• Honam Mathematical Journal
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• v.31 no.1
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• pp.75-85
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• 2009

We show the existence of the nontrivial periodic solution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between two sublevel sets. Since the functional is strongly indefinite, we use the linking theorem for the strongly indefinite functional and the notion of the suitable version of the Palais-Smale condition.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.3 s.96
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• pp.208-214
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• 1999

The purpose of this paper is to develop a profile modification technique of spur gears and its computer program for the prevention of gear tooth overlap. In the gear system, tooth overlap produces an impact at the initial contact of some tooth pairs. In this analysis, contact surface was assumed to be unbonded and frictionless under small deformation and stain. The problem is formulated by a variational statement with inequality constraint. Tooth load sharing is obtained by the application of contact theory, and overlap is known by the analysis of deformation. After carrying out the profile modification of gear tooth, we verified the reasonable results.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1101-1129
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• 2023

In this study we propose a model of optimal retirement, consumption and portfolio choice of an individual agent, which encompasses a large class of the models in the literature, and provide a methodology to solve the model. Different from the traditional approach, we consider the problems before and after retirement simultaneously and identify the difference in the dual value functions as the utility value of lifetime labor. The utility value has an option nature, namely, it is the maximized value of choosing the retirement time optimally and we discover it by solving a variational inequality. Then, we discover the dual value functions by using the utility value. We discover the value function and optimal policies by establishing a duality between the value function and the dual value function. The model and approach offer a significant advantage for computation of optimal policies for a large class of problems.

• Journal of Korean Society of Transportation
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• v.21 no.6
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• pp.77-88
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• 2003

This paper proposes a solution algorithm for solving a multi-class analytical DTA model. In the DTA model, three traveler classes are classified according to different assumptions of traveler's route choice behavior: including fixed route, Stochastic Dynamic User Optimum(SDUO), and Dynamic User Optimum(DUO). To solve this DTA model, variables of link flow and exit flow are represented solely by inflow. The resulting Linear Program(LP) subproblem in the inner iteration is solved as a typical time-dependent shortest route problem over a physical network. Accordingly, the required time-space network expansion in solving DTA models is no longer needed.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.621-639
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• 2011

The purpose of this paper is to introduce a general iterative process by viscosity approximation method with parallel method to ap-proximate a common element of the set of solutions of a mixed equilibrium problem and of the set of common fixed points of a finite family of $k_i$-strict pseudo-contractions in a Hilbert space. We obtain a strong convergence theorem of the proposed iterative method for a finite family of $k_i$-strict pseudo-contractions to the unique solution of variational inequality which is the optimality condition for a minimization problem under some mild conditions imposed on parameters. The results obtained in this paper improve and extend the corresponding results announced by Liu (2009), Plubtieng-Panpaeng (2007), Takahashi-Takahashi (2007), Peng et al. (2009) and some well-known results in the literature.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.753-762
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• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.5
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• pp.55-62
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• 2003

Subdomain-interface variational formulation is presented to solve a class of dynamic contact problems of composite structures. The penalty method is used for imposing inequality constraints on contact surfaces and for connecting finite element subdomains that satisfy interface compatibility conditions. As a result, any complex-shaped domain can be easily divided into independently modeled subdomains without considering the conformity of meshes on interfaces. Some advantageous features of the present method are shown through a set a numerical studies with a developed computer code.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.3
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• pp.1164-1183
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• 2019

The rapid development of cloud computing and high requirements of operators requires strong support from the underlying Data Center Networks. Therefore, the effectiveness of using resources in the data center networks becomes a point of concern for operators and material for research. In this paper, we discuss the online virtual-cluster provision problem for multiple tenants with an aim to decide when and where the virtual cluster should be placed in a data center network. Our objective is maximizing the total revenue for the data center networks under the constraints. In order to solve this problem, this paper divides it into two parts: online multi-tenancy scheduling and virtual cluster placement. The first part aims to determine the scheduling orders for the multiple tenants, and the second part aims to determine the locations of virtual machines. We first approach the problem by using the variational inequality model and discuss the existence of the optimal solution. After that, we prove that provisioning virtual clusters for a multi-tenant data center network that maximizes revenue is NP-hard. Due to the complexity of this problem, an efficient heuristic algorithm OMS (Online Multi-tenancy Scheduling) is proposed to solve the online multi-tenancy scheduling problem. We further explore the virtual cluster placement problem based on the OMS and propose a novel algorithm during the virtual machine placement. We evaluate our algorithms through a series of simulations, and the simulations results demonstrate that OMS can significantly increase the efficiency and total revenue for the data centers.

• Journal of Korean Society of Transportation
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• v.20 no.4
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• pp.135-150
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• 2002

The basic assumption of analytical Dynamic Traffic Assignment models is that traffic demand and network conditions are known as a priori and unchanging during the whole planning horizon. This assumption may not be realistic in the practical traffic situation because traffic demand and network conditions nay vary from time to time. The rolling horizon implementation recognizes a fact : The Prediction of origin-destination(OD) matrices and network conditions is usually more accurate in a short period of time, while further into the whole horizon there exists a substantial uncertainty. In the rolling horizon implementation, therefore, rather than assuming time-dependent OD matrices and network conditions are known at the beginning of the horizon, it is assumed that the deterministic information of OD and traffic conditions for a short period are possessed, whereas information beyond this short period will not be available until the time rolls forward. This paper introduces rolling horizon implementation to enable a multi-class analytical DTA model to respond operationally to dynamic variations of both traffic demand and network conditions. In the paper, implementation procedure is discussed in detail, and practical solutions for some raised issues of 1) unfinished trips and 2) rerouting strategy of these trips, are proposed. Computational examples and results are presented and analyzed.