• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.129-142
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• 2003

In this paper we study the chromatic sum functions for rooted nonseparable simple maps on the plane. The chromatic sum function equation for such maps is obtained . The enumerating function equation of such maps is derived by the chromatic sum equation of such maps. From the chromatic sum equation of such maps, the enumerating function equation of rooted nonseparable simple bipartite maps on the plane is also derived.

• Journal of Korea Water Resources Association
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• v.41 no.11
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• pp.1107-1121
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• 2008

The simple equation of GIUH are frequently used in many researches instead of the derived equation of GIUH. However it is still unknown whether the simple equation of GIUH is adaptable for estimating IUHs for basins with various geomorphologic conditions. To verify the applicability of the simple equation of GIUH, in this research, four basins which were Bangrim, Sanganmi, Museong, and Byeongcheon were selected and each basin was assumed as the third and fourth stream order basin according to variable resolutions. After than, IUHs were estimated using the derived and simple equations of GIUH. Eight to sixteen hydrographs were estimated from the each IUH, compared with observed graphs. In case of that the basin is assumed as a third order stream, the derived equation underestimated the peak flows while the simple equation overestimated them. When the basin is assumed as a fourth order stream, the simple equation generally overestimated the peak flows whereas the derived equation produced peak flows good agreement with the observed peak flow. Moreover, the simple equation showed various deviations in accuracy whereas the derived equation produced stable results. Based on the fact found from this research, it can be concluded that the derived equation of GIUH brings better results than the simple equation of GIUH to estimate IUHs for ungauged basins.

• Journal of the Korean Society of Safety
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• v.24 no.2
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• pp.76-82
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• 2009

The NIOSH lifting equation has been used as a dominant tool in evaluating the hazard levels of lifting tasks. Although it provides two different ways for each simple and complex lifting task, the NIOSH simple lifting equation is almost used for not only simple tasks but also complex tasks. However, most of lifting tasks in industries are in the form of complex lifting. Therefore some errors occur inevitably in the evaluation of complex lifting tasks. Among complex lifting tasks, a multi-stacking task is the most popular in lifting tasks. To compensate the error in the evaluation of multi-stacking tasks by using the NIOSH simple lifting equation, a set of calculations for finding LIs(Lifting Indices) was performed for the systematically varying multi-stacking tasks. Then a regression model which finds the equivalent height in simple lifting task for multi-stacking task was established. By using this model, multi-stacking tasks can be evaluated with less error. To validate this model, some real multi-stacking tasks were evaluated as examples.

• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.521-538
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• 2012

In this study, the transverse vibrations of an axially moving flexible beams resting on multiple supports are investigated. The time-dependent velocity is assumed to vary harmonically about a constant mean velocity. Simple-simple, fixed-fixed, simple-simple-simple and fixed-simple-fixed boundary conditions are considered. The equation of motion becomes independent from geometry and material properties and boundary conditions, since equation is expressed in terms of dimensionless quantities. Then the equation is obtained by assuming small flexural rigidity. For this case, the fourth order spatial derivative multiplies a small parameter; the mathematical model converts to a boundary layer type of problem. Perturbation techniques (The Method of Multiple Scales and The Method of Matched Asymptotic Expansions) are applied to the equation of motion to obtain approximate analytical solutions. Outer expansion solution is obtained by using MMS (The Method of Multiple Scales) and it is observed that this solution does not satisfy the boundary conditions for moment and incline. In order to eliminate this problem, inner solutions are obtained by employing a second expansion near the both ends of the flexible beam. Then the outer and the inner expansion solutions are combined to obtain composite solution which approximately satisfying all the boundary conditions. Effects of axial speed and flexural rigidity on first and second natural frequency of system are investigated. And obtained results are compared with older studies.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.6
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• pp.259-265
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• 2001

In the last two decades, many researchers proposed various usages of the orthogonal functions such as Walsh, Haar and BPF to solve the system analysis, optimal control, and identification problems from and algebraic form. In this paper, a simple procedure to design and algerbraic observer for the descriptor system is presented by using block pulse function expansions. The main characteristic of this technique is that it converts differential observer equation into an algerbraic equation. And furthermore, a simple recursive algorithm is proposed to obtain BPFs coefficients of the observer equation.

• Bulletin of the Korean Chemical Society
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• v.7 no.3
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• pp.204-210
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• 1986

It is shown that the linear stability coincides with the thermodynamic stability in the case of stress tensor evolution for simple dense fluids even if the constitutive (evolution) equation for the stress tensor is nolinear. The domain of coincidence can be defined in the space of parameters appearing in the constitutive equation and we find the domain is confined in an elliptical cone in a three-dimensional parameter space. The corresponding state theory in rheology of simple dense fluids is also further examined. The validity of the idea is strengthened by the examination.

• Proceedings of the KIEE Conference
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• 1997.07c
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• pp.1118-1120
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• 1997

This paper presents a simple method for evaluating of voltage stability using the line flow equation. Line flow equations ($P_{ij}$, $Q_{ij}$) are comprised of state variable, $V_i$, ${\delta}_i$, $V_j$ and ${\delta}_j$, and line parameter, r and x. Using the feature of polar coordinate, these becomes one equation with two variables, $V_i$ and $V_j$. Moreover, if bus j is slack or generater bus, which is specified voltage magnitude, it becomes one equation with one variable $V_i$, that is, may be formulated with the second-order equation for $V_i^2$. Therefore, multiple load flow solutions may be obtained with simple computation, and the formulated equation used for approximately evaluating of voltage stability limit considering line flow sensitivity. The proposed method was validated to 2-bus and IEEE 6-bus system.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.8 no.6
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• pp.1560-1565
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• 2007

In this study, Chiu's velocity distribution equation recently developed from the probability and entropy concepts is used to establish a linkage between the mean velocity obtained from the Manning's equation and the corresponding velocity distribution in a channel cross section. The linkage to be established enables computing the velocity distribution along with the mean velocity, from simple hydraulic data such as Manning's n, hydraulic radius and channel slope irrespective of including sediment or not.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.440-444
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• 1998

In this paper, we consider numerical solution of a H-J-B (Hamilton-Jacobi-Bellman) equation of elliptic type arising from the stochastic control problem. For the numerical solution of the equation, we take an approach involving contraction mapping and finite difference approximation. We choose the It(equation omitted) type stochastic differential equation as the dynamic system concerned. The numerical method of solution is validated computationally by using the constructed test case. Map of optimal controls is obtained through the numerical solution process of the equation. We also show how the method applies by taking a simple example of nonlinear spacecraft control.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.695-698
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• 2008

A simple proof of the fact that the j-invariants for Weierstrass equations are invariant under birational transformations which keep the forms of Weierstrass equations is given by finding a non-trivial explicit birational transformation which sends a normalized Weierstrass equation to the same equation.