• 대한수학회보
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• 제45권4호
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• pp.717-728
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• 2008

Let H be a real Hilbert space and S = {T(s) : $0\;{\leq}\;s\;<\;{\infty}$} be a nonexpansive semigroup on H such that $F(S)\;{\neq}\;{\emptyset}$ For a contraction f with coefficient 0 < $\alpha$ < 1, a strongly positive bounded linear operator A with coefficient $\bar{\gamma}$ > 0. Let 0 < $\gamma$ < $\frac{\bar{\gamma}}{\alpha}$. It is proved that the sequences {$x_t$} and {$x_n$} generated by the iterative method $$x_t\;=\;t{\gamma}f(x_t)\;+\;(I\;-\;tA){\frac{1}{{\lambda}_t}}\;{\int_0}^{{\lambda}_t}\;T(s){x_t}ds,$$ and $$x_{n+1}\;=\;{\alpha}_n{\gamma}f(x_n)\;+\;(I\;-\;{\alpha}_nA)\frac{1}{t_n}\;{\int_0}^{t_n}\;T(s){x_n}ds,$$ where {t}, {${\alpha}_n$} $\subset$ (0, 1) and {${\lambda}_t$}, {$t_n$} are positive real divergent sequences, converges strongly to a common fixed point $\tilde{x}\;{\in}\;F(S)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)\tilde{x},\;x\;-\;\tilde{x}{\rangle}\;{\leq}\;0$ for $x\;{\in}\;F(S)$.

• Korea-Australia Rheology Journal
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• 제18권4호
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• pp.199-207
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• 2006

Measurements by Luap et al. (2005) of elongational viscosity and birefringence of two nearly monodisperse polystyrene melts with molar masses $M_{w}$ of $206,000g{\cdot}mol^{-1}$ (PS206k) and $465,000g{\cdot}mol^{-1}$ (PS465k) respectively are reconsidered. At higher elongational stresses, the samples showed clearly deviations from the stress optical rule (SOR). The elongational viscosity data of both melts can be modeled quantitatively by the MSF model of Wagner et al. (2005), which is based on the assumption of a strain-dependent tube diameter and the interchain pressure term of Marrucci and Ianniruberto (2004). The only nonlinear parameter of the model, the tube diameter relaxation time, scales with $M_{w}^{2}$. In order to get agreement with the birefringence data, finite chain extensibility effects are taken into account by use of the $Pad\'{e}$ approximation of the inverse Langevin function, and the interchain pressure term is modified accordingly. Due to a selfregulating limitation of chain stretch by the FENE interchain pressure term, the transient elongational viscosity shows a small dependence on finite extensibility only, while the predicted steady-state elongational viscosity is not affected by non-Gaussian effects in agreement with experimental evidence. However, deviations from the SOR are described quantitatively by the MSF model by taking into account finite chain extensibility, and within the experimental window investigated, deviations from the SOR are predicted to be strain rate, temperature, and molar mass independent for the two nearly monodisperse polystyrene melts in good agreement with experimental data.

• 소성∙가공
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• 제9권2호
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• pp.103-111
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• 2000

It is necessary to improve mechanical and optical properties in the optical disk substrates as the information storage density using short wavelength laser are being developed. The birefringence distribution is regarded as one of the most important optical properties for optical disk. In the present study, the birefringence distrubution is calculated using the Leonov model for viscoelastic constitutive equations and Cross/WLF model for viscosity approximation. The effects of processing conditions upon the development of birefringence discosity approximation. The effects of processing conditions upon the development of birefringence distribution in the optical disk were examined theoretically. It was found that the values of the birefringence distributions were very sensitive to the mold wall temperature history which minimizes the birefringence distribution. The analytical results showed the possibility of improving mechanical and optical properties in the optical disk substrates by active control of the mold wall temperature history.

