• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.173-195
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• 2021

A new implicit discontinuous Galerkin spectral element method (DGSEM) based on the first order hyperbolic system(FOHS) is presented for solving elliptic type partial different equations, such as the Poisson problems. By utilizing the idea of hyperbolic formulation of Nishikawa[1], the original Poisson equation was reformulated in the first-order hyperbolic system. Such hyperbolic system is solved implicitly by the collocation type DGSEM. The steady state solution in pseudo-time, which is the solution of the original Poisson problem, was obtained by the implicit solution of the global linear system. The optimal polynomial orders of 𝒪(𝒽^𝑝+1)) are obtained for both the solution and gradient variables from the test cases in 1D and 2D regular grids. Spectral accuracy of the solution and gradient variables are confirmed from all test cases of using the uniform grids in 2D.

• Journal of Korean Society of Water and Wastewater
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• v.19 no.4
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• pp.487-496
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• 2005

Chlorine bulk decay tests were carried out by bottle test under controlled conditions in a laboratory. Experiments were performed at different temperatures: $5^{\circ}C$, $15^{\circ}C$, $25^{\circ}C$, and the water temperatures when samples were taken from the effluent just before entering to its distribution system. 38 bulk tests were performed for water of Al (water treatment plant), 4 bulk tests for A2 (large service reservoir), and A3(pumping station). Residual chlorine concentrations in the amber bottles were measured over time till about 100 hours and bulk decay coefficients were evaluated by assuming first-order, parallel first-order, second-order. and $n^{th}-order$ reaction. The $n^{th}-order$ coefficients were obtained using Fourth-order Runge-Kutta Method. A good-fit by the average coefficient of determination ($R^2$) was first-order ($R^2=0.90$) < parallel first-order ($R^2{_{fast}}=0.92$, $R^2{_{slow}}=0.95$) < second-order ($R^2=0.95$) < $n^{th}-order$ ($R^2=0.99$). But if fast reaction of parallel first-order bulk decay were applied to the effluent of large service reservoir with ca. 20 hours of travel time and slow reaction in the water distribution system following the first 20 hours, parallel first-order bulk decay would be best and easy for application of water quality modeling technique.

• Journal of Institute of Convergence Technology
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• v.4 no.2
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• pp.17-21
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• 2014

This paper presents the effects of the time delay on the stability of the haptic system that includes a virtual wall and a first-order-hold method. The model of a haptic system includes a haptic device model with a mass and a damper, a virtual wall model, a first-order-hold model and a time delay model. In this paper, the time delay is considered as the computational time delay that is assumed to be as much as the sampling time. As the time delay increases, the maximal available stiffness of a virtual wall model is reduced reversely. The relation among the time delay and the maximum available stiffness, the mass and the damper of the haptic device are analyzed using the MATLAB simulation.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.14 no.24
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• pp.149-154
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• 1991

The one of the important problems in the design of queueing systems is the decision of the order of service stations. The object of this problem is the decision of the order that minimizes the expected sojourn time per customer in the given arrival process and service time distributions. In this paper, the tandem queueing system in series is studied with the emphasis on the optimal order of the tandem queueing system which has three stations with single servers. In one system, customers arrive at the first station with Poisson process. This system is composed of service stations with a constant, a general distribution and a Exponential distribution is studied. To select the optimal order after the orders of each pair of two stations is decided, it is compared the two orders of system. With this results, total expected delay of the systems which has three stations is compared. The result is the best that service station with constant time is on the first place, then the service station with general distribution and the service station with Exponential distribution is followed. And the other system is consist of service stations with a constant and two probabilistic distributions. In this case, two probabilistic distributions has a non-overlapping feature. It is the optimal order that the service station with constant time is on the first place then the service station with longer service time and the service station with shorter service time is followed.

• Journal of Institute of Convergence Technology
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• v.3 no.2
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• pp.23-29
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• 2013

When a human operator interacts with a virtual wall that is modeled as a virtual spring model, the lager the stiffness of the virtual spring is, the more realistic the operator feels that the virtual wall is. In the previous studies, it is shown that the maximum available stiffness of a virtual spring to guarantee the stability can be increased when the first-order-hold method is applied, however the effects of a human impedance on the stability are not considered. This paper presents the effects of a human impedance on stability of haptic system with a virtual spring and a first-order-hold (FOH) method. The human impedance model is modeled as a linear second-order system model. The relations between the maximum available stiffness of a virtual spring and the human impedance such as a mass, a damping and a stiffness are analyzed through the MATLAB simulation. It is shown that the maximum available stiffness is proportional to the square root of the human mass or damping respectively.

• Journal of Institute of Convergence Technology
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• v.13 no.1
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• pp.29-34
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• 2023

This paper presents the effects of a virtual mass with a low-pass filter on stability boundaries of a virtual spring in the haptic system with first-order hold. A virtual mass is required to improve the realism of a virtual environment. However the second derivative of a displacement of a haptic device is needed while the inertia forces are computed, which causes the reflective force to change quickly and then makes the haptic system unstable. A low pass filter is added to resolve this problem and the stability region of a haptic system depends on the characteristics of the filter. In this paper the finite impulse response filter (FIR filter) is applied as one of low pass filters and the effect of the FIR filter on the stable region of a haptic system with first order hold is analyzed. When compared to stable region of the system without the FIR filter, the region of available virtual mass is increased by 20% and the maximum of the stable virtual spring is reduced by 32%, irrespective of the sampling time. Besides it is shown that the stable region of a virtual spring is proportional to the inverse square of the sampling period.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• Korean Journal of Optics and Photonics
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• v.8 no.2
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• pp.81-87
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• 1997

This paper presents the optimum initial design containing the first and third order properties of the four-group video camera zoom system using lens modules, and its real lens design. The optimum initial design with focal length range of 6.1693 to 58.4065 mm is derived by assigning appropriate first order quantities and third order aberrations to each module along with the specific constraints required for optimization. By scaling the focal length of each lens group, an initial real lens selected for each group has been designed to match its focal length into that of the each lens module, and then combined to establish an actual zoom system by adjusting the air space between the groups at all zoom positions. The combination of the separately designed groups results in a system which satisfies the first order properties of the zoom system consisting of original lens modules. As a result, by residual aberration correction, we could obtain a zoom system useful in video zoom camera employing the rear focus method.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.4
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• pp.389-394
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• 2014

This paper presents the effect of a reflective force computed from a first-order-hold method on the stability of a haptic system. A haptic system is composed of a haptic device with a mass and a damper, a virtual spring, a sampler and a sample-and-hold. The boundary condition of the maximum virtual stiffness is analytically derived by using the Routh-Hurwitz criterion and the condition shows that the maximum virtual stiffness is proportional to the square root of the mass and the damper of a haptic device and also is inversely proportional to the sampling time to the power of three over two. The effectiveness of the derived condition is evaluated by the simulation. When the reflective forces are computed by using the first-order-hold method, the maximum available stiffness to guarantee the stability is increased several hundred times as large as when the zero-order-hold method is applied.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.1
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• pp.74-82
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• 2015

Two key challenges in statistical relational learning are uncertainty and complexity. Standard frameworks for handling uncertainty are probability and first-order logic respectively. A Markov logic network (MLN) is a first-order knowledge base with weights attached to each formula and is suitable for classification of dataset which have variables correlated with each other. But we need domain knowledge to construct first-order logics and a computational complexity problem arises when calculating weights of first-order logics. To overcome these problems we suggest a method to generate first-order logics and learn weights using association analysis in this study.