• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.229-240
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• 2002

Whether to use linear or quadratic model in the analysis of regression data is one of the important problems in classical regression model and measurement error model (MEM). In MEM, four goodness of fit test statistics are available In solving that problem. Two are from the derivation of estimators of quadratic MEM, and one is from that of the general $k^{th}$-order polynomial MEM. The fourth one is derived as a variation of goodness of fit test statistic used in linear MEM. The purpose of this paper is to find the most powerful test statistic among them through the small-scale simulation.

• Nuclear Engineering and Technology
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• v.50 no.7
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• pp.1043-1050
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• 2018

For an efficient Monte Carlo (MC) burnup analysis, an accurate high-order depletion scheme to consider the nonlinear flux variation in a coarse burnup-step interval is crucial accompanied with an accurate depletion equation solver. In a Seoul National University MC code, McCARD, the high-order depletion schemes of the quadratic depletion method (QDM) and the linear extrapolation/quadratic interpolation (LEQI) method and a depletion equation solver by the Chebyshev rational approximation method (CRAM) have been newly implemented in addition to the existing constant extrapolation/backward extrapolation (CEBE) method using the matrix exponential method (MEM) solver with substeps. In this paper, the quadratic extrapolation/quadratic interpolation (QEQI) method is proposed as a new high-order depletion scheme. In order to examine the effectiveness of the newly-implemented depletion modules in McCARD, four problems in the VERA depletion benchmarks are solved by CEBE/MEM, CEBE/CRAM, LEQI/MEM, QEQI/MEM, and QDM for gadolinium isotopes. From the comparisons, it is shown that the QEQI/MEM predicts ${k_{inf}}^{\prime}s$ most accurately among the test cases. In addition, statistical uncertainty propagation analyses for a VERA pin cell problem are conducted by the sensitivity and uncertainty and the stochastic sampling methods.

• Bulletin of the Korean Mathematical Society
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• v.24 no.1
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• pp.23-26
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• 1987

The aim of this note is to study some properties of Schrodinger operators, the magnetic case, $H_{0}$ (a)=1/2(-i.del.-a)$^{2}$; H(a)= $H_{0}$ (a)+V, where a=( $a_{1}$,.., $a_{n}$ ).mem. $L^{2}$$_{loc}$ and V is a potential energy. Also, we are interested in solutions, .psi., of H(a).psi.=E.psi. in the sense that (.psi., $e^{-tH}$(a).PSI.)= $e^{-tE}$(.psi.,.PSI.) for all .PSI..mem. $C_{0}$ $^{\infty}$( $R^{n}$ ) (see B. Simon [1]). In section 2, under some conditions, we find that a semibounded quadratic form of H9a) exists and that the Schrodinger operator H(a) with Re V.geq.0 is accretive on a form domain Q( $H_{0}$ (a)). But, it is well-known that the Schrodinger operator H=1/2.DELTA.+V with Re V.geq.0 is accretive on $C_{0}$ $^{\infty}$( $R^{n}$ ) in N Okazawa [4]. In section 3, we want to discuss $L^{p}$ estimates of Schrodinger semigroups.ups.

• Journal of Korean Society for Quality Management
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• v.28 no.2
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• pp.161-175
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• 2000

The problem of jointly determining the optimum process mem and screening limits for each market is considered in situations where there are several markets with different price/cost structures. Two inspection procedures are considered; an inspection based on the quality characteristic of interest, and an inspection based on a surrogate variable which is highly correlated with the quality characteristic. The quality characteristic is assumed to be a normal distribution with unknown mean and known variance. A Taguchi's quadratic loss function is utilized for developing the economic model for determining the optimum process mean and screening limits. A numerical example is given.