Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed...Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed by McIntyre[1952.A method for unbiased selective sampling,using ranked sets.Australian Journal of Agricultural Research 3,385-390]as an effective way to estimate the pasture mean.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the best linear unbiased estimators(BLUEs)for the simple linear regression model.The BLUEs for this model under MERSS are derived.The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.展开更多
Since it is unrealistic to do an experimental mixture assessment on every possible combination, mathematical model plays an important role in predicting the mixture toxicity. The present study is devoted to the furthe...Since it is unrealistic to do an experimental mixture assessment on every possible combination, mathematical model plays an important role in predicting the mixture toxicity. The present study is devoted to the further application of linear concentration addition（CA）-based model（LCA） and independent action（IA）-based model（LIA） to predict the non-interactive mixture toxicity. The 26 mixtures including 312 data points were used to evaluate the predictive powers of LCA and LIA models. The models were internally validated using the leave-one-out cross-validation and y-randomization test, and the external validations were evaluated by the test tests. Both LCA and LIA models agree well with the experimental values for all mixture toxicity, and present high internally（R2 and Q2 〉 0.98） and externally（Q2F1, Q2F2, and Q2F3 〉 0.99） predictive power. The use of LCA and LIA led to improved predictions compared to the estimates based on the CA and IA models. Both LCA and LIA were found to be appropriate methods for modeling toxicity of non-interactive chemical mixtures.展开更多
Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of...Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.展开更多
Rock drilling is an essential operation in mining industries.Temperature at the bit-rock interface plays a major role in the wear rate of the drill bit.This paper primarily focuses on the wear rate of tungsten carbide...Rock drilling is an essential operation in mining industries.Temperature at the bit-rock interface plays a major role in the wear rate of the drill bit.This paper primarily focuses on the wear rate of tungsten carbide(WC)drill bit and the interrelationship between temperature and wear rate during rotary drilling operations conducted using a computer numerical control(CNC)machine.The interrelationship between the temperature and wear rate was studied with regard to three types of rock samples,i.e.,fine-grained sandstone(FG)of uniaxial compressive strength(UCS)that is 17.83 MPa,medium-grained sandstone(MG)of UCS that is 13.70 MPa,and fine-grained sandstone pink(FGP)of UCS that is 51.67 MPa.Wear rate of the drill bit has been measured using controlled parameters,i.e.,drill bit diameter(6,8,10,12,and 16 mm),spindle speed(250,300,350,400,and 450 rpm),and penetration rate(2,4,6,8,and 10 mm/min),respectively.Further,a fully instrumented laboratory drilling set-up was utilized.The weight of each bit was measured after the bit reached 30 mm depth in each type of the rock sample.Furthermore,effects of the bit-rock interface temperature and operational parameters on wear rate of the drill bits were examined.The results show that the wear rate of drill bits increased with an increase in temperature for all the bit-rock combinations considered.This is due to the silica content of the rock sample,which leads to an increase in the frictional heat between the bit-rock interfaces.However,in case of medium-grained sandstone,the weight percentage(wt%)of SiO2 is around 7.23 wt%,which presents a very low wear rate coefficient of 6.33×10^–2 mg/(N?m).Moreover,the temperature rise during drilling is also minimum,i.e.,around 74℃,in comparison to that of fine-grained sandstone and fine-grained sandstone pink.In addition,this paper develops the relationship between temperature and wear rate characteristics by employing simple linear regression analysis.展开更多
基金Supported by the National Natural Science Foundation of China(11901236)the Scientific Research Fund of Hunan Provincial Science and Technology Department(2019JJ50479)+3 种基金the Scientific Research Fund of Hunan Provincial Education Department(18B322)the Winning Bid Project of Hunan Province for the 4th National Economic Census([2020]1)the Young Core Teacher Foundation of Hunan Province([2020]43)the Funda-mental Research Fund of Xiangxi Autonomous Prefecture(2018SF5026)。
文摘Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed by McIntyre[1952.A method for unbiased selective sampling,using ranked sets.Australian Journal of Agricultural Research 3,385-390]as an effective way to estimate the pasture mean.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the best linear unbiased estimators(BLUEs)for the simple linear regression model.The BLUEs for this model under MERSS are derived.The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.
基金supported by the National Natural Science Foundation of China(21407032,21667013,51578171)Natural Science Foundation of Guangxi Province(2014GXNSFBA118233)Guilin Scientific Research and Technology Development Program(2016012505)
文摘Since it is unrealistic to do an experimental mixture assessment on every possible combination, mathematical model plays an important role in predicting the mixture toxicity. The present study is devoted to the further application of linear concentration addition（CA）-based model（LCA） and independent action（IA）-based model（LIA） to predict the non-interactive mixture toxicity. The 26 mixtures including 312 data points were used to evaluate the predictive powers of LCA and LIA models. The models were internally validated using the leave-one-out cross-validation and y-randomization test, and the external validations were evaluated by the test tests. Both LCA and LIA models agree well with the experimental values for all mixture toxicity, and present high internally（R2 and Q2 〉 0.98） and externally（Q2F1, Q2F2, and Q2F3 〉 0.99） predictive power. The use of LCA and LIA led to improved predictions compared to the estimates based on the CA and IA models. Both LCA and LIA were found to be appropriate methods for modeling toxicity of non-interactive chemical mixtures.
基金Supported by the Outstanding Youth Research Project of Anhui Colleges(Grant No.2022AH030156)。
文摘Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.
文摘Rock drilling is an essential operation in mining industries.Temperature at the bit-rock interface plays a major role in the wear rate of the drill bit.This paper primarily focuses on the wear rate of tungsten carbide(WC)drill bit and the interrelationship between temperature and wear rate during rotary drilling operations conducted using a computer numerical control(CNC)machine.The interrelationship between the temperature and wear rate was studied with regard to three types of rock samples,i.e.,fine-grained sandstone(FG)of uniaxial compressive strength(UCS)that is 17.83 MPa,medium-grained sandstone(MG)of UCS that is 13.70 MPa,and fine-grained sandstone pink(FGP)of UCS that is 51.67 MPa.Wear rate of the drill bit has been measured using controlled parameters,i.e.,drill bit diameter(6,8,10,12,and 16 mm),spindle speed(250,300,350,400,and 450 rpm),and penetration rate(2,4,6,8,and 10 mm/min),respectively.Further,a fully instrumented laboratory drilling set-up was utilized.The weight of each bit was measured after the bit reached 30 mm depth in each type of the rock sample.Furthermore,effects of the bit-rock interface temperature and operational parameters on wear rate of the drill bits were examined.The results show that the wear rate of drill bits increased with an increase in temperature for all the bit-rock combinations considered.This is due to the silica content of the rock sample,which leads to an increase in the frictional heat between the bit-rock interfaces.However,in case of medium-grained sandstone,the weight percentage(wt%)of SiO2 is around 7.23 wt%,which presents a very low wear rate coefficient of 6.33×10^–2 mg/(N?m).Moreover,the temperature rise during drilling is also minimum,i.e.,around 74℃,in comparison to that of fine-grained sandstone and fine-grained sandstone pink.In addition,this paper develops the relationship between temperature and wear rate characteristics by employing simple linear regression analysis.
