• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.17.1-17
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• 2003

We study averaging properties in Banach spaces, First, we seek an averaging property equivalent to the reflexivity in Banach spaces. Second, we investigate averaging properties in Banach space using the Brunet-Sucheston's spreading model.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.497-507
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• 2004

In this paper, we first seek the equivalent statements with averaging properties in terms of the regular summability method, secondly define some new averaging properties and study their implications. Finally, we investigate the question of what property is dual to the Banach-Saks property suggested by C. Seifert.

• Journal of Power System Engineering
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• v.4 no.2
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• pp.40-45
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• 2000

Some engineering materials are often known to have considerable spatial variation in their resisting strength and other properties. The objective of this study is to investigate the averaging effect and the applicability of extremal statistic for the statistical size effect. In the present study, it is assumed that the material property is a stationary random process in space. The theoretical autocorrelation function of the material strength are discussed for several correlation lengths. And, in order to investigate the statistical size effect, the material properties was simulated by using the non-Gaussian random process method. The material properties were plotted on the Weibull probability papers. The main results are summarized as follows: The autocorrelation function of the material properties are almost independent of the averaging length. The variance decreases with increasing the averaging length. As correlation length is smaller, the slope is larger. And also, it was found that Weibull statistics based on the weakest-link model could not explain the spatial variation of material properties with respect to the size effect satisfactory.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.259-272
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• 2017

In this paper we study the mapping properties of the finite field restricted averaging operators to various algebraic varieties. We derive necessary conditions for the boundedness of the generalized restricted averaging operator related to arbitrary algebraic varieties. It is shown that the necessary conditions are in fact sufficient in the specific case when the Fourier transform on varieties has enough decay estimates. Our work extends the known optimal result on regular varieties such as paraboloids and spheres to certain lower dimensional varieties.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1017-1030
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• 2005

In this paper, we study averaging properties in Banach spaces using the Brunel-Sucheston's spreading model. We show that the Schlumprecht space S does not have the Banach­Saks property and II is finitely representable in the Schlumprecht space S using the spreading model properties.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.189-204
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• 2021

In a regression analysis, a single best model is usually selected among several candidate models. However, it is often useful to combine several candidate models to achieve better performance, especially, in the prediction viewpoint. Model combining methods such as stacking and Bayesian model averaging (BMA) have been suggested from the perspective of averaging candidate models. When the candidate models include a true model, it is expected that BMA generally gives better performance than stacking. On the other hand, when candidate models do not include the true model, it is known that stacking outperforms BMA. Since stacking and BMA approaches have different properties, it is difficult to determine which method is more appropriate under other situations. In particular, it is not easy to find research papers that compare stacking and BMA when regression model assumptions are violated. Therefore, in the paper, we compare the performance among model averaging methods as well as a single best model in the linear regression analysis when standard linear regression assumptions are violated. Simulations were conducted to compare model averaging methods with the linear regression when data include outliers and data do not include them. We also compared them when data include errors from a non-normal distribution. The model averaging methods were applied to the water pollution data, which have a strong multicollinearity among variables. Simulation studies showed that the stacking method tends to give better performance than BMA or standard linear regression analysis (including the stepwise selection method) in the sense of risks (see (3.1)) or prediction error (see (3.2)) when typical linear regression assumptions are violated.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.665-669
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• 2002

In this paper, we study averaging properties in Banach space. We prove that the convex block Banach-Saks property is equivalent to the reflexivity in a Banach space. And we show that a weakly compact operator is a convex block Banach-Saks operator.

• The Journal of the Acoustical Society of Korea
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• v.30 no.8
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• pp.436-445
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• 2011

In this paper, equivalent properties of 2-2 mode piezocomposites were studied. Variation of the properties of 2-2 mode piezocomposites was analyzed by the finite element method, and the result was compared with experimental measurement data to confirm the validity of the analysis. The equivalent properties of a single phase material to represent the piezocomposite composed of PZT-5H and polymer were derived by the asymptotic averaging method. Accuracy of the derived equivalent properties was enhanced by minimizing the discrepancy between the impedance spectra of full 2-2 piezocomposite and equivalent single phase material resonators of various vibration modes by the least square method. The equivalent properties of 2-2 piezocomposites derived in this study can be utilized to the design of diverse acoustic sensors.

• Transactions of the Korean hydrogen and new energy society
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• v.29 no.4
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• pp.401-409
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• 2018

A numerical investigation has been conducted to find the effects of pressure losses by struts and rakes, and averaging methods on the performance of a multi-stage axial fan and a multi-stage axial compressor. Struts and rakes which produce pressure losses are installed upstream of the aerodynamic inlet plane in the fan and the compressor rigs. Some of normal stator vanes are substituted with thick vanes with total pressure probes to measure total pressure between stages. Three-dimensional Reynolds-averaged Navier- Stokes equations with $k-{\omega}$ SST turbulence model were applied to analyze the pressure losses by the struts, inlet rakes, and thick instrumented vanes. The hexahedral grids were used to construct computational domain. Inlet pressure losses were evaluated for the compressor as a function of Mach number. The passage pressure losses due to the instrumented vanes were evaluated at the two speed lines in the fan. Total properties, such as pressure and temperature, were evaluated at the exit of the fan and the compressor with two different averaging methods which are area-averaging and mass-averaging, respectively.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2002.10a
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• pp.292-295
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• 2002

In this paper, an analytical model for the prediction of the elastic properties of multi-axial warp knit fabric (MWK) composites is proposed. The geometric limitation, effect of stitching fibers and design parameters of MWK composites are considered in the model. The elastic behavior of MWK composites was conducted by using an averaging method. The predicted elastic properties are in reasonably good agreement with experimental values. Finally the effect of stitching in the MWK composites are discussed.