• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.169-178
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• 2006

For double arrays of constants ${a_{ni},\;1{\leq}i{\leq}k_n,\;n{\geq}1}$ and sequences ${X_n,\;n{\geq}1}$ of asymptotically almost negatively associated (AANA) random variables the almost sure convergence of $\sum\limits{_{i=1}}{^{k_n}}\;a_{ni}X_i$ is derived.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.275-282
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• 2004

Let {$a_{ni},\;u_n\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be an arry of constants. Let {X_{ni},\;u_n\;{\leq}\;i\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be {$a_{ni}$}-uniformly integrable random variables. Weak laws for the weighted sums ${{\Sigma}_{i=u_n}}^{{\upsilon}_n}\;a_{ni}X_{ni}$ are obtained.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.245-269
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• 1999

Multigrid method and acceleration by conjugate gradient method for first-order system least squares (FOSLS) using bilinear finite elements are developed for various boundary value problems of planar linear elasticity. They are two-stage algorithms that first solve for the displacement flux variable, then for the displacement itself. This paper focuses on solving for the displacement flux variable only. Numerical results show that the convergence is uniform even as the material becomes nearly incompressible. Computations for convergence factors and discretization errors are included. Heuristic arguments to improve the convergences are discussed as well.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.145-153
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• 2021

When {Xni|1 ≤ i ≤ n, n ≥ 1} be an array of rowwise negatively superadditive dependent(NSD) for semi-Gaussian random variables and {ani|1 ≤ i ≤ n, n ≥ 1} is an array of constants, we study the almost sure convergence of weighted sums ∑ni=1 aniXni under some appropriate conditions and we obtain some corollaries.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.815-828
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• 2006

Let {$V_{nk},\;k\;{\geq}\;1,\;{\geq}\;1$} be an array of rowwise independent random elements which are stochastically dominated by a random variable X with $E\|X\|^{\frac{\alpha}{\gamma}+{\theta}}log^{\rho}(\|X\|)\;<\;{\infty}$ for some ${\rho}\;>\;0,\;{\alpha}\;>\;0,\;{\gamma}\;>\;0,\;{\theta}\;>\;0$ such that ${\theta}+{\alpha}/{\gamma}<2$. Let {$a_{nk},k{\geq}1,n{\geq}1$) be an array of suitable constants. A complete convergence result is obtained for the weighted sums of the form $\sum{^\infty_k_=_1}\;a_{nk}V_{nk}$.

• Elastomers and Composites
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• v.54 no.4
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• pp.351-358
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• 2019

To evaluate the aging of a rubber pad in power window switch which is the part of a vehicle, the accelerated thermal aging test of rubber pad material is performed. Finite element analysis was performed using the nonlinear material constants of the rubber pad to calculate the operating force, and the Arrhenius relationship was derived from the aging temperature and time. The aging test was performed at 150, 180, 210, or 240 ℃ for 1 to 60 days. When the operating force of the rubber pad is changed by 10% from the initial value, the service life is expected to be 113 years, which is much longer than the life of the vehicle. This indicates that the aging life of the rubber pad is sufficiently safe and the operating force of the rubber pad during the life of the vehicle (20 years) was decreased by approximately 8.4%. By examining the correlation between the shear elastic modulus and operating force calculated from finite element analysis under each aging test condition, the changes in the operating force of the rubber pad and the shear elastic modulus showed good linear relationship. The aging life could be predicted by the change in shear elastic modulus and a process for predicting the aging life of automotive power window switch rubber pad parts is described herein.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.241-252
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• 2012

Let $\{X_{ni},\;1{\leq}i{\leq}n,\;n{\geq}1\}$ be a sequence of LNQD which are dominated randomly by another random variable X. We obtain the complete convergence and almost sure convergence of weighted sums ${\sum}^n_{i=1}a_{ni}X_{ni}$ for LNQD by using a new exponential inequality, where $\{a_{ni},\;1{\leq}i{\leq}n,\;n{\geq}1\}$ is an array of constants. As corollary, the results of some authors are extended from i.i.d. case to not necessarily identically LNQD case.

• Bulletin of the Korean Chemical Society
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• v.29 no.5
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• pp.948-952
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• 2008

The molecular association of acceptors with electron donors is studied in the highly-polar solvent $CH_3CN$. Tetracyanoquinodimethane (TCNQ) forms a stable charge-transfer complex with donor molecules such as 4- aminobiphenyl (4-AB), benzidine (BD) and 2-aminobiphenyl (2-AB) with high association constants. The complexes of TCNQ with 4-AB or BD show new absorption bands at around 800 and 500 nm, which can be identified as reduced $TCNQ^{{\bullet}-}$ and $TCNQ^{2-}$ species, respectively. These bands grow quickly upon photoirradiation, implying that the charge-transfer complexes are easily formed in an excited state. Conversely, a small spectral manifestation of the charge transfer was observed in the case of 2-AB complex. It is demonstrated that the structural orientation between the geminate ion pairs could play an important role in building a stable complex.

• ETRI Journal
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• v.34 no.4
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• pp.527-535
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• 2012

A general equivalent circuit model is developed for a wireless energy transfer system composed of multiple coils via coupled magnetic resonances. To verify the developed model, four types of wireless energy transfer systems are fabricated, measured, and compared with simulation results. To model a system composed of n-coils, node equations are built in the form of an n-by-n matrix, and the equivalent circuit model is established using an electric design automation tool. Using the model, we can simulate systems with multiple coils, power sources, and loads. Moreover, coupling constants are extracted as a function of the distance between two coils, and we can predict the characteristics of a system having coils at an arbitrary location. We fabricate four types of systems with relay coils, two operating frequencies, two power sources, and the function of characteristic impedance conversion. We measure the characteristics of all systems and compare them with the simulation results. The flexibility of the developed model enables us to design and optimize a complicated system consisting of many coils.