With the increasing researches on geotechnical properties of the diesel contaminated soil( DCS),the water content measured is indispensable part during the early period. In this study,the relative error of water conte...With the increasing researches on geotechnical properties of the diesel contaminated soil( DCS),the water content measured is indispensable part during the early period. In this study,the relative error of water content measurement using the traditional method is as high as 20. 78%,which is no longer suitable for contaminated soil. Through a series of tests to measure the loss coefficient of diesel in the drying time,the authors finally proposed a modified calculation formula for test samples. The results show that the maximum relative error calculated by using the modified formula is 0. 96%,far lower than that of traditional formula,which can provide accurate data for further study of diesel contaminated soil.展开更多
The influences of both the volume of PS/toluene solution in the Ubbelohde viscometer and the precision of the time measuring on the viscosity behavior in dilute and extremely dilute concentration region are investigat...The influences of both the volume of PS/toluene solution in the Ubbelohde viscometer and the precision of the time measuring on the viscosity behavior in dilute and extremely dilute concentration region are investigated. It was found that the influence of the former can neglect, but that of the latter is so prominent that the data fluctuate bitterly and linearity of the curve of the reduced viscosity vs. concentration (hsp/c^c) becomes too bad to obey the Huggins equation down to the extremely dilute region, despite the error of the flow times Dt 0.2s, which is permitted by the conventional method of viscosity measurement. Through strict mathematical analyses, it was found that the error (E) of the reduced viscosity is in proportion and inverse proportion to Dt and concentration c, respectively. So the less the concentration, the more the error is. Consequently, a lowest concentration limit cL corresponding to given experimental error may exist and it will be meaningless for further operation below cL because of the great fluctuation of the data. Therefore, it needs to seriously reconsider the application of the conventional method of Ubbelohde viscosity measurement in the extremely dilute polymer solution under traditional conditions because of the great influence of the experimental error.展开更多
Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS...Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS） were proposed in the different areas. Motivated by K. Chen et al.＇s recent work [J. Amer. Statist. Assoc., 2010, 105： 1104-1112] on the least absolute relative error （LARE） estimation for the accelerated failure time （AFT） model, in this paper, we establish the connection between relative error estimators and the M-estimation in the linear model. This connection allows us to deduce the asymptotic properties of many relative error estimators （e.g., LARE） by the well-developed M-estimation theories. On the other hand, the asymptotic properties of some important estimators （e.g., MRE and RLS） cannot be established directly. In this paper, we propose a general relative error criterion （GREC） for estimating the unknown parameter in the AFT model. Then we develop the approaches to deal with the asymptotic normalities for M-estimators with differentiable loss functions on R or R／{0} in the linear model. The simulation studies are conducted to evaluate the performance of the proposed estimates for the different scenarios. Illustration with a real data example is also provided.展开更多
In this paper, we report our recent advances on vertex centered finite volume element methods （FVEMs） for second order partial differential equations （PDEs）. We begin with a brief review on linear and quadratic fi...In this paper, we report our recent advances on vertex centered finite volume element methods （FVEMs） for second order partial differential equations （PDEs）. We begin with a brief review on linear and quadratic finite volume schemes. Then we present our recent advances on finite volume schemes of arbitrary order. For each scheme, we first explain its construction and then perform its error analysis under both HI and L2 norms along with study of superconvergence properties.展开更多
文摘With the increasing researches on geotechnical properties of the diesel contaminated soil( DCS),the water content measured is indispensable part during the early period. In this study,the relative error of water content measurement using the traditional method is as high as 20. 78%,which is no longer suitable for contaminated soil. Through a series of tests to measure the loss coefficient of diesel in the drying time,the authors finally proposed a modified calculation formula for test samples. The results show that the maximum relative error calculated by using the modified formula is 0. 96%,far lower than that of traditional formula,which can provide accurate data for further study of diesel contaminated soil.
文摘The influences of both the volume of PS/toluene solution in the Ubbelohde viscometer and the precision of the time measuring on the viscosity behavior in dilute and extremely dilute concentration region are investigated. It was found that the influence of the former can neglect, but that of the latter is so prominent that the data fluctuate bitterly and linearity of the curve of the reduced viscosity vs. concentration (hsp/c^c) becomes too bad to obey the Huggins equation down to the extremely dilute region, despite the error of the flow times Dt 0.2s, which is permitted by the conventional method of viscosity measurement. Through strict mathematical analyses, it was found that the error (E) of the reduced viscosity is in proportion and inverse proportion to Dt and concentration c, respectively. So the less the concentration, the more the error is. Consequently, a lowest concentration limit cL corresponding to given experimental error may exist and it will be meaningless for further operation below cL because of the great fluctuation of the data. Therefore, it needs to seriously reconsider the application of the conventional method of Ubbelohde viscosity measurement in the extremely dilute polymer solution under traditional conditions because of the great influence of the experimental error.
文摘Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS） were proposed in the different areas. Motivated by K. Chen et al.＇s recent work [J. Amer. Statist. Assoc., 2010, 105： 1104-1112] on the least absolute relative error （LARE） estimation for the accelerated failure time （AFT） model, in this paper, we establish the connection between relative error estimators and the M-estimation in the linear model. This connection allows us to deduce the asymptotic properties of many relative error estimators （e.g., LARE） by the well-developed M-estimation theories. On the other hand, the asymptotic properties of some important estimators （e.g., MRE and RLS） cannot be established directly. In this paper, we propose a general relative error criterion （GREC） for estimating the unknown parameter in the AFT model. Then we develop the approaches to deal with the asymptotic normalities for M-estimators with differentiable loss functions on R or R／{0} in the linear model. The simulation studies are conducted to evaluate the performance of the proposed estimates for the different scenarios. Illustration with a real data example is also provided.
基金supported by National Science Foundation of USA(Grant No.DMS1115530)National Natural Science Foundation of China(Grant No.11171359)the Fundamental Research Funds for the Central Universities of China
文摘In this paper, we report our recent advances on vertex centered finite volume element methods （FVEMs） for second order partial differential equations （PDEs）. We begin with a brief review on linear and quadratic finite volume schemes. Then we present our recent advances on finite volume schemes of arbitrary order. For each scheme, we first explain its construction and then perform its error analysis under both HI and L2 norms along with study of superconvergence properties.
