• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.245-250
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• 2002

Consider the Convex Polygon Pm={Al , A2, ‥‥, Am} With Vertex points A$\_$i/ = (a$\_$i/, b$\_$i/),i : 1,‥‥, m, interior P$\^$0/$\_$m/, and length of perimeter denoted by L(P$\_$m/). Let R$\_$n/ = {B$_1$,B$_2$,‥‥,B$\_$n/), where B$\_$i/=(x$\_$i/,y$\_$I/), i =1,‥‥, n, denote a regular polygon with n sides of equal length and equal interior angle. Kaiser[4] used the regular polygon R$\_$n/ to approximate P$\_$m/, and the problem examined in his work is to position R$\_$n/ with respect to P$\_$m/ to minimize the area of the symmetric difference between the two figures. In this paper we give the quality of a approximating regular polygon R$\_$n/ to approximate P$\_$m/.

• Proceedings of the KIEE Conference
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• 대한전기학회 1990년도 하계학술대회 논문집
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• pp.154-157
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• 1990

This paper describes a new method of calculating expected energy generation and loss of load probability (L.O.L.P) for electric power system operation and expansion planning. The method represents an equivalent load duration curve (E.L.D.C) as a mixture of cumulants approximation (M.O.C.A), which is the general case of mixture of normals approximation (M.O.N.A). By regarding a load distribution as many normal distributions-rather than one normal distribution-and representing each of them in terms of Gram-Charller expansion, we could improve the accuracy of results. We developed an algorithm which automatically determines the number of distribution and demarcation points. In modelling of a supply system, we made subsets of generators according to the number of generator outage: since the calculation of each subset's moment needs to be processed rapidly, we futher developed specific recursive formulae. The method is applied to the test systems and the results are compared with those of cumulant, M.O.N.A and Booth-Baleriaux method. It is verified that the M.O.C.A method is faster and more accurate than any other methods.

• The Transactions of the Korean Institute of Electrical Engineers
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• 제40권1호
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• pp.1-9
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• 1991

This paper describes a new method of calculating expected energy generation and loss of load probability (L.O.L.P) for electric power system operation and expansion planning. The method represents an equivalent load duration curve (E.L.D.C) as a mixture of cumulants approximation (M.O.N.A). By regarding a load distribution as many normal distributions-rather than one normal distribution-and representing each of them in terms of Gram-Charlier expansion, we could improve the accuracy of results. We developed an algorithm which automatically determines the number of distribution and demarcation points. In modeling of a supply system, we made subsets of generators according to the number of generator outage: since the calculation of each subset's moment needs to be processed rapidly, we further developed specific recursive formulae. The method is applied to the test systems and the results are compared with those of cumulant, M.O.N.A. and Booth-Baleriaux method. It is verified that the M.O.C.A. method is faster and more accure than any other method.

• Proceedings of the KIPE Conference
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• 전력전자학회 2012년도 전력전자학술대회 논문집
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• pp.244-245
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• 2012

본 논문에서는 이산 웨이블릿 변환(DWT;discrete wavelet transform)의 다해상도 분석(MRA;multi-resolution analysis)을 통해 분해된 배터리의 저주파 전압 성분(approximation;$A_n$) 기반 SOC(State-of-charge) 추정방법을 소개한다. 급격한 전압 변화의 특성을 나타내는 고주파 전압 성분(detail;$D_n$)이 제거되고 저주파 전압 성분만이 SOC 추정을 위해 사용된다. 이 경우 기존 확장 칼만필터(EKF;extended Kalman filter)에서 SOC 추정에러를 개선하기 위해 사용되었던 노이즈 모델의 생략이 가능하여 알고리즘의 복잡성이 개선된다. 개선된 확장 칼만필터 기반 SOC 추정 결과를 통해 제안된 방법을 검증하였다.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.505-514
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• 2019

In this paper we study the approximation properties of a continuous function by the sequence of (p, q)-Bernstein operators for q > p > 1. We obtain bounds of (p, q)-Bernstein operators. Further we prove that if a continuous function admits an analytic continuation into the disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, then $B^n_{p,q}(g;z){\rightarrow}g(z)(n{\rightarrow}{\infty})$ uniformly on any compact set in the given disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, ${\rho}>0$.

• The Korean Journal of Applied Statistics
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• 제12권2호
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• pp.671-681
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• 1999

이항분포의 정규근사는 중심극한정리의 한 예로서 자주 언급되는데 정규근사를 하기 위한 시행회수 n과 성공률 p에 대한 판정기준들이 다수 제시되고 있는 데, 본 논문은 이러한 판정기준들에 대하여 제약조건의 강도와 평균오차한계를 비교, 검토하였다.

