• Journal of the Korean Chemical Society
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• v.16 no.6
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• pp.349-353
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• 1972

The Faddeev-type equations for systems of more than four particles are derived from Weinberg's equation. The derivation is considerably simpler than that by others. The Faddeev-type equations thus derived can be expressed in a matrix form and the rules for constructing the inhomogeneous term and the matrix kernel of the matrix integral equation are formulated and verified explicitly for N=3, 4, and 5.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.1027-1029
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• 1998

The method of building the system state matrix described here is the direct method which constructs elements of state matrix directly by the algebraic expressions from the machine data with time constants. From this method, it is reasonable to confirm the structure of state matrix and the relation of submatrices and elements efficiently. In this paper the interrelationship of submatrices of system matrix is investigated and a constitution of system matrix considering time constants.

• Wind and Structures
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• v.39 no.2
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• pp.125-140
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• 2024

The simulation of non-stationary wind velocity is particularly crucial for the wind resistant design of slender structures. Recently, some data-driven simulation methods have received much attention due to their straightforwardness. However, as the number of simulation points increases, it will face efficiency issues. Under such a background, in this paper, a time-varying coherence matrix decomposition method based on Diagonal Proper Orthogonal Decomposition (DPOD) interpolation is proposed for the data-driven simulation of non-stationary wind velocity based on S-transform (ST). Its core idea is to use coherence matrix decomposition instead of the decomposition of the measured time-frequency power spectrum matrix based on ST. The decomposition result of the time-varying coherence matrix is relatively smooth, so DPOD interpolation can be introduced to accelerate its decomposition, and the DPOD interpolation technology is extended to the simulation based on measured wind velocity. The numerical experiment has shown that the reconstruction results of coherence matrix interpolation are consistent with the target values, and the interpolation calculation efficiency is higher than that of the coherence matrix time-frequency interpolation method and the coherence matrix POD interpolation method. Compared to existing data-driven simulation methods, it addresses the efficiency issue in simulations where the number of Cholesky decompositions increases with the increase of simulation points, significantly enhancing the efficiency of simulating multivariate non-stationary wind velocities. Meanwhile, the simulation data preserved the time-frequency characteristics of the measured wind velocity well.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.05a
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• pp.193-196
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• 2008

Z. Cao had proposed NFRM(new fuzzy reasoning method) which infers in detail using relation matrix. In spite of the small inference rules, it shows good performance than mamdani's fuzzy inference method. In this paper, we propose 2. Cao's fuzzy inference method using learning ability witch is used a gradient descent method in order to improve the performances. Because it is difficult to determine the relation matrix elements by trial and error method which is needed many hours and effort. Simulation results are applied linear and nonlinear system show that the proposed inference method has good performances.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.443-454
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• 2014

In this paper, we give linearization of generalized Fi-bonacci sequences {$g_n$} and {$q_n$}, respectively, defined by Eq.(5) and Eq.(6) below and use this result to give the matrix form of the nth power of a companion matrix of {$g_n$} and {$q_n$}, respectively. Then we re-prove the Cassini's identity for {$g_n$} and {$q_n$}, respectively.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.441-455
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• 2017

In this article we have determined the spectrum and fine spectrum of the lower triangular matrix B(r, s) on the Hahn sequence space h. We have also determined the approximate point spectrum, the defect spectrum and the compression spectrum of the operator B(r, s) on the sequence space h.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1285-1301
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• 2018

In this paper, we mainly consider the determinantal representations of the unique solution and the general solution to the restricted system of quaternion matrix equations $$\{{A_1X=C_1\\XB_2=C_2,}\;{{\mathcal{R}}_r(X){\subseteq}T_1,\;{\mathcal{N}}_r(X){\supseteq}S_1$$, respectively. As an application, we show the determinantal representations of the general solution to the restricted quaternion matrix equation $$AX+Y B=E,\;{\mathcal{R}}_r(X){\subseteq}T_1,\;{\mathcal{N}}_(X){\supseteq}S_1,\;{\mathcal{R}}_l(Y){\subseteq}T_2,\;{\mathcal{N}}_l (Y){\supseteq}S_2$$. The findings of this paper extend some known results in the literature.

• Transactions of Materials Processing
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• v.6 no.4
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• pp.346-356
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• 1997

The fiber orientation distribution and interface bonding in hot extrusion process have an effect on the maechanical properties of metal matrix composites(MMC's). Aluminium alloy matrix composites reinforced with alumina short fibers are fabricated by compocasting method. MMC's billets are extruded at high temperature through conical and curved shaped dies with various extrusion ratios and temperature. This present study was directed to describe the systematic correlation between extrusion die shape and subsequent results such as fiber breakage, fiber orientation and tensile strength to hot extruded MMC's billet. Extrusion load, tensile strength and hardness for variation of extrusion ratios and temperature are investigated to examine mechanical properties of extruded MMC's SEM fractographs of tensile specimens are observed to analyze the fracture mechanism.

• East Asian mathematical journal
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• v.32 no.1
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• pp.13-25
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• 2016

We consider the nonlinear matrix equation $X^p+AX^qB+CXD+E=0$, where p and q are positive integers, A, B and E are $n{\times}n$ nonnegative matrices, C and D are arbitrary $n{\times}n$ real matrices. A sufficient condition for the existence of the elementwise minimal nonnegative solution is derived. The monotone convergence of Newton's method for solving the equation is considered. Several numerical examples to show the efficiency of the proposed Newton's method are presented.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1273-1283
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• 2019

In matrix analysis, the Wielandt-Mirsky conjecture states that $$dist({\sigma}(A),{\sigma}(B)){\leq}{\parallel}A-B{\parallel}$$ for any normal matrices $A,B{\in}{\mathbb{C}}^{n{\times}n}$ and any operator norm ${\parallel}{\cdot}{\parallel}$ on $C^{n{\times}n}$. Here dist(${\sigma}(A),{\sigma}(B)$) denotes the optimal matching distance between the spectra of the matrices A and B. It was proved by A. J. Holbrook (1992) that this conjecture is false in general. However it is true for the Frobenius distance and the Frobenius norm (the Hoffman-Wielandt inequality). The main aim of this paper is to study the Hoffman-Wielandt inequality and some weaker versions of the Wielandt-Mirsky conjecture for matrix polynomials.