• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.691-700
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• 2004

Let X and Y be operators acting on a Hilbert space and let (equation omitted) be a subspace lattice of orthogonal projections on the space containing 0 and I. We investigate normal interpolation problems in Alg(equation omitted): Given operators X and Y acting on a Hilbert space, when does there exist a normal operator A in Alg(equation omitted) such that AX = Y?

• Honam Mathematical Journal
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• v.27 no.3
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• pp.431-443
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• 2005

We investigate the equation Ax = y, where the vectors x and y are given and the operator A is normal and required to lie in CSL-algebra $AlG{\mathcal{L}}$. We desire a necessary and sufficient condition for the existence of a solution A.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.329-334
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• 2008

Given operators X and Y acting on a Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that AX = Y. In this article, the following is proved: Let $\mathcal{L}$ be a subspace lattice on $\mathcal{H}$ and let X and Y be operators acting on a Hilbert space H. Let P be the projection onto the $\overline{rangeX}$. If PE = EP for each E ${\in}$ $\mathcal{L}$, then the following are equivalent: (1) sup ${{\frac{{\parallel}E^{\perp}Yf{\parallel}}{{\parallel}E^{\perp}Xf{\parallel}}}:f{\in}\mathcal{H},\;E{\in}\mathcal{L}}$ < ${\infty},\;\overline{rangeY}\;{\subset}\;\overline{rangeX}$, and there is a bounded operator T acting on $\mathcal{H}$ such that < Xf, Tg >=< Yf, Xg >, < Tf, Tg >=< Yf, Yg > for all f and gin $\mathcal{H}$ and $T^*h$ = 0 for h ${\in}\;{\overline{rangeX}}^{\perp}$. (2) There is a normal operator A in AlgL such that AX = Y and Ag = 0 for all g in range ${\overline{rangeX}}^{\perp}$.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.293-299
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• 2005

Let ${\cal{L}}$ be a commutative subspace lattice on a Hilbert space ${\cal{H}}$ and X and Y be operators on ${\cal{H}}$. Let $${\cal{M}}_X=\{{\sum}{\limits_{i=1}^n}E_{i}Xf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}$$ and $${\cal{M}}_Y=\{{\sum}{\limits_{i=1}^n}E_{i}Yf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}.$$ Then the following are equivalent. (i) There is an operator A in $Alg{\cal{L}}$ such that AX = Y, Ag = 0 for all g in ${\overline{{\cal{M}}_X}}^{\bot},A^*A=AA^*$ and every E in ${\cal{L}}$ reduces A. (ii) ${\sup}\;\{K(E, f)\;:\;n\;{\in}\;{\mathbb{N}},f_i\;{\in}\;{\cal{H}}\;and\;E_i\;{\in}\;{\cal{L}}\}\;<\;\infty,\;{\overline{{\cal{M}}_Y}}\;{\subset}\;{\overline{{\cal{M}}_X}}$and there is an operator T acting on ${\cal{H}}$ such that ${\langle}EX\;f,Tg{\rangle}={\langle}EY\;f,Xg{\rangle}$ and ${\langle}ET\;f,Tg{\rangle}={\langle}EY\;f,Yg{\rangle}$ for all f, g in ${\cal{H}}$ and E in ${\cal{L}}$, where $K(E,\;f)\;=\;{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Y\;f_{i}{\parallel}/{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Xf_{i}{\parallel}$.

• 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.

• Journal of Ocean Engineering and Technology
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• v.14 no.2
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• pp.121-127
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• 2000

In this paper a new technique of inverse fairing problem for ship hull is proposed. Recently Lu solved the inverse fairing problem for automobile's body that was made by one surface element. In this system however hull surface is constructed by Gregory's composite surface interpolation method. So reflection line at boundary position is used as a tool of solving inverse problem in surface fairing. But the results are not good. The new concepts of Normal vector line and Constrained reflection line are introduced as an alternative tool. Energy minimization method for Normal Vector Line curve net and the inverse method for Constrained Reflection Line by using optimization technique are examined And the final lines from this proposed surface fairing method shows good fairness.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.5
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• pp.38-45
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• 1998

The Z-map model which is quite similar to the non-parametric patch is widely used to describe the shape of a surface because of its simplicity. Despite the inherent advantage of z-map model. it has drawbacks that there exists difficulty in expressing the vertical walls and its related contact treatment method. In the region of vertical walls, there is a convergence problem in searching the contact point. In this study a contact point finding scheme is presented, based on the z value of the z-map model on the sheet normal direction. To show the utility of this scheme a compared with the experimental results. The effects of the Z-map grid distances and the interpolations of the inside Z-map value are also discussed.

• Interaction and multiscale mechanics
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• v.5 no.3
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• pp.287-318
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• 2012

We apply a partitioned-solution (iterative-staggered) coupling method based on a fixed Eulerian mesh with the level set function to a large-deformation fluid-structure interaction (FSI) problem where a large-deformable thin structure moves in a high-speed flow field, as an airbag does during deployment. This method combines advanced fluid and structure solvers-specifically, the constrained interpolation profile finite element method (CIP-FEM) for fluid Eulerian mesh and large-deformable structural elements for Lagrangian structural mesh. We express the large-deformable interface as a zero isosurface by the level set function, and introduce virtual nodes with level sets and structural normal velocities to generate the level set function according to the large-deformable interfacial geometry and enforce the kinematic condition at the interface. The virtual nodes are located in the direction normal to the structural mesh. It is confirmed that application of the method to unfolded airbag deployment simulation shows the adequacy of the method.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.8
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• pp.2473-2489
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• 2022

Urban development has brought about the increasing saturation of urban traffic demand, and traffic congestion has become the primary problem in transportation. Roads are in a state of waiting in line or even congestion, which seriously affects people's enthusiasm and efficiency of travel. This paper mainly studies the discrete domain path planning method based on the flow data. Taking the traffic flow data based on the highway network structure as the research object, this paper uses the deep learning theory technology to complete the path weight determination process, optimizes the path planning algorithm, realizes the vehicle path planning application for the expressway, and carries on the deployment operation in the highway company. The path topology is constructed to transform the actual road information into abstract space that the machine can understand. An appropriate data structure is used for storage, and a path topology based on the modeling background of expressway is constructed to realize the mutual mapping between the two. Experiments show that the proposed method can further reduce the interpolation error, and the interpolation error in the case of random missing is smaller than that in the other two missing modes. In order to improve the real-time performance of vehicle path planning, the association features are selected, the path weights are calculated comprehensively, and the traditional path planning algorithm structure is optimized. It is of great significance for the sustainable development of cities.

• Journal of Wellbeing Management and Applied Psychology
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• v.4 no.3
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• pp.23-33
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• 2021

Purpose: In the course of the domestic environmental impact assessment, the current status survey was improperly conducted, and the issue of false and inaccurate environmental impact assessment reports has been raised several times recently through media reports. Research design, data and methodology: There is a continuous demand for improvement measures for the current status measurement method, such as having difficulties in securing a normal measurement date in consideration of equipment operation and rainfall days in the field. Results: In addition, in order to grasp the general air quality status of the evaluation target area, it is necessary to check the various current status concentrations by season and time series per year. However, there is a problem that is currently being carried out based on limited results such as measurement for 1 day or 3 days. Conclusions: Therefore, in this study, based on the national atmospheric measurement network, an inverse distance weighted (IDW) interpolation method was applied to calculate the current state concentration. This study suggested a method to use it in preparing the air quality item in the environmental impact assessment report.