• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.613-625
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• 2001

In this paper, we investigate a simplified model of a particle suspended elastically from two towers by two nonlinear elastic springs, with a restoring force similar to Hooke’s law under extension and with no resistance to compression. Numerical results are presented, showing the solutions can be either of the same period oscillation the forcing term, can be a subharmonic response of multiple period, or can be noisy periodic which is apparently chaotic. Multiplicity of periodic solutions for certain physical parameters are demonstrated.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.9
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• pp.1711-1721
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• 1992

A nonlinear dissipative dynamical system can often have multiple attractors. In this case, it is important to study the global behavior of the system by determining the global domain of attraction of each attractor. In this paper we study the global behavior of a forced beam with two mode interaction. The governing equation of motion is reduced to two second-order nonlinear nonautonomous ordinary differential equations. When .omega. /=3.omega.$_{1}$ and .ohm.=.omega $_{1}$, the system can have two asymptotically stable steady-state periodic solutions, where .omega./ sub 1/, .omega.$_{2}$ and .ohm. denote natural frequencies of the first and second modes and the excitation frequency, respectively. Both solutions have the same period as the excitation period. Therefore each of them shows up as a period-1 solution in Poincare map. We show how interpolated mapping method can be used to determine the two four-dimensional domains of attraction of the two solutions in a very effective way. The results are compared with the ones obtained by direct numerical integration.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.401-413
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• 2020

In this article we consider the following system of piecewise linear difference equations: x_n+1 = |x_n| - y_n - 1 and y_n+1 = x_n + |y_n| - 1. We show that when the initial condition is an element of the closed second or fourth quadrant the solution to the system is either a prime period-3 solution or one of two prime period-4 solutions.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.269-282
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• 2005

We study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation $$x_{n+1}\;=\;{\alpha}-{\frac{x_{n-1}}{x_{n}},\;n=0,1,\;{\cdots}$$, where ${\alpha}\;\in\; R$ is a real number, and the initial conditions $x_{-1},\;x_0$ are arbitrary real numbers.

• Journal of Korean Institute of Industrial Engineers
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• v.35 no.3
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• pp.185-193
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• 2009

We consider a two-fare, two-period airline seat capacity allocation problem where consumers may choose different options in purchasing an airline ticket. A consumer may decide to wait for reopening of the same fare class ticket which is originally intended to buy, or may buy a different fare class ticket within the same period, if the originally requested fare is unavailable. We investigate the impact of the consumer buying behavior on the optimal solutions and the expected revenue.

• Industrial Engineering and Management Systems
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• v.9 no.2
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• pp.70-79
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• 2010

Makespan and cost minimization are two important factors in project investment. This paper considers a multi-mode resource-constrained project scheduling problem with the objective of minimizing costs, subject to a deadline constraint. A number of studies have focused on minimizing makespan or resource availability cost with a specified deadline. This problem assumes a fixed cost for the availability of each renewable resource per period, and the project cost to be minimized is the sum of the variable cost associated with the execution mode of each activity. The presented memetic algorithm (MA) consists of three features: (1) a truncated branch and bound heuristic that serves as effective preprocessing in forming the initial population; (2) a strategy that maintains two populations, which respectively store deadline-feasible and infeasible solutions, enabling the MA to explore quality solutions in a broader resource-feasible space; (3) a repair-and-improvement local search scheme that refines each offspring and updates the two populations. The MA is tested via ProGen generated instances with problem sizes of 18, 20, and 30. The experimental results indicate that the MA performs exceptionally well in both effectiveness and efficiency using the optimal solutions or the current best solutions for the comparison standard.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2002.10a
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• pp.169-172
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• 2002

In this study, the effects of the number of coat and immersion period on strength properties, waterproofness and chemical resistance of painted and immersed cement mortars using two admixture were examined. Test results showed that the flexural and the compressive strengths of the coated and immersed cement mortars increase with increasing number of coat and immersion period. The water absorption of the coated and immersed cement mortars tended to decrease with increasing number of coated and immersion period. In the case of the change of weight and the immersion period for the solutions, a decreasing tendency was shown as the immersion period increases regardless of solution, with a little variation.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.09b
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• pp.951-951
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• 2005

The characteristics of Boussinesq starting forced plumes were investigated in this study. Two distinct periods in the transient plume penetration were identified, namely the Period of Flow Development (PFD) and Period of Developed Flow (PDF). PFD refers to the time period whereby the penetration rate is governed by the complex vortex dynamics initiated by the exit conditions that can include vortex coalescence, vortex leapfrogging, pinching off of the head vortex from the trailing stem and the eventual reconnection. The pinch-off and reconnection leads to an overshoot of the plume front which is a common observation reported in previous studies. The penetration rate in PDF is more predictable and depends on the continuous feeding of buoyancy and momentum into the head vortex by the trailing buoyant-jet stem. Similarity solutions are developed for PDF to describe the temporal variation of the penetration rate, by incorporating the behavior of an isolated buoyant vortex ring and recent laboratory results on the trailing buoyant jet. In particular, the variations of velocity ratios between the head vortex and trailing buoyant jet are analytically computed. To verify the similarity solutions, experiments were conducted on vertical starting forced plumes using planar laser induced fluorescence (PLIF).

• Korean Management Science Review
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• v.7 no.2
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• pp.51-57
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• 1990

The purpose of this thesis is to find the shortest path between two nodes on an acyclic network where the arc costs are determined by the starting time at the starting node of the arc. A branch and bound method for optimal solutions and a heuristic method is developed. In heuristic method Dijkstra algorithm is modified to maintain the minimum arrival times of maximum informations in the each time period at each node and is updated by the result with the insertion technique. Expermetal results among two methods are presented with regard to run time and solution qualities.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.2
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• pp.159-166
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• 2018

The proliferation of information technologies made it possible to produce information products of different versions at much lower cost comparing to traditional physical products. Thus it is common for information product manufacturers to consider vertically differentiated product line for more profit through improved market coverage. Another salient characteristic of most information product is network externality. Existing researches dealing with vertical differentiation and network externality usually assumed oligopolistic market where vertically differentiated products are provided by competing companies, respectively. Moreover, they analyzed the essentially dynamic characteristic of network externality statically. In this study, different from the previous researches, the vertical differentiation strategy of a monopolistic company under network externality is dynamically analyzed. We used a two-period model to accommodate the dynamic feature of network externality. Based on the two-period model, the profit maximizing solutions are analyzed. The results showed that a monopolistic company has no incentive to differentiate products vertically when the network externality is absent. On the contrary, when the network externality exists, the monopolistic company can derive more profit by vertically differentiating the product line. It is also shown that, for more profit, the monopolistic company should keep the quality difference between the high quality product and the low quality product as greater as possible.