as harmonic drives are installed. An integral manifold feedback control (IMFC) is proposed to reshape the motor dynamics. Based on the integral manifold approach, it is theoretically proved that the IMFC reshapes motor dynamics exactly even with bounded disturbances such as motor friction. The performance of the proposed IMFC is verified experimentally using a single degree-of-freedom flexible-joint robot under gravity conditions.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.349-362
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• 2010

We establish the various relationships among the integral transform ${\mathcal{F}}_{{\alpha},{\beta}}F$, the convolution product $(F*G)_{\alpha}$ and the first variation ${\delta}F$ for a class of functionals defined on K(Q), the space of complex-valued continuous functions on $Q=[0,S]{\times}[0,T]$ which satisfy x(s, 0) = x(0, t) = 0 for all $(s,t){\in}Q$. And also we obtain Parseval's and Plancherel's relations for the integral transform of some functionals defined on K(Q).

• Geophysics and Geophysical Exploration
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• v.27 no.1
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• pp.51-56
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• 2024

In this paper, the vector gravity and gravity gradient tensor of an elliptical disk are derived. The vector gravity of an elliptical disk is defined by differentiating the gravitational potential due to the elliptical disk expressed by a double integral with respect to each axial direction. The vector gravity defined by the double integral is then transformed into a line integral of a closed curve along the elliptical disk boundary using the complex Green's theorem. Finally, vector gravity due to the elliptical disk is derived by 1D parametric numerical integration along the elliptical disk boundary. The xz, yz, zz components of the gravity gradient tensor due to the elliptical disk are obtained by differentiating the vector gravity with respect to vertical direction. The xx, yy, xy components are derived by differentiating the horizontal components of the vector gravity in the form of a double integral with respect to horizontal directions and then using the complex Green's theorem.

• The Mathematical Education
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• v.22 no.1
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• pp.53-56
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• 1983