• Honam Mathematical Journal
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• v.29 no.1
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• pp.55-60
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• 2007

Given operators X and Y acting on a Hilbert space $\cal{H}$, an interpolating operator is a bounded operator A such that AX = Y. In this article, we showed the following : Let $\cal{L}$ be a subspace lattice acting on a Hilbert space $\cal{H}$ and let X and Y be operators in $\cal{B}(\cal{H})$. Let P be the projection onto $\bar{rangeX}$. If FE = EF for every $E\in\cal{L}$, then the following are equivalent: (1) $sup\{{{\parallel}E^{\perp}Yf\parallel\atop \parallel{E}^{\perp}Xf\parallel}\;:\;f{\in}\cal{H},\;E\in\cal{L}\}\$ < $\infty$, $\bar{range\;Y}\subset\bar{range\;X}$, and < Xf, Yg >=< Yf,Xg > for any f and g in $\cal{H}$. (2) There exists a self-adjoint operator A in Alg$\cal{L}$ such that AX = Y.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.487-493
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• 2002

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for the n-operators satisfies the equation AX$\_$i/ : Y$\_$i/, for i = 1, 2 …, n. In this article, we obtained the following : Let X = (x$\_$ij/) and Y = (y$\_$ij/) be operators acting on H such that $\varkappa$$\_$ i$\sigma$ (i)/ 0 for all i. Then the following statements are equivalent. (1) There exists a unitary operator A in Alg(equation omitted) such that AX = Y and every E in (equation omitted) reduces A. (2) sup{(equation omitted)}<$\infty$ and (equation omitted) = 1 for all i = 1, 2, ….

• Earthquakes and Structures
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• v.2 no.4
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• pp.323-336
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• 2011

The problem of reconstruction of complete building response from a limited number of response measurements is considered. The response at the intermediate degrees of freedom is reconstructed by using piecewise cubic Hermite polynomial interpolation in time domain. The piecewise cubic Hermite polynomial interpolation is preferred over the spline interpolation due to its trend preserving character. It has been shown that factorization of response data in variable separable form via singular value decomposition can be used to derive the complete set of normal modes of the structural system. The time domain principal components can be used to derive empirical transfer functions from which the natural frequencies of the structural system can be identified by peak-picking technique. A reduced-rank approximation for the system flexibility matrix can be readily constructed from the identified mass-orthonormal mode shapes and natural frequencies.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.46-51
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• 1991

An algorithm of finding a solution to an $H^{\infty}$-minimization problem is proposed, and the solution is obtained explicity in terms of closed-form. We construct an optimal controller subject to the interpolation constraints such that $H^{\infty}$-norm and the minimized value of transfer function matrix are equal.l.

• Korean Journal of Computational Design and Engineering
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• v.19 no.2
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• pp.119-128
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• 2014

Computing the natural-looking interpolation of different shapes is a fundamental problem of computer graphics. It is proved by some researchers that such an interpolation can be achieved by pursuing the isometry. In this paper, a novel coordinate system that is invariant under isometries is defined. The coordinate system can easily be converted from the global vertex coordinates. Furthermore, the global coordinates can be efficiently recovered from the new coordinates by simply solving two sparse least-squares problems. Since the proposed coordinate system is invariant under isometries, then transformations such as global rigid trans-formations, articulated posture deformations, or any other isometric deformations, do not change the coordinate values. Therefore, shape interpolation can be done in this framework without being affected by the distortions caused by the isometry.

• Journal of Mechanical Science and Technology
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• v.15 no.2
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• pp.192-198
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• 2001

We consider an interpolation problem with nonuniform rational B-spline curves given ordered data points. The existing approaches assume that weight for each point is available. But, it is not the case in practical applications. Schneider suggested a method which interpolates data points by automatically determining the weight of each control point. However, a drawback of Schneiders approach is that there is no guarantee of avoiding undesired poles; avoiding negative weights. Based on a quadratic programming technique, we use the weights of the control points for interpolating additional data. The weights are restricted to appropriate intervals; this guarantees the regularity of the interpolating curve. In a addition, a knot placement is proposed for pleasing interpolation. In comparison with integral B-spline interpolation, the proposed scheme leads to B-spline curves with fewer control points.

• Journal of computational fluids engineering
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• v.7 no.2
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• pp.8-16
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• 2002

A numerical study on the use of the momentum interpolation method for flows with a large body force is presented. The inherent problems of the momentum interpolation method are discussed first. The origins of problems of the momentum interpolation methods are the validity of linear assumptions employed for the evaluation of the cell-face velocities, the enforcement of mass conservation for the cell-centered velocities and the specification of pressure and pressure correction at the boundary. Numerical experiments are performed for a typical flow involving a large body force. The numerical results are compared with those by the staggered grid method. The fact that the momentum interpolation method may result in physically unrealistic solutions is demonstrated. Numerical experiments changing the numerical grid have shown that a simple way of removing the physically unrealistic solution is a proper grid refinement where there is a large pressure gradient. An effective way of specifying the pressure and pressure correction at the boundary by a local mass conservation near the boundary is proposed, and it is shown that this method can effectively remove the inherent problem of the specification of pressure and pressure correction at the boundary when one uses the momentum interpolation method.

• Journal of Korea Game Society
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• v.14 no.3
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• pp.55-62
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• 2014

In particle-based fluid simulation, applying sudden power to particle raise unnatural flow when wave is breaking. To solve this problem, we have used an linear interpolation technique that interpolate between fluid particle by subdividing the time interval in the previous work. Acceleration vector of the particle with increased pressure in boundary could change smoothly. However, particle looks like flow with viscosity because the number of the minimum samples to interpolate increases. We propose an weighted-interpolation technique to represent the realistic movement of fluid. it is accumulating that has added and assigned different weights to the previous acceleration vector and current one repeatedly. weighted-interpolation technique using less minium samples to flow than linear interpolation, so it can solve the problem which particle looks like flow with viscosity.

• Journal of the Society of Disaster Information
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• v.20 no.1
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• pp.82-92
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• 2024

Purpose: The purpose of this study is to find a solution to the massive data construction that occurs when fire simulation data is linked to augmented reality and the resulting data overload problem. Method: An experiment was conducted to set the interval between appropriate input data to improve the reliability and computational complexity of Linear Interpolation, a data estimation technology. In addition, a validity verification was conducted to confirm whether Linear Interpolation well reflected the dynamic changes of fire. Result: As a result of application to the underground common area, which is the study target building, it showed high satisfaction in improving the reliability of Interpolation and the operation processing speed of simulation when data was input at intervals of 10 m. In addition, it was verified through evaluation using MAE and R-Squared that the estimation method of fire simulation data using the Interpolation technique had high explanatory power and reliability. Conclusion: This study solved the data overload problem caused by applying digital twin technology to fire simulation through Interpolation techniques, and confirmed that fire information prediction and visualization were of great help in real-time fire prevention.

• Journal of Broadcast Engineering
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• v.24 no.2
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• pp.227-233
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• 2019

In this paper, we propose a deep neural network-based sound interpolation method for realizing virtual reality sound. Through this method, sound between two points is generated by using acoustic signals obtained from two points. Sound interpolation can be performed by statistical methods such as arithmetic mean or geometric mean, but this is insufficient to reflect actual nonlinear acoustic characteristics. In order to solve this problem, in this study, the sound interpolation is performed by training the deep neural network based on the acoustic signals of the two points and the target point, and the experimental results show that the deep neural network-based sound interpolation method is superior to the statistical methods.