Air pollution control has always been a global challenge, and significant progress has been made in recent years in controlling air pollutants. However, in some major cities, air pollutant concentrations still exceed ...Air pollution control has always been a global challenge, and significant progress has been made in recent years in controlling air pollutants. However, in some major cities, air pollutant concentrations still exceed the standards. Some scholars have used linear models or conditional autoregressive iterative models to apply the VaR method to predict pollutant concentrations. However, traditional methods based on quantile regression estimation can lead to inadequate risk estimates. Therefore, we propose a method based on the Conditional Autoregressive Value at Risk (CAViaR) model, which uses the kth power expectile regression to estimate VaR. This method does not specify the type of the distribution of data, is easier to calculate the asymptotic variance, more sensitive to extreme values. Applying our method to the data of PM10 in Beijing, we investigate the fitting effects in the case of k = 1, k = 2, and k = 1.9 through predictive tests. The results show that the kth power expectile regression estimates are better than quantile and expectile regression estimates to some extent.展开更多
Let p be an odd prime and let n ≥1, k ≥0 and r be integers. Denote by B_k the kth Bernoulli number. It is proved that (i) If r ≥1 is odd and suppose p ≥r + 4, then (ii)If r ≥2 is even and suppose p ≥ r + 3, then...Let p be an odd prime and let n ≥1, k ≥0 and r be integers. Denote by B_k the kth Bernoulli number. It is proved that (i) If r ≥1 is odd and suppose p ≥r + 4, then (ii)If r ≥2 is even and suppose p ≥ r + 3, then (modp^2). (iii)-(2n+1)p (modp^2). This result generalizes the Glaisher’s congruence. As a corollary, a generalization of the Wolstenholme’s theorem is obtained.展开更多
The generalized order statistics which introduced by [1] are studied in the present paper. The Gompertz distribution is widely used to describe the distribution of adult deaths, and some related models used in the eco...The generalized order statistics which introduced by [1] are studied in the present paper. The Gompertz distribution is widely used to describe the distribution of adult deaths, and some related models used in the economic applications [2]. Previous works concentrated on formulating approximate relationships to characterize it [3-5]. The main aim of this paper is to obtain the distribution of single, two, and all generalized order statistics from Gompertz distribution with some special cases. In addition the conditional distribution of two generalized order statistics from the same distribution is obtained. The Gompertz distribution has a continuous probability density function with location parameter a and shape parameter b, , where x restricted by the interval . The nth moment generated function of the Gompertz distributed random variable X is given on the form: where, is the generalized integro-exponential function [6]. In this paper we shall obtain joint distribution, distribution of product of two generalized order statistics from the Gompertz distribution, and then derive some useful formulas of these distributions as special cases.展开更多
In this note. the relationship between polymer radii and moments is revealed. In the polycondensation relaction of A_a-B_b type, monomer A_a having a-functionalities may react on monomer B_b having b-functionalities. ...In this note. the relationship between polymer radii and moments is revealed. In the polycondensation relaction of A_a-B_b type, monomer A_a having a-functionalities may react on monomer B_b having b-functionalities. The Kth polymer moment M_K can be defined展开更多
There are several fatigue-based approaches that estimate the evolution of rolling contact fatigue(RCF) on rails over time and built to be used in tandem with multibody simulations of vehicle dynamics. However, most of...There are several fatigue-based approaches that estimate the evolution of rolling contact fatigue(RCF) on rails over time and built to be used in tandem with multibody simulations of vehicle dynamics. However, most of the models are not directly comparable with each other since they are based on different physical models even though they shall predict the same RCF damage at the end.This article studies different approaches to quantifying RCF and puts forward a measure for the degree of agreement between them. The methodological framework studies various steps in the RCF quantification procedure within the context of one another, identifies the ‘primary quantification step’ in each approach and compares results of the fatigue analyses. In addition to this, two quantities—‘similarity’ and ‘correlation’—have been put forward to give an indication of mutual agreement between models.Four widely used surface-based and sub-surface-based fatigue quantification approaches with varying complexities have been studied. Different operational cases corresponding to a metro vehicle operation in Austria have been considered for this study. Results showed that the best possible quantity to compare is the normalized damage increment per loading cycle coming from different approaches. Amongst the methods studied, approaches that included the load distribution step on the contact patch showed higher similarity and correlation in their results.While the different approaches might qualitatively agree on whether contact cases are ‘damaging’ due to RCF, they might not quantitatively correlate with the trends observed for damage increment values.展开更多
Recently Hong Shaofang[6] has investigated the sums (np + j)-r ( with an odd prime number p 5 and n, r N) by Washington’s p-adic expansion of these sums as a power series in n where the coefficients are values of p-a...Recently Hong Shaofang[6] has investigated the sums (np + j)-r ( with an odd prime number p 5 and n, r N) by Washington’s p-adic expansion of these sums as a power series in n where the coefficients are values of p-adic L-fuctions[12]. Herethe author shows how a more general sums (npl +j)-r,l N, may be studied by elementary methods.展开更多
文摘Air pollution control has always been a global challenge, and significant progress has been made in recent years in controlling air pollutants. However, in some major cities, air pollutant concentrations still exceed the standards. Some scholars have used linear models or conditional autoregressive iterative models to apply the VaR method to predict pollutant concentrations. However, traditional methods based on quantile regression estimation can lead to inadequate risk estimates. Therefore, we propose a method based on the Conditional Autoregressive Value at Risk (CAViaR) model, which uses the kth power expectile regression to estimate VaR. This method does not specify the type of the distribution of data, is easier to calculate the asymptotic variance, more sensitive to extreme values. Applying our method to the data of PM10 in Beijing, we investigate the fitting effects in the case of k = 1, k = 2, and k = 1.9 through predictive tests. The results show that the kth power expectile regression estimates are better than quantile and expectile regression estimates to some extent.
