• Journal of the Korea Society of Computer and Information
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• v.20 no.6
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• pp.77-85
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• 2015

This paper proposes a location algorithm that locates newly built p-facilities in the optimal area with minimum cost in a city of n districts. This problem has been classified as NP-hard, to which no polynomial time algorithm exists. The proposed algorithm improves the shortcomings of existing Myopic algorithm by constructing until p-facilities and exchanging locations of p-th facility for p=[1, n-1]. When applied to experimental data of n=5, 7, 10, 55, the proposed algorithm has obtained an approximate value nearest possible to the optimal solution take precedence of reverse-delete method. This algorithm is also simply executable using Excel.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.4
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• pp.64-71
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• 2015

In this paper, we present a multi-period 0-1 knapsack problem which has the cardinality constraints. Theoretically, the presented problem can be regarded as an extension of the multi-period 0-1 knapsack problem. In the multi-period 0-1 knapsack problem, there are n jobs to be performed during m periods. Each job has the execution time and its completion gives profit. All the n jobs are partitioned into m periods, and the jobs belong to i-th period may be performed not later than in the i-th period, i = 1, ${\cdots}$, m. The total production time for periods from 1 to i is given by $b_i$ for each i = 1, ${\cdots}$, m, and the objective is to maximize the total profit. In the extended problem, we can select a specified number of jobs from each of periods associated with the corresponding cardinality constraints. As the extended problem is NP-hard, the branch and bound method is preferable to solve it, and therefore it is important to have efficient procedures for solving its linear programming relaxed problem. So we intensively explore the LP relaxed problem and suggest a polynomial time algorithm. We first decompose the LP relaxed problem into m subproblems associated with each cardinality constraints. Then we identify some new properties based on the parametric analysis. Finally by exploiting the special structure of the LP relaxed problem, we develop an efficient algorithm for the LP relaxed problem. The developed algorithm has a worst case computational complexity of order max[$O(n^2logn)$, $O(mn^2)$] where m is the number of periods and n is the total number of jobs. We illustrate a numerical example.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.51 no.12
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• pp.603-610
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• 2002

In this paper, a new economic dispatch algorithm for unit commitment is proposed to improve both the accuracy of the final solution and the calculation speed of economic dispatch. By using the inverse incremental cost functions, economic dispatch can be transformed into a simple optimization problem associated with an n-th order polynomial equation. The proposed method remarkably reduces the computation time with adaptability to any higher order generation cost functions. The proposed method is tested with sample system, which shows that the proposed algorithm yields more accurate and economical generation scheduling results with high computation speed.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.157-174
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• 2004

In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical $L^{p}(\mu)$ spaces. In the case $1\;{\leq}\;p\;{\leq}\;2$ we obtain optimal results and for finite dimensional complex Banach spaces, in a special case, we have improved an early result by K. Ball [3]. By using these results, in some cases we are able to find best possible lower bounds for the norms of homogeneous polynomials which are products of linear forms. In particular, we give an estimate in the case of a real Hilbert space which seems to be a difficult problem. We have also obtained some results on the so-called n-th (linear) polarization constant of a Banach space which is an isometric property of the space. Finally, known polynomial inequalities have been derived as simple consequences of various results related to plank problems.

• Journal of The Korean Astronomical Society
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• v.31 no.1
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• pp.27-37
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• 1998

We have made semi-analytical studies to investigate the configurations of caustics and the probability distribution of the flux factor K for the binary microlensing including external shears. A parametric equation of critical curve is derived in a 4th order complex polynomial. We present the topological dependencies of the caustics for selected gamma parameters (0, 0.3, 0.6, 1.3, 2.0, and 2.5) and convergence terms (0., 0.4, 0.8, 1.2, 1.6, and 2.0). For the purpose of analyzing the efficiency of High Amplification Event (HAE) on each caustics, we examine the probability distribution of the flux factor by a Monte Carlo method. Changing the separation of the binary system from 0.8 to 1.3 (in normalied unit), we examine the probability distribution of the K-values in various gamma parameters. The relationship between gamma parameters, seperations and their probabilties of the flux factor K have been studied. Our results show that the relatively higher K values (K>1.5) are increased as increasing the separation of the binary system. We therfore conclude that, in the N-body microlensing, the probabilities of higher HAEs are inversely proportional to the star density as well. We also point out that the present research might be used as a preliminary step toward investigating heavy N-body microlensing simulations.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.483-495
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• 2007

