• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.207-214
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• 2010

In this paper, a generalized variational inequality problem is considered. An iterative method is studied for approximating a solution of the generalized variational inequality problem. Strong convergence theorem are established in a real Hilbert space.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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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.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1363-1379
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• 2011

Halpern iterative algorithm is one of the most cited in the literature of approximation of fixed points of nonexpansive mappings. Different authors modified this iterative algorithm in Banach spaces to approximate fixed points of nonexpansive mappings. One of which is Hu [8] and Yao et al [21] modification of Halpern iterative algorithm for nonexpansive mappings in Banach spaces. It is the purpose of this paper to thoroughly analyze this modification and its convergence conditions. Unfortunately, Hu [8] and Yao et al [21] control conditions imposed on the modified Halpern iterative algorithm to have strong convergence are found to be not sufficient. In this paper, counterexamples are constructed to prove that the strong convergence conditions of Hu [8] and Yao et al [21] are not sufficient. It is also proved that with some additional conditions on the control parameters, strong convergence of the defined iterative algorithm is obtained in different Banach space settings.

• Journal of the Korean Chemical Society
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• v.14 no.3
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• pp.263-269
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• 1970

A theory of surface tension developed by using the approximation that the surface of liquids consists of a monomolecular layer has been applied to the molten salts (NaCl, KCl, NaBr, KBr) and the strong electrolyte solutions. By considering that the ionic forces are the long-range forces and with the use of the partition functions developed, the surface tension of molten salts and strong electrolyte solutions has been calculated. The results show good agreement between theory and experiment at various temperatures and over a wide concentration ranges (0.1-4.0m)

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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• pp.191-198
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• 2003

The generalized knapsack problem or gknap is the combinatorial optimization problem of optimizing a nonnegative linear function over the integral hull of the intersection of a polynomially separable 0-1 polytope and a knapsack constraint. The knapsack, the restricted shortest path, and the constrained spanning tree problem are a partial list of gknap. More interesting1y, all the problem that are known to have a fully polynomial approximation scheme, or FPTAS are gknap. We establish some necessary and sufficient conditions for a gknap to admit an FPTAS. To do so, we recapture the standard scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a weaker sufficient condition than the strong NP-hardness that a gknap does not have an FPTAS. Finally, we apply the conditions to explore the fully polynomial approximability of the constrained spanning problem whose fully polynomial approximability is still open.

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.559-570
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• 2008

This paper proposes an improved particle swarm optimization named PSO with Controllable Random Exploration Velocity (PSO-CREV) behaving an additional exploration behavior. Different from other improvements on PSO, the updating principle of PSO-CREV is constructed in terms of stochastic approximation diagram. Hence a stochastic velocity independent on cognitive and social components of PSO can be added to the updating principle, so that particles have strong exploration ability than those of conventional PSO. The conditions and main behaviors of PSO-CREV are described. Two properties in terms of "divergence before convergence" and "controllable exploration behavior" are presented, which promote the performance of PSO-CREV. An experimental method based on a complex test function is proposed by which the proper parameters of PSO-CREV used in practice are figured out, which guarantees the high exploration ability, as well as the convergence rate is concerned. The benchmarks and applications on FCRNN training verify the improvements brought by PSO-CREV.

• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.511-533
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• 2010

As a truly meshfree method, meshless equilibrium on line method (MELM), for 2D elasticity problems is presented. In MELM, the problem domain is represented by a set of distributed nodes, and equilibrium is satisfied on lines for any node within this domain. In contrary to conventional meshfree methods, test domains are lines in this method, and all integrals can be easily evaluated over straight lines along x and y directions. Proposed weak formulation has the same concept as the equilibrium on line method which was previously used by the authors for enforcement of the Neumann boundary conditions in the strong-form meshless methods. In this paper, the idea of the equilibrium on line method is developed to use as the weak forms of the governing equations at inner nodes of the problem domain. The moving least squares (MLS) approximation is used to interpolate solution variables in this paper. Numerical studies have shown that this method is simple to implement, while leading to accurate results.

• Structural Engineering and Mechanics
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• v.76 no.2
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• pp.251-267
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• 2020

Transmission tower-line systems have come to represent one of the most important infrastructures in today's society. Recent strong earthquakes revealed that transmission tower-line systems are vulnerable to earthquake excitations, and that ground motions may arrive at such structures from any direction during an earthquake event. Considering these premises, this paper presents experimental and numerical studies on the dynamic responses of a 1000 kV ultrahigh-voltage (UHV) transmission tower-line system under different seismic incidence angles. Specifically, a 1:25 reduced-scale experimental prototype model is designed and manufactured, and a series of shaking table tests are carried out. The influence of the seismic incidence angle on the dynamic structural response is discussed based on the experimental data. Additionally, the incidence angles corresponding to the maximum peak displacement of the top of the tower relative to the ground (referred to herein as the critical seismic incidence angles) are summarized. The experimental results demonstrate that seismic incidence angle has a significant influence on the dynamic responses of transmission tower-line systems. Subsequently, an approximation method is employed to orient the critical seismic incidence angle, and a corresponding finite element (FE) analysis is carried out. The angles obtained from the approximation method are compared with those acquired from the numerical simulation and shaking table tests, and good agreement is observed. The results demonstrate that the approximation method can properly predict the critical seismic incidence angles of transmission tower-line systems. This research enriches the available experimental data and provides a simple and convenient method to assess the seismic performance of UHV transmission systems.

• The Korean Journal of Rheology
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• v.11 no.1
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• pp.18-27
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• 1999

Predicting the deformation behaviors of sheets in thermoforming processes has been a daunting challenge due to the strong nonlinearities arising from very large deformations, mold-polymer contact condition and hyperelasticity constitutive equations. Nonlinear numerical analysis is always required to face this challenge especially for realistic processing conditions. In this study a 3-D algorithm and the membrane approximation are developed for thermoforming processes. The constitutive equation is expressed in terms of the 2nd Piola-Kirchhoff stress tensor and the Cauchy-Green deformation tensor. The 2-term Mooney-Rivlin model is used for the material model equation. The algorithm is established by the finite element formulation employing the total Lagrangian coordinate. The deformation behavior and the stress distribution results of 3-D algorithm with various point boundary conditions are compared to those of the membrane approximation algorithm. Also, the slip boundary condition and the no-slip boundary condition are applied for the systems that have molds. Finally, the effect of sheet temperatures on the final thickness distribution is investigated for the ABS material.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.773-788
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• 2014

We introduce an iterative process which converges strongly to a common minimum-norm point of solutions of variational inequality problem for a monotone mapping and fixed points of a finite family of relatively nonexpansive mappings in Banach spaces. Our theorems improve most of the results that have been proved for this important class of nonlinear operators.