• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.531-540
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• 2008

We discuss the decomposition problems on circuit graphs and triangular graphs, and show how they can be applied to obtain results on spanning trees or hamiltonian cycles. We also prove that every circuit graph containing no separating 3-cycles can be extended by adding new edges to a triangular graph containing no separating 3-cycles.

• Current Applied Physics
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• v.18 no.11
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• pp.1327-1337
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• 2018

This paper investigates the vibration behavior of pristine and defected triangular graphene sheets; which has recently attracted the attention of researchers and compare these two types in natural frequencies and sensitivity. Here, the molecular dynamics method has been employed to establish a virtual laboratory for this purpose. After measuring the different parameters obtained by the molecular dynamics approach, these data have been analyzed by using the frequency domain decomposition (FDD) method, and the dominant frequencies and mode shapes of the system have been extracted. By analyzing the vibration behaviors of pristine triangular graphene sheets in four cases (right angle of 45-90-45 configuration, right angle of 60-90-30 configuration, equilateral triangle and isosceles triangle), it has been demonstrated that the natural frequencies of these sheets are higher than the natural frequency of a square sheet, with the same number of atoms, by a minimum of 7.6% and maximum of 26.6%. Therefore, for increasing the resonance range of sensors based on 2D materials, nonrectangular structures, and especially the triangular structure, can be considered as viable candidates. Although the pristine and defective equilateral triangular sheets have the highest values of resonance, the sensitivity of defective (45,90,45) triangular sheet is more than other configurations and then, defective (45,90,45) sheet is the worst choice for sensor applications.

• Proceedings of the KIEE Conference
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• 1987.07a
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• pp.185-189
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• 1987

An analysis and design of large-scale linear multivariable systems often requires to be block triangularized form for good sensitivity of the systems when their poles and zeros are varied. But the decomposition algorithms presented up to now need a procedure of permutation, rescaling and a solution of nonlinear algebraic equations, which are usually burden. To avoid these problem, in this paper we develop a newly alternative block triangular decomposition algorithm which used the generalized matrix sign function on the Z-plane. Also, the decomposition algorithm demonstrated using the fifth order linear model of a distillation tower system.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.585-590
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• 2005

An efficient procedure for finding the inverse of a nonsingular matrix is developed by solving directly for the UL decomposition of the inverse based on the entries of the original nonsingular matrix.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.49 no.3
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• pp.31-37
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• 2012

This paper presents an efficient hardware architecture to enable the high-speed Givens rotation-based QR decomposition. The proposed architecture achieves a highly parallel givens rotation process by maximizing the number of pivots selected for parallel zero-insertions. Sign-select lookahed (SSL)-CORDIC is also efficiently used for the high-speed givens rotation. The performance of QR decomposition hardware considerably increases compared to the conventional triangular systolic array (TSA) architecture. Moreover, the circuit area of QR decomposition hardware was reduced by decreasing the number of flip-flops for holding the pre-computed results during the decomposition process. The proposed QR decomposition hardware was implemented using TSMC $0.25{\mu}m$ technology. The experimental results show that the proposed architecture achieves up to 70 % speed-up over the TACR/TSA-based architecture for the $8{\times}8$ matrix decomposition.

• Wind and Structures
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• v.9 no.3
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• pp.231-243
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• 2006

An improvement to the spectral representation algorithm for the simulation of wind velocity fields on large scale structures is proposed in this paper. The method proposed by Deodatis (1996) serves as the basis of the improved algorithm. Firstly, an interpolation approximation is introduced to simplify the computation of the lower triangular matrix with the Cholesky decomposition of the cross-spectral density (CSD) matrix, since each element of the triangular matrix varies continuously with the wind spectra frequency. Fast Fourier Transform (FFT) technique is used to further enhance the efficiency of computation. Secondly, as an alternative spectral representation, the vectors of the triangular matrix in the Deodatis formula are replaced using an appropriate number of eigenvectors with the spectral decomposition of the CSD matrix. Lastly, a turbulent wind velocity field through a vertical plane on a long-span bridge (span-wise) is simulated to illustrate the proposed schemes. It is noted that the proposed schemes require less computer memory and are more efficiently simulated than that obtained using the existing traditional method. Furthermore, the reliability of the interpolation approximation in the simulation of wind velocity field is confirmed.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.9
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• pp.37-48
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• 1996

In this paper, for the single s-a-E fault detected in a triangular cellular permutation network (TCPN), we propose a method which can tolerate a fault by reconfiguring the netowrk and analyze the possibilities of the reconfiguration. The network is set up through iterative decomposition of a permutation into the right or left coset. For the s-a-E fault of a cell which is to be transpositioned for an increasing order mapping, we cna reconfigure it merely by switching te decomposition scheme from right coset to left coset or vice versa. Also for a decreasing order mapping, we make a detour around the faulty cell. Reconfiguring with the redundant connectivity of a TCPN, we could realize form 17% to 90% of the permutation for the number of inputs from 4 to 40. REconfiguration of the network by exchanging the first input with the last input and the first output with the last output resulted in more than 99% realization of the permutation. Also with the exchange of all inputs and outputs with neighboring cells, we could have 100% realization of the permutation.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.11
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• pp.53-59
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• 2011

We propose an adaptive resource allocation algorithm with generalized triangular decomposition scheme in downlink multi-user multiple-input-multiple-output channel to maximize the system throughput when we adopt the modulation scheme such as BPSK, QPSK, 16QAM, and 64QAM. The proposed scheme also considers an bit-error-rate performance as well as system throughput while performing resource allocation. We present simulation results to show that the proposed scheme achieves the system throughput up to 2bit difference by capacity and has better BER performance than SVD based resource allocation scheme in all SNR regions.

• Journal of Aerospace System Engineering
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• v.16 no.3
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• pp.63-72
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• 2022

The purpose of this paper was to understand the dynamics of deployment of large mesh antennas, and to provide a numerical method for determining the dynamic stiffness and the driving forces for the design. The deployment structure was numerically modeled using the frame elements. The eigenvalue analysis was demonstrated, with respect to the folded and unfolded configurations of the antenna. A multibody dynamic model was formulated with Kane's equation, and simulated using the pseudo upper triangular decomposition (PUTD) method for resolving the constrained problem. Based on the multibody model, the kinetics of the deployment, the motor driving forces, and the feasibility of the designed deployment structure were investigated.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.50 no.10
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• pp.691-699
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• 2022

Large aperture antennas with long focal lengths in space have important application for telecommunications, Earth observation and science missions. This paper aims to understand the dynamics of deployment of large mesh antennas and to provide a multibody model for determining the driving forces for the design of reflectors and booms. The modular deployable reflector and boom are designed based on the deployment unit cell. A multibody dynamic model is formulated with Kane's equation and simulated using the pseudo upper triangular decomposition (PUTD) method for solving the constrained problem. Based on the multibody dynamic model, the kinetics of the deployment, the motor driving forces, and the structural dynamic deformation are investigated.