Linear driving force (LDF) model is widely used in a diffusion process. However thismodel has inherent weakness. When the dimensionless time is less than 0.1, its relativeerror is up to 95%. In this paper a new concen...Linear driving force (LDF) model is widely used in a diffusion process. However thismodel has inherent weakness. When the dimensionless time is less than 0.1, its relativeerror is up to 95%. In this paper a new concentration profile is proposed, and then a newmodified LDF model (MLDF) is deduced. Compared with the exact solution ofintraparticle diffusion equation, the transient volume-average amount adsorbedcalculated from the MLDF is more accurate than that calculaled from the LDF modeL .Ifone takes ±10% relative error for the limit of validity of approximation, the new model isvalid when the dimensionless time is just larger than 0. 0002, while the LDF model is notvalid until the dimension time is large than 0.05. The new model is superior to the LDFmodel. The new concentration profiles corresponding to the MLDF model are much closeto the exact concentration profiles within a particle than the parabolic propescorresponding to the LDF model.展开更多
As a potential adsorption material,it is still a challenge for activated carbon fiber(ACF)in efficient adsorption of ethanol due to its nonpolar surface,which is mainly emitted from the grain drying industry.This stud...As a potential adsorption material,it is still a challenge for activated carbon fiber(ACF)in efficient adsorption of ethanol due to its nonpolar surface,which is mainly emitted from the grain drying industry.This study prepared surface polarity-modified ACF using the heteroatom doping method.The modified ACF possessed a richer array of strongly polar oxygen/nitrogen-containing functional groups(primarily phenolic hydroxyl and lactone groups),a larger specific surface are1,and a more developed micropore structure.The adsorption capacities of ethanol for O-ACF and N-ACF were 4.110 mmol/g and 1.698 mmol/g,respectively,which were 11.3 times and 4.7 times those of unmodified ACF.This was a significant improvement over our previous work(0.363 mmol/g).The improvement of adsorption capacity for the N-ACF was mainly due to the higher specific surface are1,greater number of micropores(more adsorption sites)and abundant existence of defects,whereas,for O-ACF,the improvement mainly relied on the abundant presence of oxygen-containing functional groups on the surface.However,water had a negative effect on the adsorption of ethanol for the modified ACF due to competitive adsorption and the disappearance of capillary condensation.It was further revealed that the adsorption process of ethanol and water was quite different.It obeyed the linear driving force(LDF)model for ethanol adsorption,however,the intraparticle diffusion(IPD)model for water adsorption.展开更多
There are four serious problems in the discriminant analysis. We developed an optimal linear discriminant function （optimal LDF） based on the minimum number of misclassification （minimum NM） using integer programm...There are four serious problems in the discriminant analysis. We developed an optimal linear discriminant function （optimal LDF） based on the minimum number of misclassification （minimum NM） using integer programming （IP）. We call this LDF as Revised IP-OLDF. Only this LDF can discriminate the cases on the discriminant hyperplane （Probleml）. This LDF and a hard-margin SVM （H-SVM） can discriminate the lineary separable data （LSD） exactly. Another LDFs may not discriminate the LSD theoretically （Problem2）. When Revised IP-OLDF discriminate the Swiss banknote data with six variables, we find MNM of two-variables model such as （X4, X6） is zero. Because MNMk decreases monotounusly （MNMk 〉= MNM（k＋1））, sixteen MNMs including （X4, X6） are zero. Until now, because there is no research of the LSD, we surveyed another three linear separable data sets such as： 18 exam scores data sets, the Japanese 44 cars data and six microarray datasets. When we discriminate the exam scores with MNM=0, we find the generalized inverse matrix technique causes the serious Problem3 and confirmed this fact by the cars data. At last, we claim the discriminant analysis is not the inferential statistics because there is no standard errors （SEs） of error rates and discriminant coefficients （Problem4）. Therefore, we poroposed the ＂100-fold cross validation for the small sample＂ method （the method）. By this break-through, we can choose the best model having minimum mean of error rate （M2） in the validation sample and obtaine two 95% confidence intervals （CIs） of error rate and discriminant coefficients. When we discriminate the exam scores by this new method, we obtaine the surprising results seven LDFs except for Fisher＇s LDF are almost the same as the trivial LDFs. In this research, we discriminate the Japanese 44 cars data because we can discuss four problems. There are six independent variables to discriminate 29 regular cars and 15 small cars. This data is linear separable by the emission rate （X1） and the number of seats （X3）. We examine the validity of the new model selection procedure of the discriminant analysis. We proposed the model with minimum mean of error rates （M2） in the validation samples is the best model. We had examined this procedure by the exam scores, and we obtain good results. Moreover, the 95% CI of eight LDFs offers us real perception of the discriminant theory. However, the exam scores are different from the ordinal data. Therefore, we apply our theory and procedure to the Japanese 44 cars data and confirmed the same conclution.展开更多
文摘Linear driving force (LDF) model is widely used in a diffusion process. However thismodel has inherent weakness. When the dimensionless time is less than 0.1, its relativeerror is up to 95%. In this paper a new concentration profile is proposed, and then a newmodified LDF model (MLDF) is deduced. Compared with the exact solution ofintraparticle diffusion equation, the transient volume-average amount adsorbedcalculated from the MLDF is more accurate than that calculaled from the LDF modeL .Ifone takes ±10% relative error for the limit of validity of approximation, the new model isvalid when the dimensionless time is just larger than 0. 0002, while the LDF model is notvalid until the dimension time is large than 0.05. The new model is superior to the LDFmodel. The new concentration profiles corresponding to the MLDF model are much closeto the exact concentration profiles within a particle than the parabolic propescorresponding to the LDF model.
