• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.879-889
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• 2011

In this paper, we investigate the local asymptotic stability, the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation $x_{n+1}=\frac{a+bx_nx_{n-k}}{A+Bx_n+Cx_{n-k}}$, n = 0, 1,${\ldots}$, where the parameters a, b, A, B, C and the initial conditions $x_{-k}$, ${\ldots}$, $x_{-1}$, $x_0$ are positive real numbers.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.737-743
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• 2003

The purpose of this paper is to consider some existence results for vector nonlinear inequalities without any monotonicity assumption. As consequences of our main result, we give some existence results for vector equilibrium problem, vector variational-like inequality problem and vector variational inequality problems as special cases.

• Journal of Technology Innovation
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• v.13 no.1
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• pp.113-139
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• 2005

The purpose of this study is to analyse the diffusion process of personal computer (PC) in Korea during the 1990's. To achieve the goal, five research steps have been done such as the literature survey of diffusion theory, set-up of theoretic equilibrium model of supply and demand, derivation of an equilibrium path using Hamiltonian, and empirical analysis. The empirical analysis has been performed based on that equilibrium path. The results can be summarized as follows : First, technological attribute of diffusing product influences the diffusion speed of Product. It has been proven that the size of the network has a significant effect on the diffusion of PC in empirical study Second, supply factors have an important role in the diffusion process. According to the empirical analysis, decreasing cost of production as a result of technological advance promotes the speed of diffusion. This point seems to be manifest theoretically, but existing empirical models have not included supply factors explicitly, Third, it has been found out that expectation of decreasing cost would influence the speed of diffusion negatively as expected ex ante. Theoretically this result is supported by arbitrage condition of purchasing timing.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.18 no.34
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• pp.15-23
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• 1995

We study how to determine backorder cost at the warehouse in a one-warehouse/N-retailer distribution system such that channel efficiency (minimizing total system costs) is improved. We define backorder costs as compensation that the warehouse pays to the retailer for the number or orders delayed due to stockout at the warehouse. We answer two questions : (1) "Should the warehouse compensate for his backorder\ulcorner" and (2) "Is there any equilibrium for both the warehouse and retailer while they are seeking for their own profits\ulcorner" We show that : (1) "The warehouse should pay backorder costs for the sake of channel efficiency." and (2) "There exists an equilibrium that is infiuenced by the amount of compensation." First, we prove the existence of a mutually acceptable equilibrium for both the warehouse and the retailer, which is different from Nash equilibrium because they independently maximize their respective profits with incomplete information about each other. Second, we prove that the equilibrium moves to a point such that channel efficiency is improved if the warehouse compensates the retailers for his backorders. We show the existence of an optimal compensation that minimizes total system costs. Third, we show that the amount of optimal compensation increases as the ratio of mean lead time for the warehouse to that for the retailer increases.ouse to that for the retailer increases.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.1
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• pp.43-48
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• 2002

We show that humans execute the postural control ingeniously by regulating the impedance properties of the musculo-skeletal system as the motor command against the alteration of the environment. Adjusting muscle activity can control the impedance properties of the musculo-skeletal system. To quantify the changes in human arm viscoelasticity on the vertical plane during interaction with the environment, we asked our subject to hold an object. By utilizing surface electromyographic(EMG) studies, we determined a relationship between the perturbation and a time-varying muscle co-activation. Our study showed when the subject lifts the object by himself the muscle stiffness increases while the torque remains the same just before the lift-off. These results suggest that the central nervous system(CNS) simultaneously controls not only the equilibrium point(EP) and the torque, but also the muscle stiffness as themotor command in posture control during the contact task.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.7
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• pp.337-344
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• 2005

An energy function is derived on the basis of the EMM(Equivalent Mechanical Model) to take account of the effects of tap changer, and then the VC(Voltage Collapse) criteria is proposed to predict the voltage collapse in Power systems. The VC criterion can be evaluated by using the energy margin given by the energy gap between UEP(Unstable Equilibrium Point) and SEP(Stable Equilibrium Point) of the energy function adopted, in which it is noted that the energy contour should be considered due to energy discontinuity associated with tap changing. This paper shows that the proposed VC criterion improves the accuracy of voltage stability analysis with application to a two-bus sample system.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.645-651
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• 2010

In this note we study positive solutions of the mth order rational difference equation $x_n=(a_0+\sum{{m\atop{i=1}}a_ix_{n-i}/(b_0+\sum{{m\atop{i=1}}b_ix_{n-i}$, where n = m,m+1,m+2, $\ldots$ and $x_0,\ldots,x_{m-1}$ > 0. We describe a sufficient condition on nonnegative real numbers $a_0,a_1,\ldots,a_m,b_0,b_1,\ldots,b_m$ under which every solution $x_n$ of the above equation tends to the limit $(A-b_0+\sqrt{(A-b_0)^2+4_{a_0}B}$/2B as $n{\rightarrow}{\infty}$, where $A=\sum{{m\atop{i=1}}\;a_i$ and $B=\sum{{m\atop{i=1}}\;b_i$.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.759-766
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• 1995

In this paper, we give equivalent forms of the selection theorem of Ding-Kim-Tan. As applications of the selection theorem of Ding-Kim-Tan, we obtain a fixed point theroem of Gale and Mas-Colell type and establish an equilibrium existence theorem for a qualitative game under suitable assumptions in a locally convex Hausdorff topological vector space.

• Journal of Mechanical Science and Technology
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• v.18 no.4
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• pp.649-663
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• 2004

While a great number of studies on human motor control have provided a wide variety of viewpoints concerning the strategy of the central nervous system (CNS) in controlling limb movement, none were able to reveal the exact methods how the movement command from CNS is mapped onto the neuromuscular activity. As a preliminary study of human-machine interface design, the characteristics of human leg motion and its underlying motor control scheme are studied through experiments and simulations in this paper. The findings in this study suggest a simple open-loop motor control scheme in leg motion. As a possible candidate, an equilibrium point control model appears consistent in recreating the experimental data in numerical simulations. Based on the general leg motion analysis, the braking motion by the driver's leg is modeled.

• Proceedings of the KSR Conference
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• 2007.11a
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• pp.927-939
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• 2007

This paper concerns dynamics of a wheel-axle set on a tangent track which was already published in a book titled "Dynamics of Railway Vehicle Systems" authored by Garg and Dukkipati [1], pointing out several missing terms and erroneous parts in the derived expressions on the conventional governing equations of motion. It is indicated that the x-direction components of normal forces at left and right wheel-rail contact points in the equilibrium axis were missed. Another point is that in deriving the creepages the disturbed velocity components in both x and y directions in the equilibrium axis should not be disregarded in the first term of the numerators. When considering the creepage in the y direction in the body coordinate system, the second term of lateral velocity at the contact point also cannot be neglected. Besides, the hyper-assumptions in the final expressions of vertical components of normal forces at left and right wheel-rail contact points have been recovered in reaching the final stage of analytical model development. Finally it is noteworthy that the process of applying creep theory is deemed to contain a little bit inconsistencies and ambiguities to be clear.