• Korean Journal of Mathematics
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• v.27 no.4
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• pp.831-841
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• 2019

A Radiocoloring (RC) of a graph G is a function f from the vertex set V (G) to the set of all non-negative integers (labels) such that |f(u) - f(v)| ≥ 2 if d(u, v) = 1 and |f(u) - f(v)| ≥ 1 if d(u, v) = 2. The number of discrete labels and the range of labels used are called order and span, respectively. In this paper, we concentrate on the minimum order span Radiocoloring Problem (RCP) of trees. The optimization version of the minimum order span RCP that tries to find, from all minimum order assignments, one that uses the minimum span. We provide attainable lower and upper bounds for trees. Moreover, a complete characterization of caterpillars (as a subclass of trees) with the minimum order span is given.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1667-1690
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• 2018

We consider the minimum order of a graph G with a given lazy cop number $c_L(G)$. Sullivan, Townsend and Werzanski [7] showed that the minimum order of a connected graph with lazy cop number 3 is 9 and $k_3{\square}k_3$ is the unique graph on nine vertices which requires three lazy cops. They conjectured that for a graph G on n vertices with ${\Delta}(G){\geq}n-k^2$, $c_L(G){\leq}k$. We proved that the conjecture is true for k = 4. Furthermore, we showed that the Petersen graph is the unique connected graph G on 10 vertices with ${\Delta}(G){\leq}3$ having lazy cop number 3 and the minimum order of a connected graph with lazy cop number 4 is 16.

• Journal of Environmental Science International
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• v.14 no.1
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• pp.33-40
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• 2005

The size of minimum order stream has a very sensitive effect on runoff analysis model using the divergence characteristic of stream. Therefore, in this study, the threshold area of minimum order stream has been examined the change characteristic of topographical parameters. The subject basin of the research was the upper basin of the Kumho water gage station which is located in the middle of the Kumho river. The 1:25,000 numerical geography which was constructed $10{\times}10m$ mesh was used. The range of investigation of topographical parameters are number of stream order, length, area, slope, basin relief, sinuosity ratio, drainage density and total stream length etc. It was found from the result of analysis that the threshold value of minimum order stream has a very big effect on topographical parameters of basin. It was found that the threshold area of minimum ord er stream revealed under $0.10km^{2}.$ Furthermore, the parameters showed a serious change except for over $0.10km^{2}.$

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.5
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• pp.364-373
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• 1990

When digital filters are implemented on a computer or with spectial purpose hardware, they unavoidably suffer from errors due to finite wordlength implementation. These errors are classified into coefficient quantiz ation error and roundoff error. The synthesizing method for realizations with minimum coefficient quantization error and minimum roundoff error has been studied. In this paper, it is shown that there is an equivalent transform relation between realizations with minimum coefficient quatization error and minimum roundoff error. To show tha validity of this equivalent transform, we derived the 2nd order digital filter with minimum coefficient quantization error from the 2nd order digital filter with minimum roundoff error and proved the efficiency of realization with minimum coefficient quantization error by simulation.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.11
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• pp.38-45
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• 2004

This paper discusses the minimum cutting thickness with a continuous chip in sub-micrometer order precision diamond cutting. An ultra precision cutting model is proposed, in which the tool edge radius and the friction coefficient are the principal factors determining the minimum cutting thickness. The experimental results verify the proposed model and provide various supporting evidence. In order to reduce the minimum cutting thickness a vibration cutting method is applied, and the effects are investigated through a series of experiments under the same conditions as conventional cutting method.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.339-351
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• 1998

Designs for discriminating between two linear regression models are studied under $\Lambda$-type optimalities maximizing the measure for the lack of fit for the designs with fixed model inadequacy. The problem of selecting an appropriate $\Lambda$-type optimalities is shown to be closely related to the estimation method. $\Lambda$-type optimalities for the least squares and minimum bias estimation methods are considered. The minimum bias designs are suggested for the designs invariant with respect to the two estimation methods. First order minimum bias designs optimal under $\Lambda$-type optimalities are then derived. Finally for the case where the lack of fit test is significant, an approach to the construction of a second order design accommodating the optimal first order minimum bias design is illustrated.

• Proceedings of the KIEE Conference
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• 1998.11a
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• pp.171-175
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• 1998

This paper proposes a speed sensorless vector control of induction motor using a minimum-order EKF(extended kalman filter). Minimum-order EKF has the advantage of reducing the computational estimation cost because the stator current is not estimated. EKF does not deteriorate the performance of the overall speed control system, even though the measurements are relatively noisy. The estimated rotor speed is used for vector control and overall speed control. Computer simulations of the speed sensorless vector control are carried out to test the usefulness of the minimum-order EKF algorithm.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.1205-1208
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• 1996

This paper proposes balanced model reduction of non-minimum phase plant. The algorithm presented in this paper is to convert high-order non-minimum phase plant into low-oder minimum phase plant using balanced model reduction. Balanced model reduction requires the error bound that Hankel singular value produces. This algorithm shows the tolerance that admits the method of this paper.

• Journal of Mechanical Science and Technology
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• v.15 no.4
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• pp.433-440
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• 2001

A new design of the sliding mode control is proposed for the uncertain linear time-varying second order system. The proposed control drives system states to the target point in the minimum time with specified ranges of parametric uncertainties and disturbances. One of the advantages of the proposed control scheme is that the control inputs do not go beyond saturation limits of the actuators. The other advantage is that the minimum arrival time and the acceleration of the second order actuators system can be estimated with given parametric bounds and can be expressed in the closed from; conversely, the designer can select actuators based on the condition of the minimum arrival time to the target point. The superior performance of the proposed control scheme to other sliding mode controllers is validated by computer simulations.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.526-528
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• 2004

This paper focuses on planning strategies for object interception, especially with minimum time. Herein, the goal is for robot to intercept object with minimum time on a conveyor line that flows to x-axis with respect to world coordinate system. In order to do it, conveyor system needs the algorithms for minimizing time. This objective is achieved by solving about two problems: selection of a minimum-time interception point and planning of an optimal robot trajectory. Herein, the first problem is formulated a minimization of the robot-object interception time.