基金supported by the National Key R&D Program of China(Nos.2022YFB4101500 and 2022YFE0209500)the National Natural Science Foundation of China(Nos.22276191 and 21976177)the Qinghai Province Air Pollution Assessment and Fine Management Support Project,and the University of Chinese Academy of Science.
文摘As a potential adsorption material,it is still a challenge for activated carbon fiber(ACF)in efficient adsorption of ethanol due to its nonpolar surface,which is mainly emitted from the grain drying industry.This study prepared surface polarity-modified ACF using the heteroatom doping method.The modified ACF possessed a richer array of strongly polar oxygen/nitrogen-containing functional groups(primarily phenolic hydroxyl and lactone groups),a larger specific surface are1,and a more developed micropore structure.The adsorption capacities of ethanol for O-ACF and N-ACF were 4.110 mmol/g and 1.698 mmol/g,respectively,which were 11.3 times and 4.7 times those of unmodified ACF.This was a significant improvement over our previous work(0.363 mmol/g).The improvement of adsorption capacity for the N-ACF was mainly due to the higher specific surface are1,greater number of micropores(more adsorption sites)and abundant existence of defects,whereas,for O-ACF,the improvement mainly relied on the abundant presence of oxygen-containing functional groups on the surface.However,water had a negative effect on the adsorption of ethanol for the modified ACF due to competitive adsorption and the disappearance of capillary condensation.It was further revealed that the adsorption process of ethanol and water was quite different.It obeyed the linear driving force(LDF)model for ethanol adsorption,however,the intraparticle diffusion(IPD)model for water adsorption.
文摘There are four serious problems in the discriminant analysis. We developed an optimal linear discriminant function （optimal LDF） based on the minimum number of misclassification （minimum NM） using integer programming （IP）. We call this LDF as Revised IP-OLDF. Only this LDF can discriminate the cases on the discriminant hyperplane （Probleml）. This LDF and a hard-margin SVM （H-SVM） can discriminate the lineary separable data （LSD） exactly. Another LDFs may not discriminate the LSD theoretically （Problem2）. When Revised IP-OLDF discriminate the Swiss banknote data with six variables, we find MNM of two-variables model such as （X4, X6） is zero. Because MNMk decreases monotounusly （MNMk 〉= MNM（k＋1））, sixteen MNMs including （X4, X6） are zero. Until now, because there is no research of the LSD, we surveyed another three linear separable data sets such as： 18 exam scores data sets, the Japanese 44 cars data and six microarray datasets. When we discriminate the exam scores with MNM=0, we find the generalized inverse matrix technique causes the serious Problem3 and confirmed this fact by the cars data. At last, we claim the discriminant analysis is not the inferential statistics because there is no standard errors （SEs） of error rates and discriminant coefficients （Problem4）. Therefore, we poroposed the ＂100-fold cross validation for the small sample＂ method （the method）. By this break-through, we can choose the best model having minimum mean of error rate （M2） in the validation sample and obtaine two 95% confidence intervals （CIs） of error rate and discriminant coefficients. When we discriminate the exam scores by this new method, we obtaine the surprising results seven LDFs except for Fisher＇s LDF are almost the same as the trivial LDFs. In this research, we discriminate the Japanese 44 cars data because we can discuss four problems. There are six independent variables to discriminate 29 regular cars and 15 small cars. This data is linear separable by the emission rate （X1） and the number of seats （X3）. We examine the validity of the new model selection procedure of the discriminant analysis. We proposed the model with minimum mean of error rates （M2） in the validation samples is the best model. We had examined this procedure by the exam scores, and we obtain good results. Moreover, the 95% CI of eight LDFs offers us real perception of the discriminant theory. However, the exam scores are different from the ordinal data. Therefore, we apply our theory and procedure to the Japanese 44 cars data and confirmed the same conclution.