In a general fractional factorial design, the n-levels of a factor are coded by the $n^{th}$ roots of the unity. Pistone and Rogantin (2007) gave a full generalization to mixed-level designs of the theory of the polynomial indicator function using this device. This article discusses the optimal blocking scheme for nonregular designs. According to hierarchical principle, the minimum aberration (MA) has been used as an important criterion for selecting blocked regular fractional factorial designs. MA criterion is mainly based on the defining contrast groups, which only exist for regular designs but not for nonregular designs. Recently, Cheng et al. (2004) adapted the generalized (G)-MA criterion discussed by Tang and Deng (1999) in studying $2^p$ optimal blocking scheme for nonregular factorial designs. The approach is based on the method of replacement by assigning $2^p$ blocks the distinct level combinations in the column with different blocks. However, when blocking level is not a power of two, we have no clue yet in any sense. As an example, suppose we experiment during 3 days for 12-run Plackett-Burman design. How can we arrange the 12-runs into the three blocks? To solve the problem, we apply G-MA criterion to nonregular mixed-level blocked scheme via the mixed-level indicator function and give an answer for the question.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.3
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• pp.291-302
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• 2005

Due to the importance of the parameter in structural response, the uncertain elastic modulus was located at the center of stochastic analysis, where the response variability caused by the uncertain system parameters is pursued. However when we analyze the so-called stochastic systems, as many parameters as possible must be included in the analysis if we want to obtain the response variability that can reach a true one, even in an approximate sense. In this paper, a formulation to determine the statistical behavior of in-plane structures due to multiple uncertain material parameters, i.e., elastic modulus and Poisson's ratio, is suggested. To this end, the polynomial expansion on the coefficients of constitutive matrix is employed. In constructing the modified auto-and cross-correlation functions, use is made of the general equation for n-th moment. For the computational purpose, the infinite series of stochastic sub-stiffness matrices is truncated preserving required accuracy. To demons4rate the validity of the proposed formulation, an exemplary example is analyzed and the results are compared with those obtained by means of classical Monte Carlo simulation, which is based on the local averaging scheme.

• Journal of the Microelectronics and Packaging Society
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• v.24 no.1
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• pp.67-73
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• 2017

An analysis of thermal degradation of epoxy based adhesive performed by thermogravimetry tests are presented in this study. Six different heating rates were employed for the weight change measurements. Based on the data, an Arrhenius type modeling equation was developed by calculating activation energies and proportional constants, and $n^{th}$ polynomial function was adopted to predict the weight change rates. The prediction results by the modeling was compared with the data using the average activation energy. It was found that the activation energy at the each heating rate was not same due to the different degradation kinetics, especially at the high heating rate. To overcome this pitfall, a new approach using exponential function series was introduced and employed. The calculation results showed very good agreements with the test data regardless of the heating rates.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.25 no.6
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• pp.619-627
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• 2014

In this paper, we designed a blade antenna for VHF-UHF band(500 MHz~3 GHz) to be used as aircraft antennas. Unlike previously reported researches that use high-dielectric materials and insert rectangular extended grounds, the antenna structure was designed by optimizing the curvature of both a radiator and an extended ground whose shape is varied by changing the exponent of an n-th polynomial. Based on the optimized structure, we measured impedance matching and gain performances to evaluate the antenna in the VHF-UHF band(500 MHz~3 GHz). As a result, we confirmed that the antenna shows matching characteristics of less than -6 dB and has average gains of greater than -5 dBi in the entire VHF-UHF band.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.7
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• pp.5009-5014
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• 2015

Hydraulic uplift which is caused by the action of pore water pressure can be occurred in clay underlain by granular soil during conducting narrow excavation. Estimation of hydraulic uplift is done by considering soil beam. In order to execute more precise estimation of hydraulic uplift, determination of stress distribution in soil beam is necessary. This study presents stress distribution and displacement distribution in the soil beam based on the theory of elasticity. Stress distribution developed in the soil beam by self weight was derived using stress function depicted by $5^{th}$ order of polynomial and it was seen that vertical stresses along the depth of the soil beam show parabolic distribution and those directions be downward. Regarding soil beam which has the weight of $16kN/m^3, thickness and depth are 1m respectively, maximum vertical stress was about 1.7kPa. Stress distribution by the aciton of pore water pressure was derived via superposition of the stresses corresponding to the self weight and it can be seen that vertical compressive stresses act along the depth of the soil beam when the magnitude of pore water pressure equal to 5 times of the self weight is considered. Equations for prediction of the displacements in the soil beam are also presented.