• 설비공학논문집
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• 제18권4호
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• pp.359-369
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• 2006

This study aims deriving analysis the flow characteristic of kitchen hood system with using 3-D numerical analysis method and improving the system to expel pollutes more efficiently. This system is applied with $k-{\varepsilon}$ turbulent model and using incompressibility viscosity flow range and boundary condition which are related to Bossinesq approximation following density variation in control volume. To understand the flow characteristics of four models, this study only focuses on velocity field, temperature field, and concentration field varying with followings whether separation plate is set or not and the shapes of separation plates. The quantity of air, speed of exhaust fan and temperature and concentration of heating source are concerned as constant values.

• 대한수학회논문집
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• 제24권3호
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• pp.381-393
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• 2009

Strong convergence theorems on viscosity approximation methods for finding a common zero of a finite family accretive operators are established in a reflexive and strictly Banach space having a uniformly G$\hat{a}$teaux differentiable norm. The main theorems supplement the recent corresponding results of Wong et al. [29] and Zegeye and Shahzad [32] to the viscosity method together with different control conditions. Our results also improve the corresponding results of [9, 16, 18, 19, 25] for finite nonexpansive mappings to the case of finite pseudocontractive mappings.

• East Asian mathematical journal
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• 제24권1호
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• pp.81-95
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T\;:\;C\;{\rightarrow}\;E$ a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For $f\;:\;C\;{\rightarrow}\;C$ a contraction and $t\;{\in}\;(0,\;1)$, let $x_t$ be a unique fixed point of a contraction $T_t\;:\;C\;{\rightarrow}\;E$, defined by $T_tx\;=\;tf(x)\;+\;(1\;-\;t)Tx$, $x\;{\in}\;C$. It is proved that if {$x_t$} is bounded, then $x_t$ converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm.

• Journal of Mechanical Science and Technology
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• 제16권4호
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• pp.522-531
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• 2002

In order to study the thermal-hydraulic behavior of the cable-in-conduit-conductor (CICC), a numerical model has been developed. In the model, the high heat transfer approximation between superconducting strands and supercritical helium is adopted. The strong coupling of heat transfer at the front of normal zone generates a contact discontinuity in temperature and density. In order to obtain the converged numerical solutions, a moving mesh method is used to capture the contact discontinuity in the short front region of the normal zone. The coupled equation is solved using the finite element method with the artificial viscosity term. Details of the numerical implementation are discussed and the validation of the code is performed for comparison of the results with thse of GANDALF and QSAIT.

• 천문학회지
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• 제34권4호
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• pp.251-254
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• 2001

To examine the structure and dynamics of thick accretion disks, we use a two-dimensional viscous hydrodynamic code coupled with radiation transport. The $\alpha$-model and the full viscous stress-tensor description for the kinematic viscosity are used. The radiation transport is treated in the gray, flux-limited diffusion approximation. The finite difference methods used are based on an explicit-implicit method. We apply the numerical code to the Super-Eddington black-hole model for SS 433.@The result for a very small viscosity parameter a reproduces well the characteristic features of SS 433, such as the relativistic jets with $\~$0.26c, the small collimation degree of the jets, the mass-outflow rate of ${\ge}5{\times}10^{-7}M{\bigodot}yr^{-1}$, and the formation of the X-ray iron emission lines.

• Tribology and Lubricants
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• 제5권2호
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• pp.48-54
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• 1989

The effects of angular misalignment, coning and the temperature difference between the primary seal ring and the seal seat on the pressure distribution in mechanical face seals are analyzed. The modified Reynolds equation for the temperature dependent viscosity was solved by a finite difference approximation and Gauss-Seidel method. It is shown that the amplitude of pressure is significantly affected by the misalignment of the seals and a large temperature difference between the rotor and the stator.

• 대한수학회보
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• 제51권2호
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• pp.479-499
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• 2014

In this paper, we propose new iteration methods for finding a common point of the solution set of a pseudomonotone equilibrium problem and the solution set of a monotone equilibrium problem. The methods are based on both the extragradient-type method and the viscosity approximation method. We obtain weak convergence theorems for the sequences generated by these methods in a real Hilbert space.