• Honam Mathematical Journal
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• v.29 no.4
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• pp.523-533
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• 2007

Let $\cal{B}$ be a reflexive Banach space of functions analytic on the open unit disc and M be an invariant subspace of the multiplication operator by the independent variable, $M_z$. Suppose that $\varphi\;\in\;\cal{H}^{\infty}$ and $M_{\varphi}$ : M ${\rightarrow}$ M, defined by $M_{\varphi}f={\varphi}f$, is the operator of multiplication by ${\varphi}$. We would like to investigate the spectrum and the essential spectrum of $M_{\varphi}$ and we are looking for the necessary and sufficient conditions for $M_{\varphi}$ to be a Fredholm operator. Also we give a sufficient condition for a sequence $\{w_n\}$ to be an interpolating sequence for $\cal{B}$. At last the commutant of $M_{\varphi}$ under certain conditions on M and ${\varphi}$ is determined.

• Korean Journal of Computational Design and Engineering
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• v.4 no.2
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• pp.127-138
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• 1999

For reverse engineering, curves and surfaces are modeled for new products by interpolating the digitized data points. But there are many measuring or deviation errors. Therefore, it is important to handle errors during the curve or surface modeling. If the errors are ignored, designer could get undesirable results. For this reason, fairing procedure with the aesthetics criteria is necessary in computer modeling. This paper presents methods of 3D NURBS curve fairing. The techniques are based on automatic repositioning of the digitized dat points or the NURBS curve control points by a constrained nonlinear optimization algorithm. The objective function is derived variously by derived curved. Constraints are distance measures between the original and the modified digitized data points. Changes I curve shape are analyzed by illustrations of curve shapes, and continuous plotting of curvature and torsion.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.04a
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• pp.573-578
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• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfies the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfies the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beam.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.274-279
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• 1991

The development of a guided weapon system, such as a tactical missile, requires a performance analysis of a nonlinear system. Generally, the Monte Carlo analysis method is used for this purpose. The limitation of this method, a large number of simulations, for a nonlinear system performance analysis strongly motivated the development of a more efficient analytic technique. In this paper, the statisfical linearization methods is used for the performance analysis to the guided weapon system with the help of covariance analysis technique. Because the statistical linearization methods cannot be used to the look-up table nonlinear form such as aerodynamic coefficients, the second order polynomial representations is obtained from the table using the Lagrange interpolating polynomial and linearized statistically. Simple simulations about initial state conditions and random component in guidance command shows the results of this technique.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.907-911
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• 2014

Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax = y. We show the following: Let $Alg{\mathcal{L}}$ be a tridiagonal algebra on $\mathcal{H}$ and let $x=(x_i)$ and $y=(y_i)$ be vectors in $\mathcal{H}$. Then the following are equivalent: (1) There exists a unitary operator $A=(a_{ij})$ in $Alg{\mathcal{L}}$ such that Ax = y. (2) There is a bounded sequence $\{{\alpha}_i\}$ in $\mathbb{C}$ such that ${\mid}{\alpha}_i{\mid}=1$ and $y_i={\alpha}_ix_i$ for $i{\in}\mathbb{N}$.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.685-691
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• 2008

Given operators $X_i$ and $Y_i$ (i = 1, 2, ${\cdots}$, n) acting on a Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A acting on $\mathcal{H}$ such that $AX_i$ = $Y_i$ for i= 1, 2, ${\cdots}$, n. In this article, if the range of $X_k$ is dense in H for a certain k in {1, 2, ${\cdots}$, n), then the following are equivalent: (1) There exists a self-adjoint operator A in $\mathcal{B}(\mathcal{H})$ stich that $AX_i$ = $Y_i$ for I = 1, 2, ${\cdots}$, n. (2) $sup\{{\frac{{\parallel}{\sum}^n_{i=1}Y_if_i{\parallel}}{{\parallel}{\sum}^n_{i=1}X_if_i{\parallel}}:f_i{\in}H}\}$ < ${\infty}$ and < $X_kf,Y_kg$ >=< $Y_kf,X_kg$> for all f, g in $\mathcal{H}$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.8
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• pp.3473-3487
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• 2020

In this paper, we present a new approach to creating speech animation with emotional expressions using a small set of example models. To generate realistic facial animation, two example models called key visemes and expressions are used for lip-synchronization and facial expressions, respectively. The key visemes represent lip shapes of phonemes such as vowels and consonants while the key expressions represent basic emotions of a face. Our approach utilizes a text-to-speech (TTS) system to create a phonetic transcript for the speech animation. Based on a phonetic transcript, a sequence of speech animation is synthesized by interpolating the corresponding sequence of key visemes. Using an input parameter vector, the key expressions are blended by a method of scattered data interpolation. During the synthesizing process, an importance-based scheme is introduced to combine both lip-synchronization and facial expressions into one animation sequence in real time (over 120Hz). The proposed approach can be applied to diverse types of digital content and applications that use facial animation with high accuracy (over 90%) in speech recognition.

• Korean Journal of Computational Design and Engineering
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• v.4 no.1
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• pp.32-42
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• 1999

Approximate lofting or skinning is one of practical surface modeling techniques well used in CAD and reverse engineering applications. Presented in this paper is a method for approximately lofting a given set of curves wihin a specified tolereance. It is based on refitting input curves simultaneously on a common knot vector and interpolating them to get a resultant NURBS surface. A concept of reducing the number of interior knots of the common knot vector is well adopted to acquire more compact representation for the resultant surface. Energy minimization is newly introduced in curve refitting process to stabilize the solution of the fitting problem and get more fair curve. The proposed approximate lofting provides more smooth surface models and realizes more efficient data reduction expecially when the parameterization and compatibility of input curves are not good enough. The method has been successfully implemented in a new CAD/CAM product VX Vision? of Varimetrix Corporation.

• International Journal of CAD/CAM
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• v.12 no.1
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• pp.38-47
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• 2012

The paper proposes a method for generating a sequence of images with smooth transition of illumination from two input images with different lighting conditions. Our relighting approach is image-based, such as the light field rendering. We store the luminances (pixel RGB values) into "lighting functions" consisting of a couple of parameters related to normal vectors. Images with different light positions are rendered by interpolating the luminances retrieved from the lighting functions. The proposed method is a promising technique for many applications requiring a scene with variety of lighting effects, such as movies, TV games, and so on.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.794-801
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• 2006

The linkage framework of geometric modeling and analysis based on the NURBS technology is developed in this study. The NURBS surfaces are generated by interpolating the given set of data points or by extracting the necessary information to construct the NURBS surface from the IGES format file which is generated by the commercial CAD systems in the present study. Numerical examples shows the rate of displacement convergence according to the paramterization methods of the NURBS surface. NURBS can generate quadric surfaces in an exact manner. It is the one of the advantages of the NURBS. A trimmed NURBS surface that is often encountered in the modeling process of the CAD systems is also presented in the present study. The performance of the developed geometrically exact shell element integrated with the exact geometric representations by the NURBS equation is compared to those of the previous reported FE shell elements in the selected benchmark problems.