• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.767-772
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• 1994

For an $n \times n$ complex matrix $A = [A_{ij}]$, the permanent of A, per A, is defined by $$ per A = \sub_{\sigma \in S_n}{a_{1 \sigma(1)} a_{2 \sigma(2)} \cdots a_{n \sigma(n)} $$ where $S_n$ stands for the symmetric group on the set {1, 2, ..., n}.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.471-471
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• 2000

This paper presents a new kurtosis-based algorithm for blind separation of convolutively mixed source signals. The algorithm whitens the signals not only spatially but also temporally beforehand. A separator is built for the whitened signals and it exists in the set of para-unitary matrices. Since the set forms a curved manifold, it is hard to treat its elements. In order to avoid the difficulty, this paper introduces the Cayley transformation for the para-unitary matrices. The transformed matrix is referred to as para-skew-Hermitian matrix and the set of such matrices forms a linear space. In the set of all para-skew-Hermitian matrices, the kurtosis-based algorithm obtains a desired separator. This paper also shows the algorithm's application to electrogastrogram datum which are observed by 4 electrodes on subjects' abdomen around their stomachs. An electrogastrogram contains signals from a stomach and other organs. This paper obtains independent components by the algorithm and then extracts the signal corresponding to the stomach from the data.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.57-65
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• 1990

The finite element menthod for the investigation of the static and dynamic stability of the plane framed structures subjected to non-conservative forces is presented. By using the Hermitian polynomial as the shape function, the geometric stiffness matrix, the load correction stiffness matrix for non-conservative forces, and the matrix equation of internal and external damping are derived. Then, a matrix equation of the motion for the non-conservative system is formulated and the critical divergence and flutter loads are determined from this equation.

• Structural Engineering and Mechanics
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• v.19 no.1
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• pp.73-96
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• 2005

For the spatially coupled free vibration analysis of shear deformable thin-walled non-symmetric curved beam subjected to initial axial force, an exact dynamic element stiffness matrix of curved beam is evaluated. Firstly equations of motion and force-deformation relations are rigorously derived from the total potential energy for a curved beam element. Next a system of linear algebraic equations are constructed by introducing 14 displacement parameters and transforming the second order simultaneous differential equations into the first order simultaneous differential equations. And then explicit expressions for displacement parameters are numerically evaluated via eigensolutions and the exact $14{\times}14$ dynamic element stiffness matrix is determined using force-deformation relations. To demonstrate the accuracy and the reliability of this study, the spatially coupled natural frequencies of shear deformable thin-walled non-symmetric curved beams subjected to initial axial forces are evaluated and compared with analytical and FE solutions using isoparametric and Hermitian curved beam elements and results by ABAQUS's shell elements.

• Journal of Korean Society of Steel Construction
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• v.13 no.6
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• pp.703-713
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• 2001

Derivation procedures of exact dynamic stiffness matrices of thin-walled straight beams subjected to eccentrically axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of displacement parameters are exactly derived and finally exact stiffness matrices are determined using element force-displacement relationships. The natural frequencies of nonsymmetric thin-walled straight beams are evaluated and compared with analytical solutions or results by thin-walled beam element using the cubic Hermitian polynomials and ABAQU's shell elements in order to demonstrate the validity of this study.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.369-376
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• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.291-294
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• 1995

In this paper, two algorithms for computing multiple or clustered eigenvalues are proposed. The algorithm can be applied to all kinds of Hermitian matrix unlike the existing algorithm. Characteristics of the proposed algorithms is examined by MATLAB simulations.

• Computational Structural Engineering
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• v.11 no.1
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• pp.191-204
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• 1998

The general formulation for free vibration and stability analysis of unsymmetric thin-wared space frames is presented in case where the shear deformation effects are neglected. The kinetic and total potential energies are derived by applying the extended virtual work principle, introducing displacement parameters defined at the arbitrarily chosen axis and including warping deformation and second order terms of finite semitangential rotations. In formulating the finite element procedure, cubic Hermitian polynomials are utilized as shape functions of the two node space frame element. Mass, elastic stiffness, and geometric stiffness matrices for the unsymmetric thin-walled section are evaluated, and load-correction stiffness matrices for off-axis distributed loadings are considered. In order to illustrate the accuracy and practical usefulness of this formulation, finite element solutions for the free vibration and stability problems of thin-walled beam-columns and space frames are presented and compared with available solutions.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.1
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• pp.93-103
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• 1994

Two beam/column elements are developed in order to analyze the geometric nonlinear plane irames including the effects of internal hinge and transverse shear deformation. In the case of the first element (finite segment method), tangent stiffness matrix is derived by directly integrating the equilibrium equations whereas in the case of the second element (finite element method) elastic and goemetric stiffness matrices are calculated by using the hermitian polynomials including the effects of internal hinge and shear deformation as the shape function. Numerical results are presented for the selected test problems which demonstrate that both elements represent reliable and highly accurate tools.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.1
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• pp.27-36
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• 1990

Two beam/column elements in order to analyze the geometric nonlinear plane framed structures including the effects of transverse shear deformation and bending stretching coupling are developed. In the case of the first element (finite segment method), tangent stiffness matrix are derived by directly integrating the equilibrium equations whereas in the case of the second element (finite element method) elastic and geometric stiffness matrices are calculated by using the hermitian polynomials including shear deformation effect as the shape function. Both elements possess the usual six degree of freedoms. Numerical results are presented for the selected test problems which demonstrate that both elements represent reliable and highly accurate tools.