• Journal of the Korean Society of Manufacturing Process Engineers
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• v.12 no.2
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• pp.68-74
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• 2013

In this paper, an average surface roughness, $R_a$, was measured by optical measurement and its mathematical model according to spindle speed and feedrate was obtained by least square method. Also, its result is compared and investigated with real measured average surface roughness. The optical measurement of surface roughness is performed by CLSM(confocal laser scanning microscope) and the captured HEI(height encoded image) data is used as an original data for the generation of average surface roughness and its mathematical plane or contour surface of surface roughness. Using this polynomial model with two independent variables, the behavior of an average surface roughness is investigated and analyzed with an experimental modeling of least square algorithm. And it can be used for the prediction of $R_a$ in different condition of machining.

• Computers and Concrete
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• v.25 no.4
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• pp.303-310
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• 2020

In this research, a hybrid mathematical model is derived using the higher-order polynomial kinematic model in association with soft computing technique for the prediction of best fiber volume fractions and the minimal mass of the layered composite structure. The optimal values are predicted further by taking the frequency parameter as the constraint and the projected values utilized for the computation of the eigenvalue and deflections. The optimal mass of the total layered composite and the corresponding optimal volume fractions are evaluated using the particle swarm optimization by constraining the arbitrary frequency value as mass/volume minimization functions. The degree of accuracy of the optimal model has been proven through the comparison study with published well-known research data. Further, the predicted values of volume fractions are incurred for the evaluation of the eigenvalue and the deflection data of the composite structure. To obtain the structural responses i.e. vibrational frequency and the central deflections the proposed higher-order polynomial FE model adopted. Finally, a series of numerical experimentations are carried out using the optimal fibre volume fraction for the prediction of the optimal frequencies and deflections including associated structural parameter.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.4
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• pp.51-60
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• 2007

In this study, we consider the minimum ADM problem which is the fundamental problem for the cost-effective design of SONET ADM embedded in WDM ring networks. To minimize the number of SONET ADMs, efficient algorithms for the routing and wavelength assignment are needed. We propose a mathematical model based on the graph theory for the problem and propose a branch-and-price approach to solve the suggested model effectively within reasonable time. By exploiting the mathematical structure of ring networks, we developed polynomial time algorithms for column generation subroutine at branch-and-bound tree. In a computer simulation study, the suggested approach can find the optimal solution for sufficient size networks and shows better performance than the greedy heuristic method.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.835-840
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• 2000

The objective of the present study is to investigate the characteristics of pressure wave propagation of viscous fluid flow in a circular pipe line. The goal of this study is to select the best frequency of each control factor of a circular pipe. We intend to approach a formalized mathematical model by a very exact and reasonable polynomial for fluid transmission lines. and we computed this mathematical model by computer. The results show that the oil viscosity decreased as the length of the circular pipe increases. and The energy of pressure wave propagation decreased as the pipe diameter decreases. The factor is that density of oil was changed resonant frequency. It has been found the viscosity characteristics is changed largely by length of hydraulic pipe and volume of cavity tank.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.27 no.1
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• pp.84-86
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• 1982

The experiment was conducted with three varieties (Hicks, Burley 21, and Sohyang) and cultivation type (Improved mulching, general mulching, and non mulching) of NC 2326 to model to curve of tabacco growth against time. The basic growth data were obtained by harvest method at intervals of ten days from transplanting at 7-8 times and analyzed by polynomial regression, orthogonal polynomial, and logarithmic transformation. It is shown that the C model of growth curve: T = A +$\sqrt{(1.4 AK + K)}$2K provides an excellent fit.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.4
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• pp.709-714
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• 2017

The curved panel is widely used for display of TVs and smart phones. This paper proposes a new auto-focusing method for curved panel inspection system. Since the distance between the camera and the panel varies with the curve position, the camera should change its focus at every inspection time. In order to reduce the focusing time, we propose an effective focusing method that considers the mathematical model of panel curve. The Lagrange polynomial equation is applied to modeling the panel curve. The foci of initial three points are used to get the curve equation, and the other foci are calculated automatically from the curve equation. The experiment result shows that the proposed method can reduce the focusing time.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1799-1816
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• 2013

Privacy preserving multiset union (PPMU) protocol allows a set of parties, each with a multiset, to collaboratively compute a multiset union secretly, meaning that any information other than union is not revealed. We propose efficient PPMU protocols, using multiplicative homomorphic cryptosystem. The novelty of our protocol is to directly encrypt a polynomial by representing it by an element of an extension field. The resulting protocols consist of constant rounds and improve communication cost. We also prove the security of our protocol against malicious adversaries, in the random oracle model.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.145-156
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• 2016

It is known that certain convolution sums can be expressed as a combination of divisor functions and Bernoulli formula. In this article, we consider relationship between fifth-order combinatoric convolution sums of divisor functions and Bernoulli polynomials. As applications of these identities, we give a concrete interpretation in terms of the procedural modeling method.

• Journal of the Korea Institute of Military Science and Technology
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• v.22 no.2
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• pp.255-265
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• 2019

In the present study, the effect of opening patterns of a flow control valve on underwater discharge systems using a linear pump was investigated numerically. For that, a improved mathematical model was developed. The improvement is to separate a middle tank from a water cylinder because the cross-section area of the inlet of the middle tank is an important parameter. To validate the improved model, calculation results were compared with a previous study. The results showed that $2^{nd}$ order or more polynomial opening patterns had an advantage over ramp opening patterns. Higher an order of polynomial resulted in wider operating limits. An escape velocity and a maximum acceleration of underwater vehicle were affected by time derivative of the cross-section area of the flow control valve. Besides, as a velocity profile of the vehicle got closer to linearity, the escape velocity got faster and the maximum acceleration got smaller. And velocities of the vehicle and piston had similar variation trend.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.569-580
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• 2003

The Lotka-McKendrick equation which describes the evolution of a single population under the phenomenological conditions is developed from the well-known Malthus’model. In this paper, we introduce the Lotka-McKendrick equation for the description of the dynamics of a population. We apply a discontinuous Galerkin finite element method in age-time domain to approximate the solution of the system. We provide some numerical results. It is experimentally shown that, when the mortality function is bounded, the scheme converges at the rate of $h^2$ in the case of piecewise linear polynomial space. It is also shown that the scheme converges at the rate of $h^{3/2}$ when the mortality function is unbounded.