• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.1-18
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• 2012

The aim of this paper is to investigate the superstability of the pexider type sine(hyperbolic sine) functional equation $f(\frac{x+y}{2})^{2}-f(\frac{x+{\sigma}y}{2})^{2}={\lambda}g(x)h(y),\;{\lambda}:\;constant$ which is bounded by the unknown functions ${\varphi}(x)$ or ${\varphi}(y)$. As a consequence, we have generalized the stability results for the sine functional equation by P. M. Cholewa, R. Badora, R. Ger, and G. H. Kim.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2001.05a
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• pp.190-193
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• 2001

Hot deformation behavior of Udimet 720Li was characterized by compression tests in the temperature range of $1025^{\circ}C\;to\;1150^{\circ}C$ and the strain rate rage of $0.0005s^{-1}\;to\;5s^{-1}$. In order to characterize the dependence of flow stress on strain, strain rate and temperature, a constitutive equation based on hyperbolic sine formation was used. Isothermal forging of Udimet 720Li was performed in the temperature range $1050-1150^{\circ}C$ at strain rates of $0.05s^{-1}\;and\;0.005s^{-1}$. FE simulation was also carried out to predict deformation microstructures during isothermal forging.

• Transactions of Materials Processing
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• v.7 no.2
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• pp.158-167
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• 1998

Hot restoration mechanism flow stress and stain of the Al2024 composites reinforced with 1,8,15,36, and $44{\mu}m\;SiC_p$(10 vol. %) were studied by hot torsion tests. The hot restoration mechanism of all the composites was found to be dynamic recrystallization(DRX) at $320^{\circ}C$ while that of the composites reinforced with 1 and $8{\mu}m\;SiC_p$ was found to be dynamic recovery(DRX) at $480^{\circ}C$. It was found that the Al2024 composite with $15{\mu}m\;SiC_p$ showed the highest flow stress(${\sim}$223 MPa) at $320^{\circ}C$ under a strain rate of 1.0/sec. Also the highest flow strain of the composites was obtained at $430^{\circ}C$. The com-posites reinforced with 1 and $8{\mu}m\;SiC_p$ showed lower flow stress and higher flow strain at $480^{\circ}C$ than those of the composites reinforced with 15, 36, and $44\;{\mu}m\;SiC_p$ These result were discussed in relation to the transition of the hot restoration mechanism. $DRX{\leftrightarrow}DRV$. The dependence of flow stress on strain rate and temperature was attempted to fit with the hyperbolic sine equation ($\dot{\varepsilon}=A[sinh({\alpha}{\cdot}{\sigma}_p]^n$ exp(-Q/RT)and Zener-Hollomon parameter($Z=\;\dot{\varepsilon}\;exp(Q/RT))$.

• Bulletin of the Korean Chemical Society
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• v.13 no.4
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• pp.413-419
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• 1992

The theoretical equation for the relaxation spectrum of nonlinear viscoelastic polymeric material was derived from the Ree-Eyring and Maxwell non-Newtonian model. This model consists of infinite number of hyperbolic sine law Maxwell elements coupled in parallel plus a spring without a dashpot. Infinite number of nonlinear viscoelastic Maxwell elements can be used by specifying distribution of relaxation times, hole volumes, molecular weights, crystallite size and conformational size, etc. The experimentals of stress relaxation were carried out using the tensile tester with the solvent chamber. The relaxation spectra of nylon 6 filament fibers in various electrolytic solutions were obtained by applying the experimental stress relaxation curves to the theoretical equation of relaxation spectrum. The determination of relaxation spectra was performed from computer calculation.

• Bulletin of the Korean Chemical Society
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• v.12 no.5
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• pp.468-473
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• 1991

Viscoelastic properties of PET filament fibers on stress relaxation were investigated in the solvents of $H_2$O, 0.05% NaOH and 50% DMF using an Instron (UTM4-100 Tensilon) with solvent chamber. The theoretical stress relaxation equation derived by applying the Ree-Eyring's hyperbolic sine law to dashpot of three element non-Newtonian model was applied to the experimental stress relaxation curves, and the model parameters $G_1,G_2$, ${\alpha}$ and ${\beta}$ were obtained. By analyzing temperature dependency of the relaxation time, the values of activation entropy, activation enthalpy and activation free energy for flow in PET filament fiber were evaluated, the activation free energy being about 25.7 kcal/mol. The self diffusion coefficient and hole distance were obtained from parameters ${\alpha}$, ${\beta}$ and crystallite size in order to study the self diffusion and the orientation of crystallites in amorphous region and the effect of solvent.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.4
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• pp.457-465
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• 2010

In this study, a Taylor series (T-S) model based on the Arrhenius, McVetty, and Monkman-Grant equations was developed using a mathematical analysis. In order to reduce fitting errors, the McVetty equation was transformed by considering the first three terms of the Taylor series equation. The model parameters were accurately determined by a statistical technique of maximum likelihood estimation, and this model was applied to the creep data of alloy 617. The T-S model results showed better agreement with the experimental data than other models such as the Eno, exponential, and L-M models. In particular, the T-S model was converted into an isothermal Taylor series (IT-S) model that can predict the creep strength at a given temperature. It was identified that the estimations obtained using the converted ITS model was better than that obtained using the T-S model for predicting the long-term creep life of alloy 617.