• 충청수학회지
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• 제25권1호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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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.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2001년도 춘계학술대회 논문집
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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.

• 소성∙가공
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• 제7권2호
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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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• 제13권4호
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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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• 제12권5호
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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.

• 대한기계학회논문집A
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• 제34권4호
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• pp.457-465
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• 2010

본 연구에서는 McVetty 와 Monkman-Grant 의 모델에 기초하여 만들어진 새로운 크리프 수명예측 모델인 Taylor 급수(T-S) 모델을 제안하였다. 본 모델은 회귀분석에서 발생하는 오차를 줄이기 위하여 McVetty 모델에서 sinh 함수를 Taylor 급수에 의해 변환한 후 첫 3 개항을 취한 것으로서 모델중의 상수 값은 통계학적 방법인 최대가능성 기법을 이용하여 결정되었다. T-S 모델을 이용하여 Alloy 617 의 크리프 수명을 예측한 결과 Eno, 지수함수 및 Larson-Miller(L-M) 방법에 비해 더 정확한 예측을 하는 것으로 나타났다. 또한 T-S 모델은 특정 온도에서 크리프 수명 예측을 할 수 있는 등온 T-S(IT-S) 모델로 표현될 수 있었으며, IT-S 모델은 Alloy 617 의 장시간 크리프 수명예측에서 가장 좋은 예측을 하는 것으로 나타났다.