• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.545-565
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• 2014

In this paper we derive a priori $L^{\infty}(L^2)$ error estimates for expanded mixed finite element formulations of semilinear Sobolev equations. This formulation expands the standard mixed formulation in the sense that three variables, the scalar unknown, the gradient and the flux are explicitly treated. Based on this method we construct finite element semidiscrete approximations and fully discrete approximations of the semilinear Sobolev equations. We prove the existence of semidiscrete approximations of u, $-{\nabla}u$ and $-{\nabla}u-{\nabla}u_t$ and obtain the optimal order error estimates in the $L^{\infty}(L^2)$ norm. And also we construct the fully discrete approximations and analyze the optimal convergence of the approximations in ${\ell}^{\infty}(L^2)$ norm. Finally we also provide the computational results.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.555-563
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• 2002

This paper discusses cubic equations in general saddlepoint approximations. Exact roots are found for various cases by trigonometric identities, the root which is appropriate for the general saddlepoint approximations is selected and discussed, and the defective cases in which the general saddlepoint approximations cannot be used are found.

• Nuclear Engineering and Technology
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• v.31 no.2
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• pp.172-181
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• 1999

Series expansion methods to compute the exponential of a matrix have been compared by applying them to fuel depletion calculations. Specifically, Taylor, Pade, Chebyshev, and rational Chebyshev approximations have been investigated by approximating the exponentials of bum matrices by truncated series of each method with the scaling and squaring algorithm. The accuracy and efficiency of these methods have been tested by performing various numerical tests using one thermal reactor and two fast reactor depletion problems. The results indicate that all the four series methods are accurate enough to be used for fuel depletion calculations although the rational Chebyshev approximation is relatively less accurate. They also show that the rational approximations are more efficient than the polynomial approximations. Considering the computational accuracy and efficiency, the Pade approximation appears to be better than the other methods. Its accuracy is better than the rational Chebyshev approximation, while being comparable to the polynomial approximations. On the other hand, its efficiency is better than the polynomial approximations and is similar to the rational Chebyshev approximation. In particular, for fast reactor depletion calculations, it is faster than the polynomial approximations by a factor of ∼ 1.7.

• The Korean Journal of Applied Statistics
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• v.2 no.1
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• pp.48-53
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• 1989

In contrast to the customary approximations based on standard normal percentage points, direct approximations involve simple functions of parameters (such as degrees of freedom and tail area of the t distributions). This article used techniques of exploratory data analysis following Hoaglin to develop direct approximations for percentage points in the commonly used portions of upper tail of the t distribution with small to moderate numbers of degrees of freedom. These approximations are convenient to use and they compare favorably in accuracy with the popular approximations based on standard normal percentage points such as Peiser's. They can be used as an initial value generator in algorithms for getting more accurate percentage points.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.219-232
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• 2011

We investigated the properties of rough approximations induced by two families of preordered sets and closure systems. We study the relations among the lower and upper rough approximations, closure and interior systems, preordered sets.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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• pp.299-304
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• 2011

In this paper, we investigate the properties of rough approximations defined by preordered sets. We study the relations among the lower and upper rough approximations, closure and interior systems, and closure and interior operators.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.897-915
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• 2011

In this paper, we develop a symmetric Galerkin method with interior penalty terms to construct fully discrete approximations of the solution for nonlinear Sobolev equations. To analyze the convergence of discontinuous Galerkin approximations, we introduce an appropriate projection and derive the optimal $L^2$ error estimates.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.1035-1045
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• 2001

We present two decomposition approximations for the mean sojourn times in open single class queing networks. If there is a single bottleneck station, the approximations are asymptotically exact in both light and heavy traffic. When applied to a Jackson network or an M/G/1 queue, these approximations are exact for all values of the traffic intensity.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.3
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• pp.8-13
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• 2015

One of the most usual indicators to measure the performance of any inventory policy is the mean physical stock. In general, when estimating the mean physical stock in periodic review inventory systems, approximate approaches are often utilized by practitioners and researchers. The mean physical stock is generally calculated by a simple approximation. Still these simple methods are frequently used to analyze various single stockpoint and multi-echelon inventory systems. However, such a simple approximation can be very inaccurate. This is particularly true for low service levels. Even though exact methods to calculate the mean physical stock have been derived, they are available for specific cases only and computationally not very efficient, and therefore less useful in practice. In literature, approximate approaches, such as the simple, the linear, and Simpson approximations, were derived for the periodic review inventory systems that allow backorders. This paper modifies the approximate approaches for the lost sales case and evaluates the modified approximate approaches. Through computational experiments, average (and maximum) percentage deviations of mean physical stock between the exact method and the modified approximations are compared in the periodic review inventory system with lost sales. The same comparison between the modified and the original approximations are also conducted, in order to examine the performance of modified approximations. The results show that all modified approximations perform well for high service levels, but also that the performance may deteriorate fast with decreasing service level. The modified Simpson approximation is clearly better. In addition, the comparison between the modified and the original approximations in the periodic review inventory system with lost sales shows that the modified approximation outperforms the original approximation.

• Journal of the Korean Data and Information Science Society
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• v.19 no.2
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• pp.497-504
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• 2008

In this paper we studied the saddlepoint approximations to the distribution of quadratic forms in normal variables. We derived the approximations as a special case of Na & Kim (2005). Also applications to a statistic which concerns intraclass correlation coefficient are presented. Simulations show the accuracy and availability of the suggested approximations.