• Proceedings of the Computational Structural Engineering Institute Conference
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• 1989.10a
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• pp.46-50
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• 1989

Methods for the estimation of the coefficient matrices in the equation of motion for a linear multi-degree-of-freedom structure arc studied. For this purpose, the equation of motion is transformed into an auto-regressive and moving average with auxiliary input (ARMAX) model. The ARMAX parameters are evaluated using several methods of parameter estimation; such as toe least squares, the instrumental variable, the maximum likelihood and the limited Information maximum likelihood methods. Then the parameters of the equation of motion are recovered therefrom. Numerical example is given for a 3-story building model subjected to an earthquake exitation.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.481-493
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• 2011

We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.743-750
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• 2009

A class of Hermitian operators B admitting a positive semidefinite solution of the linear operator equation ${\sum}^n_{j=1}A^{n-j}XA^{j-1}=B$ for a fixed positive definite operator A is given via the Furuta inequality.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.749-763
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• 2021

This research article deals with the Mittag-Leffler-Hyers-Ulam stability of linear and impulsive fractional order differential equation which involves the Caputo derivative. The application of the generalized fractional Fourier transform method and fixed point theorem, evaluates the existence, uniqueness and stability of solution that are acquired for the proposed non-linear problems on Lizorkin space. Finally, examples are introduced to validate the outcomes of main result.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.465-477
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• 2023

In this study, we consider a heat equation with a variable-coefficient linear forcing term and a time-periodic boundary condition. Under some decay and smoothness assumptions on the coefficient, we establish the existence and uniqueness of a time-periodic solution satisfying the boundary condition. Furthermore, possible connections to the closed boundary layer equations were discussed. The difficulty with a perturbed leading order coefficient is demonstrated by a simple example.

• Journal of the Korean Chemical Society
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• v.7 no.4
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• pp.264-270
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• 1963

The general equation for the substituent effect test, which was derived in the previous paper, has been extended to correlate thermodynamic parameters of solvolysis reaction by modifying the potential energy term to represent the effect of changes in solvent composition. The linear fits of the new equation, $\Delta{\Delta}H^\neq=a'Y+b\Delta{\Delta}S^\neq$, were tested with 35 examples from literature and average correlation coefficient of 0.977 was obtained. Examination of results showed that the equation is generally applicable to solvolysis reaction and helps elucidate some the difficulties experienced with the Grunwald-Winsteln equation. It has been stressed that the linear enthalpy-entropy effect exists only between the external enthalpy and entropy of activation, and therefore strictly it is the linear external enthalpy-entropy effect.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.281-308
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• 2009

In the process of solving a linear equation, some questions had equal sign('=') relation properly, while other questions did not have equal sign('=') relation properly. Since whether students could express equal sign('=') relation properly or not is determined by questions, the direction for teaching should be instituted, and instruction and teaching should be conducted by comparing and analyzing after conducing tests on may items. Most of students who got the answer for items without the method of solving a linear equation solved the items using binomial. For questions asking to solve using the characteristic of equality, most of students solved the questions using binomial instead of using the characteristic of equality. Therefore, instruction and learning to solve equations using both the characteristic of equality and binomial have to be achieved.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.12-15
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• 1994

To establish the sea surface temperature estimation scheme for the upcoming advanced remote sensor, the quasi-analytical solution of the approximated radiative transfer equation which express the radiative transfer process of the radiant energy radiated from the sea surface to the satellite is approximated into the non-linear equation. To solve the simultaneous approximated radiative transfer equation which express the radiative transfer process of the radiant energy radiated from the sea surface to the satellite is approximated into the nonlinear equation. To solve the simultaneous approximated radiative transfer equation at each channel, the constrained non-linear optimization technique is adopted. To define the coefficients of the approximated radiative transfer equation and the constraints, the satellite detected radiance and the total transmittance are computed from the 1350 kinds of simulated atmosphere / surface models via radiative transfer code. The verification from the simulated data show the sufficient result.

• Journal of Industrial Technology
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• v.14
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• pp.19-28
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• 1994

We can get a tridiagonal block Toeplitz linear system by the finite difference approximation of 2-D Poisson equation. To exploit the nice property of this linear equation, we transform the equation into a Lyapunov equation and apply DST (discrete sine transform) to get diagonal matrix based Lyapunov equation. DST can be performed using FFT, which enables high-speed computaion. All the computations are performed on an SIMD parallel computer, the MasPar MP-2 with 4,096 processing elements. In this paper, parallel algorithm, mapping method of the algorithm onto the MP-2, and timing results are presented.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.229-241
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• 2020

For a second order linear differential equation f" + A(z)f' + B(z)f = 0, with A(z) and B(z) being transcendental entire functions under some restrictions, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions, with a condition, have exponent of convergence of zeros equal to infinity. Also, we have extended these results to higher order linear differential equations.