文摘Let p be an odd prime and let n ≥1, k ≥0 and r be integers. Denote by B_k the kth Bernoulli number. It is proved that (i) If r ≥1 is odd and suppose p ≥r + 4, then (ii)If r ≥2 is even and suppose p ≥ r + 3, then (modp^2). (iii)-(2n+1)p (modp^2). This result generalizes the Glaisher’s congruence. As a corollary, a generalization of the Wolstenholme’s theorem is obtained.
文摘The generalized order statistics which introduced by [1] are studied in the present paper. The Gompertz distribution is widely used to describe the distribution of adult deaths, and some related models used in the economic applications [2]. Previous works concentrated on formulating approximate relationships to characterize it [3-5]. The main aim of this paper is to obtain the distribution of single, two, and all generalized order statistics from Gompertz distribution with some special cases. In addition the conditional distribution of two generalized order statistics from the same distribution is obtained. The Gompertz distribution has a continuous probability density function with location parameter a and shape parameter b, , where x restricted by the interval . The nth moment generated function of the Gompertz distributed random variable X is given on the form: where, is the generalized integro-exponential function [6]. In this paper we shall obtain joint distribution, distribution of product of two generalized order statistics from the Gompertz distribution, and then derive some useful formulas of these distributions as special cases.
基金Project supported by the National Natural Science Foundation of China
文摘In this note. the relationship between polymer radii and moments is revealed. In the polycondensation relaction of A_a-B_b type, monomer A_a having a-functionalities may react on monomer B_b having b-functionalities. The Kth polymer moment M_K can be defined
基金funding from the Shift2Rail Joint Undertaking (JU) under the European Union’s Horizon 2020 research and innovation programme under grant agreement (No. 826206)。
文摘There are several fatigue-based approaches that estimate the evolution of rolling contact fatigue(RCF) on rails over time and built to be used in tandem with multibody simulations of vehicle dynamics. However, most of the models are not directly comparable with each other since they are based on different physical models even though they shall predict the same RCF damage at the end.This article studies different approaches to quantifying RCF and puts forward a measure for the degree of agreement between them. The methodological framework studies various steps in the RCF quantification procedure within the context of one another, identifies the ‘primary quantification step’ in each approach and compares results of the fatigue analyses. In addition to this, two quantities—‘similarity’ and ‘correlation’—have been put forward to give an indication of mutual agreement between models.Four widely used surface-based and sub-surface-based fatigue quantification approaches with varying complexities have been studied. Different operational cases corresponding to a metro vehicle operation in Austria have been considered for this study. Results showed that the best possible quantity to compare is the normalized damage increment per loading cycle coming from different approaches. Amongst the methods studied, approaches that included the load distribution step on the contact patch showed higher similarity and correlation in their results.While the different approaches might qualitatively agree on whether contact cases are ‘damaging’ due to RCF, they might not quantitatively correlate with the trends observed for damage increment values.
文摘Recently Hong Shaofang[6] has investigated the sums (np + j)-r ( with an odd prime number p 5 and n, r N) by Washington’s p-adic expansion of these sums as a power series in n where the coefficients are values of p-adic L-fuctions[12]. Herethe author shows how a more general sums (npl +j)-r,l N, may be studied by elementary methods.