• Journal of Korean Society for Quality Management
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• 제27권1호
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• pp.46-58
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• 1999

The exact distributions of the sample variance $(S^2_n)$ and the estimator ($\hat{C}_p$) of the process capability index are not easily obtained in general. In this paper, the approximations using saddlepoint techniques to the distributions of these statistics are suggested and compared with the other approximation methods. For comparisons, the exact values obtained by extensive Monte-Carlo (simulation) studies are also given. As a result, the suggested approximation methods are very accurate even in moderate or small sample sizes and are easy to use. Also, the suggested methods can be adapted to approximate the distributions of more complicated statistics, including $\hat{C}_pk$ ,$\hat{C}_pm$, etc.

• Communications of the Korean Mathematical Society
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• 제37권3호
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• pp.765-800
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• 2022

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.

• Proceedings of the Korean Society of Near Infrared Spectroscopy Conference
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• 한국근적외분광분석학회 2001년도 NIR-2001
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• pp.1132-1132
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• 2001

This work is a further development of the method created by G. Krivoshiev in 1996 for elimination of peel interference and prediction of fruit flesh optical density. In this investigation, as it was earlier, the objects are observed as being structured by three successive layer “AlongrightarrowOlongrightarrowB” denoting “peel-flesh-peel”. In the first version of the method the transmittances of the surface layers A and B were measured according to Kubelka-Munk theory by means of their diffuse reflectance. At that the overall transmittance T was approximated in the form of a multiplication approximation being valid for plane-parallel layers of a non-scattering material. In this work this approximation was done away with applying the theory of discontinuum, respectively Benfor's equations. As a result two mathematical models were created for non-destructive prediction of fruit flesh optical density. These models are different from the ones based solely on Kubelka-Munk theory, the destruction being marked by the terms 1n (1 - $R_{A}R_{0}$) and 1n (1 - $R_{A}R_{B}$), where: $R_{A}$ and $R_{B}$ are reflectance values for the surface layers A and B; $R_{0}$ is the average reflectance of the internal layer that could be obtained empirically by means of a preliminary measurement of sufficiently large number of physically peeled fruits of a given species and variety.

• Korean Journal of Soil Science and Fertilizer
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• 제9권3호
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• pp.211-220
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• 1976

The objective of this paper is to summarize and disicuss the results of studies for the prediction of fertilizer demands up to the year of 2000, from the agromic biew points. 1. The approximated demands of fertilizers figured out from the view point of nutrient requirement and fertilizer efficiency of major crops are 1,162,000M/T (N;554,100 M/T, $P_2O_5$; 360,100 M/T and $K_2O$, 247,000 M/T) at 1980, 1,471,400 M/T (N: 694,800 M/T, $P_2O_5$;465,400M/T and $K_2O$ ;311,200 M/T) at 1990 and 1,764,00 M/T (N;812,500 M/T, $P_2O_5$; 592,300 M/T and $K_2O$;359,200 M/T) at 2000${\cdots}{\cdots}$ (Approximation I) 2. Upon the basis of approximation on the yield levels of major crops per unit area and on the expansion of arable land, the demands of fertilizers at the years of 1980, 1990 and 2000 are predicted as 1,149,300 M/T (N;603,700 M/T $P_2O_5$; 305,500 M/T and $K_2O$, 240,100 M/T) 1,551,100 M/T(N:814,700M/T, $P_2O_5$;412,300 M/T and $K_2O$;324,00 M/T) and 2,253,800 M/T (N;1,183,800M/T, $P_2O_5$; 586,400M/T and $K_2O$, 470,900 M/T), respectively${\cdots}{\cdots}$(Approximation II) 3. When the recent relationships between the increases in yeid of major crops and the amounts of fertilizers for those crops per unit area are brought into consideration for the estimation of future demands of fertilizers, the predicted demands at the years of 1980, 1990 and 2000 are 1,287.600 M/T (N;677,100 M/T, $P_2O_5$; 342,000 M/T, and $K_2O$;268,500 M/T), 2,085,600M/T (N;1,096,700 M/T, $P_2O_5$;533,900 M/T, and $K_2O$;435,000 M/T and 3,380,600 M/T (N;1,777,800M/T, $P_2O_5$;897,800M/T and $K_2O$;705,000M/T) respectively (Approximation III) 4. Approximation I will be closer estimate under such condition that only rice will maintain self suficiency and other food crops will be covered by domestic production by around 50 percent, which is not desirable situation. 5. When higher self suficiency leveles of major food crops are sought through the introduction of improved varieties and expansion of cropping area and arable land by increased land utilization and reclamation of hillside land and tidal land, the Approximations II and III will become close to reality, If improved fertilizers and improved method of fertilizer applications are widely applied at the farmers fields to increase the fertilizer efficiency the former will be closer figure, if not, the latter may be better estimates.