• East Asian mathematical journal
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• 제5권1호
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• pp.95-110
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• 1989

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translaion and have minimum bias (analogously to estimation theory of mean value parameters). Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist the one of minimum norm is characterized. This characterization is achieved by systems of necessary and sufficient condition, and by a cone restricted pseudoinverse. In models where the decomposing covariance matrices span a commutative quadratic subspace, a representation of the considered estimator is derived that requires merely to solve an ordinary convex quadratic optimization problem. As an example, we present the two way nested classification random model. An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator, for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced two way nested classification model with ramdom effects if considered.

• 산업공학
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• 제12권2호
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• pp.237-246
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• 1999

The Automated Storage/Retrieval System(AS/RS) is very expensive to be built. But there are few tools available which can be used to design the storage systems optimally considering overall system building costs and constraints. In this paper, we propose a design support system for optimal design of AS/RS which includes different sized cells using expert systems and mathematical models considering customer's demands. The optimization models are to be used to minimize the total cost including building, equipment and operation costs. Expert system technique is utilized for using the experiences of skilled designers. By using the proposed system, AS/RS can be designed accurately, economically and efficiently.

• International Journal of Automotive Technology
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• 제6권5호
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• pp.491-499
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• 2005

There are different types of vehicle impacts recorded every year, resulting in many injuries and fatalities. The severity of these impacts depends on the aggressivety and incompatibility of vehicle-to-roadside hardware impacts. The aim of this paper is to investigate and to enhance crashworthiness in the case of full barrier impact using a new idea of crash improvement. Two different types of smart structures have been proposed to support the function of the existing vehicle. The work carried out in this paper includes developing and analyzing mathematical models of vehicle-to-barrier impact for the two types of smart structures. It is proven from analytical analysis that the mathematical models can be used in an effective way to give a quick insight of real life crashes. Moreover, it is shown that these models are valid and flexible, and can be useful in optimization studies.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제25권2호
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• pp.135-158
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• 2022

This study aimed to building models to understand the relationships between reasoning resources and content knowledge. We applied Support Vector Machine and linear models to the data including fifth graders' scores in the Cornel Critical Thinking Test and the Iowa Assessments, demographic information, and learning science approach (a student-centered approach to learning called the Science Writing Heuristic [SWH] or traditional). The SWH model showing the relationships between critical thinking domains and academic achievement at grade 5 was developed, and its validity was tested across different learning environments. We also evaluated the stability of the model by applying the SWH models to the data of the grade levels. The findings can help mathematics educators understand how critical thinking and achievement relate to each other. Furthermore, the findings suggested that reasoning in mathematics classrooms can promote performance on standardized tests.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.615-625
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• 2018

In this paper, we discuss the connection between the 5-dimensional complex Lie algebra ${\mathcal{K}} _5$ and Special functions. We construct certain two variable models of the irreducible representations of ${\mathcal{K}}_5$. We also use an Euler type integral transformation to obtain the new transformed models, in which the basis function appears as $_2F_1$. Further, we utilize these models to get some generating functions and recurrence relations.

• 대한수학회논문집
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• 제5권2호
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• pp.87-111
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• 1990

• 충청수학회지
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• 제21권3호
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• pp.385-393
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• 2008

This paper gives transient distributions for the number of customers in the system in the Geo/Geo/1 queue for both the early arrival and the late arrival models.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2010년도 춘계학술대회 논문집
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• pp.445-446
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• 2010

• 대한수학회지
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• 제48권4호
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• pp.797-822
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• 2011

Log Enriques surface is a generalization of K3 and Enriques surface. We will classify all the rational log Enriques surfaces of rank 18 by giving concrete models for the realizable types of these surfaces.

• 대한수학회보
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• 제44권2호
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• pp.265-270
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• 2007

The modern approach for wavelets imposes a Bayesian prior model on the wavelet coefficients to capture the sparseness of the wavelet expansion. The idea is to build flexible probability models for the marginal posterior densities of the wavelet coefficients. In this note, we derive exact expressions for a popular model for the marginal posterior density.