• 한국수자원학회논문집
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• 제55권10호
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• pp.775-784
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• 2022

본 연구에서는 임의지속기간의 확률강우량 산정을 위해 실무에서 주로 사용되고 있는 전대수 다항식형 확률강우강도식의 최적차수 결정을 위하여 경상북도 내 9개 지점을 대상으로 확률강우량을 산정하고 전대수 다항식형 강우강도식의 회귀계수를 추정하였다. 추정된 지점별 다항식을 대상으로 단계선택법을 이용하여 각 지점별 다항식의 최적변수를 선정하고 선정된 변수들의 통계적 유의성을 검토하기 위하여 분산분석을 통한 유의성 검정을 실시하였으며, 이들 결과를 이용하여 각 지점별 통계적으로 적절하게 산정된 강우강도식을 제시하였다. 경북 9개 지점의 전대수 다항식형 강우강도식의 변수선정 결과는 6개 지점에서 1~3차식이 최적식으로 나타났고 1개 지점이 불완전 3차식이 최적식으로 나타났다. 그 중 1차는 Sherman 식, 2차는 General 식의 형태와 유사하므로 독립변수의 수를 증가시켜 적합도를 높이고 사용 편의를 위해 통일된 형태의 강우강도식으로 제시한다면 전대수 다항식형 강우강도식은 3차 회귀식까지만 고려하여도 통계학적으로 문제가 없는 것으로 판단된다.

• 대한수학회지
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• 제34권4호
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• pp.973-1008
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• 1997

We reconsider the problem of calssifying all classical orthogonal polynomial sequences which are solutions to a second-order differential equation of the form $$ \ell_2(x)y"(x) + \ell_1(x)y'(x) = \lambda_n y(x). $$ We first obtain new (algebraic) necessary and sufficient conditions on the coefficients $\ell_1(x)$ and $\ell_2(x)$ for the above differential equation to have orthogonal polynomial solutions. Using this result, we then obtain a complete classification of all classical orthogonal polynomials : up to a real linear change of variable, there are the six distinct orthogonal polynomial sets of Jacobi, Bessel, Laguerre, Hermite, twisted Hermite, and twisted Jacobi.cobi.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권2호
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• pp.55-68
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• 2008

One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the form $P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m$, where $A_0$, $A_1$, ${\cdots}$, $A_m$ and X are $n{\times}n$ complex matrices. Newton's method was introduced a useful tool for solving the equation P(X)=0. Here, we suggest an improved approach to solve each Newton step and consider how to incorporate line searches into Newton's method for solving the matrix polynomial. Finally, we give some numerical experiment to show that line searches reduce the number of iterations for convergence.

• 한국식품영양과학회지
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• 제30권3호
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• pp.466-470
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• 2001

Response surface methodology was used for monitoring extraction conditions, based on quality properties of old pumpkin extracts. Hunter's color L value of extracts was maximized at 101℃, 2.6 hr and decreased gradually after maximum point. The polynomial equation for Hunter's color L value showed 10% of significance level and 0.8799 of R². Hunter's color a value was minimized at 117℃, 3.9 hr and R² of polynomial equation was 0.9852 within 1% significance level. Hunter's color b value and ΔE value increased as the extracting temperature and time increased. Extraction yield of old pumpkin was maximized at 110℃, 4 hr and increased in proportional to the extracting temperature and time, but decreased after 113℃ and 2 hr. Viscosity of pumpkin extracts were maximized at 120℃, nearly 3 hr. R² of polynomial equations for yield, viscosity and sugar content were 0.9532, 0.9812 and 0.8869, respectively. Optimum ranges of extraction conditions for quality properties of old pumpkin were 102∼109℃, 2.5∼3.5 hr, respectively. Predicted values at the optimum extraction condition agreed with experimental values.

• 대한기계학회논문집A
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• 제20권8호
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• pp.2546-2554
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• 1996

In order to investigate the characteristics of sound-structure interaction problems, we modeled a rectangular cavity and the flexible wall of the cavity. Because the governing equations of motion are coupled through velocity terms, we could redefine them using the velocity potential. We calculated the natural frequencies of plate using orthogonal polynomial functions which satisfy the boundary conditions in the Rayleigh-Ritz Method. As the result, comparisons of theory and experiment show good agreement. and using orthogonal polynomial functions which satisfy the boundary conditions in the Rayleigh-Ritz method show useful method for sound-structure interaction problems too.

• 전기학회논문지
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• 제58권9호
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• pp.1827-1833
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• 2009

This paper deals with the trajectory tracking control of wheeled mobile robots with input constraint. The proposed method converts the trajectory tracking problem to the system stability problem using the control inputs composed of feedforward and feedback terms, and then, by using Taylor series, nonlinear terms in origin system are transformed into polynomial equations. The composed system model can make it possible to obtain the control inputs using numerical tool named as SOSTOOL. From the simulation results, the mobile robot can track the reference trajectory well and can have faster convergence rate of the trajectory errors than the existing nonlinear control method. By using the proposed method, we can easily obtain the control input for nonlinear systems with input constraint.

• Korean Journal of Mathematics
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• 제28권2호
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• pp.295-309
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• 2020

In this paper we study the growth of solutions of some non-linear complex differential equations in connection to Brück conjecture using the theory of complex differential equation.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1996년도 춘계학술발표회논문집(1)
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• pp.137-141
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• 1996

A new general high order consistent nodal method for solving the 3-D multigroup neutron kinetic equations in (x-y-z) geometry has been derived by expending the flux in a multiple polynomial series for the space variables by without the quadratic fit approximations of the transverse leakage and for the time variable and using a weighted-integral technique. The derived equation set is consistent mathematically, and therefore, we can expect very accurate solutions and less computing time since we can use coarse meshes in time variable as well as in spatial variables and the solution would converge exactly in fine mesh limit.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.65-73
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• 2021

In this paper, we investigate the growth properties of solutions of the non-homogeneous linear complex differential equation L(f) = b (z) f + c (z), where L(f) is a linear differential polynomial and b (z), c (z) are entire functions and give some of its applications on sharing value problems.

• Structural Engineering and Mechanics
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• 제60권4호
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• pp.547-565
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• 2016

In this work a new 3-unknown non-polynomial shear deformation theory for the buckling and vibration analyses of functionally graded material (FGM) sandwich plates is presented. The present theory accounts for non-linear in plane displacement and constant transverse displacement through the plate thickness, complies with plate surface boundary conditions, and in this manner a shear correction factor is not required. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only 3 unknowns as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT). The plate properties are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton's principle. Analytical solutions of natural frequency and critical buckling load for functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the present non-polynomial plate theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions.