Integrated continuous stirred-tank reactors and distillation columns with recycle(CSTR-DC-recycle)are essential components in chemical processes.This paper proposes a method to establish a normal operating zone(NOZ)mo...Integrated continuous stirred-tank reactors and distillation columns with recycle(CSTR-DC-recycle)are essential components in chemical processes.This paper proposes a method to establish a normal operating zone(NOZ)model to represent allowable variations of the CSTR-DC-recycle chemical processes.The NOZ is a geometric space containing all safe operating points of the CSTR-DC-recycle chemical processes,so that it is an effective model for process monitoring.The novelty of the proposed method is to establish the NOZ model based on boundary points.The boundary points make it possible to capture the actual geometric space irrespective of the space shape.In contrast,existing methods represent the NOZ of processes by fixed mathematical models such as ellipsoidal and convex-hull models;they are not suitable for the CSTR-DC-recycle chemical processes whose NOZs cannot be exactly defined by fixed mathematical structures.Simulated case studies based on Aspen Hysys software are given to illustrate the proposed method.展开更多
Microstructure, precipitate and magnetic characteristic of fmal products with different normalizing cooling processes for Fe-3.2%Si low-temperature hot-rolled grain-oriented silicon steel were analyzed and compared wi...Microstructure, precipitate and magnetic characteristic of fmal products with different normalizing cooling processes for Fe-3.2%Si low-temperature hot-rolled grain-oriented silicon steel were analyzed and compared with the hot-rolled plate by optical microscopy （OM）, transmission electron microscopy （TEM）, and energy dispersive spectrometry （EDS）. The results show that, the surface microstructure is uniform, the proportion of recrystallization in matrix increases, and the banding textures are narrowed; the precipitates, whose quantity in normalized plate is more than that in hot-rolled plate greatly, are mainly A1N, MnS, composite precipitates （Cu,Mn）S and so on. Normalizing technology with a temperature of 1120 ℃, holding for 3 min, and a two-stage cooling is a most advantaged method to obtain oriented silicon steel with sharper Goss texture and higher magnetic properties, owing to the uniform surface microstructures and the obvious inhomogeneity of microstructures along the thickness. The normalizing technology with the two-stage cooling is the optimum process, which can generate more fine precipitates dispersed over the matrix, and be beneficial for finished products to get higher magnetic properties.展开更多
This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is ...This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is an autoregressive model of order p,representing a time series with dependencies on its p previous values.Additionally,the study evaluates the accuracy of both explicit and numerical integral equation(NIE)solutions for AR(p)using the TEWMA control chart,focusing on the absolute percentage relative error.The results indicate that the explicit and approximate solutions are in close agreement.Furthermore,the study investigates the performance of exponentially weighted moving average(EWMA)and TEWMA control charts in detecting changes in the process,using the relative mean index(RMI)as a measure.The findings demonstrate that the TEWMA control chart outperforms the EWMA control chart in detecting process changes,especially when the value ofλis sufficiently large.In addition,an analysis using historical data from the SET index between January 2024 and May 2024 and historical data of global annual plastic production,the results of both data sets also emphasize the superior performance of the TEWMA control chart.展开更多
Statistical Quality Control （SQC） is used to analyze and monitor quality characteristic measurements of normal neonatal weight in a maternity clinic in Banjarmasin in this paper. The objective of this study is to as...Statistical Quality Control （SQC） is used to analyze and monitor quality characteristic measurements of normal neonatal weight in a maternity clinic in Banjarmasin in this paper. The objective of this study is to assist medical practitioners in observing pregnant women to deliver their babies with normal weight. It is also assumed that pregnant women who delivered their babies in the clinic have been monitored during their nine-month pregnancy. Thus, they can manage their own pregnancy to deliver normal weight babies. The use of Statistical Process Control （SPC） tools, such as frequency histogram, probability plot, and the implementation of Shewhart, R, and S control charts as primary techniques, are presented to display the monitoring aspects of the process. In addition, Process Capability Analysis （PCA） is performed to ensure that the process outcomes are capable of meeting certain requirements or specifications. The Process Capability Ratio （PCR） for the process is also presented. This analysis is an essential part of an overall quality improvement program.展开更多
A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance con...A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance condition.We obtain the well-posedness using nonlinear semigroup theory arguments.Moreover,the exponential stability result of the solution is shown by using the energy method to produce a suitable Lyapunov function.展开更多
In order to evaluate radiometric normalization techniques, two image normalization algorithms for absolute radiometric correction of Landsat imagery were quantitatively compared in this paper, which are the Illuminati...In order to evaluate radiometric normalization techniques, two image normalization algorithms for absolute radiometric correction of Landsat imagery were quantitatively compared in this paper, which are the Illumination Correction Model proposed by Markham and Irish and the Illumination and Atmospheric Correction Model developed by the Remote Sensing and GIS Laboratory of the Utah State University. Relative noise, correlation coefficient and slope value were used as the criteria for the evaluation and comparison, which were derived from pseudo-invarlant features identified from multitemporal Landsat image pairs of Xiamen （厦门） and Fuzhou （福州） areas, both located in the eastern Fujian （福建） Province of China. Compared with the unnormalized image, the radiometric differences between the normalized multitemporal images were significantly reduced when the seasons of multitemporal images were different. However, there was no significant difference between the normalized and unnorrealized images with a similar seasonal condition. Furthermore, the correction results of two algorithms are similar when the images are relatively clear with a uniform atmospheric condition. Therefore, the radiometric normalization procedures should be carried out if the multitemporal images have a significant seasonal difference.展开更多
The paper deals with the estimation of parameters of multidimensional diffusion processes that are discretely observed. We construct estimator of the parameters based on the minimum Hellinger distance method. This met...The paper deals with the estimation of parameters of multidimensional diffusion processes that are discretely observed. We construct estimator of the parameters based on the minimum Hellinger distance method. This method is based on the minimization of the Hellinger distance between the density of the invariant distribution of the diffusion process and a nonparametric estimator of this density. We give conditions which ensure the existence of an invariant measure that admits density with respect to the Lebesgue measure and the strong mixing property with exponential rate for the Markov process. Under this condition, we define an estimator of the density based on kernel function and study his properties (almost sure convergence and asymptotic normality). After, using the estimator of the density, we construct the minimum Hellinger distance estimator of the parameters of the diffusion process and establish the almost sure convergence and the asymptotic normality of this estimator. To illustrate the properties of the estimator of the parameters, we apply the method to two examples of multidimensional diffusion processes.展开更多
This paper investigates Carrier Frequency Offset (CFO) estimation in the uplink of the Orthogonal Frequency-Division Multiple Access (OFDMA) systems with the interleaved subcarrier assignment. CFOs between the transmi...This paper investigates Carrier Frequency Offset (CFO) estimation in the uplink of the Orthogonal Frequency-Division Multiple Access (OFDMA) systems with the interleaved subcarrier assignment. CFOs between the transmitters and the uplink receiver will destroy orthogonality among different subcarriers, hence resulting in inter-carrier interference and multiuser interference. A two-stage frequency offset estimation algorithm based on subspace processing is proposed. The main advantage of the proposed method is that it can obtain the CFOs of all users simultaneously using only one OFDMA block. Compared with the previously known methods, it not only has a relatively low implementation complexity but is also suitable for random subchannel assignment.展开更多
In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test s...In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions.展开更多
P. M. Djuric, etc.(1992) researched on the segmentation of nonstationary stochastic process into piecewise stationary stochastic process by Bayesian criterion ,and gave a dynamic equation about the number of segments,...P. M. Djuric, etc.(1992) researched on the segmentation of nonstationary stochastic process into piecewise stationary stochastic process by Bayesian criterion ,and gave a dynamic equation about the number of segments, their boundaries and AR model orders for each segment, but did not give detailed solution for the equation. Because the solution for the equation is very complex, this paper investigates the solution, derives some recursive relations, simplifies the problem ,saves computation time and goes further into the segmentation of nonstationary stochastic process into piecewise stationary stochastic process.展开更多
This paper describes the preparation and properties of TiN_x-SiO_2 double-layered antireflective(AR) coatings that were applied with print process. The coating material was analyzed and TiN_x was used instead of TiO_2...This paper describes the preparation and properties of TiN_x-SiO_2 double-layered antireflective(AR) coatings that were applied with print process. The coating material was analyzed and TiN_x was used instead of TiO_2 as high refractive material. The influence of solution concentration on AR property was studied. The testing result shows that the coatings using print process are featured with excellent mechanical property and the AR property is comparable to American Southwall AR product. It is expected that the study would promote the industrialization progress in AR coatings.展开更多
Let variables in the {X, Xn, n ≥ 1} be a sequence of strictly stationary φ-mixing positive random domain of attraction of the normal law. Under some suitable conditions the principle for self-normalized products of ...Let variables in the {X, Xn, n ≥ 1} be a sequence of strictly stationary φ-mixing positive random domain of attraction of the normal law. Under some suitable conditions the principle for self-normalized products of partial sums is obtained.展开更多
The Linear Gaussian white noise process is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution N (0, σ2 ) . Hence, if X1, x2, …, Xn is a realization of such...The Linear Gaussian white noise process is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution N (0, σ2 ) . Hence, if X1, x2, …, Xn is a realization of such an iid sequence, this paper studies in detail the covariance structure of X1d, X2d, …, Xnd, d=1, 2, …. By this study, it is shown that: 1) all powers of a Linear Gaussian White Noise Process are iid but, not normally distributed and 2) the higher moments (variance and kurtosis) of Xtd, d=2, 3, … can be used to distinguish between the Linear Gaussian white noise process and other processes with similar covariance structure.展开更多
Seismological Bureau of Sichuan Province, Chengdu 610041, China2) Center for Analysis and Prediction, State Seismological Bureau, Beijing 100036, China3) Observation Center for Prediction of Earthquakes and Volcanic E...Seismological Bureau of Sichuan Province, Chengdu 610041, China2) Center for Analysis and Prediction, State Seismological Bureau, Beijing 100036, China3) Observation Center for Prediction of Earthquakes and Volcanic Eruptions, Faculty of Sciences, Tohoku University, Sendai 98077, Japan展开更多
An algorithm of broadband minimum variance distortionless response(MVDR) based on the frequency energy normalization is proposed.First,every narrowband frequency component of the broadband signal is normalized by the ...An algorithm of broadband minimum variance distortionless response(MVDR) based on the frequency energy normalization is proposed.First,every narrowband frequency component of the broadband signal is normalized by the total narrowband energy of all array elements,and the narrowband power is calculated by MVDR.Finally,final spatial energy spectrum can be obtained by averaging or summing all results of every narrowband frequency bin.Any prior-information about the noise or the signal is unnecessary for the proposed method in this paper.The processing gain of the proposed method compared to the conventional broadband MVDR can be obtained as long as the amplitude fluctuation of the array noise frequency spectrum is severer than that of the target signal.The validity of the method is validated by the optimal signal detection theory.Simulation and real data are used to validate the performance of the method.Analysis results show that about 4 dB processing gain compared to the general broadband MVDR can be reached by the proposed method.展开更多
The linear Gaussian white noise process (LGWNP) is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution . Some processes, such as the simple bilinear white noi...The linear Gaussian white noise process (LGWNP) is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution . Some processes, such as the simple bilinear white noise process (SBWNP), have the same covariance structure like the LGWNP. How can these two processes be distinguished and/or compared? If is a realization of the SBWNP. This paper studies in detail the covariance structure of . It is shown from this study that;1) the covariance structure of is non-normal with distribution equivalent to the linear ARMA(2, 1) model;2) the covariance structure of is iid;3) the variance of can be used for comparison of SBWNP and LGWNP.展开更多
According to the current understanding, electromagnetic interaction is invariable under time reversal. However, the proof of time reversal symmetry in quantum theory of field has not considered the effects of high ord...According to the current understanding, electromagnetic interaction is invariable under time reversal. However, the proof of time reversal symmetry in quantum theory of field has not considered the effects of high order perturbation normalizations. It is proved in the paper that when the renormalization effect of third order vertex angles process is taken into account, the symmetry of time reversal will be violated in electromagnetic interaction process. Because the magnitude order of symmetry violation is about 10–5, but the precision of current experiments on time reversal in particle physics is about 10–3, this kind of symmetry violation can not be found. The result reveals the micro-origin of asymmetry of time reversal and can be used to solve the famous irreversibility paradox in the evolution processes of macro- material systems.展开更多
The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to con...The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.展开更多
基金partially funded by the National Natural Science Foundation of China(62273215)。
文摘Integrated continuous stirred-tank reactors and distillation columns with recycle(CSTR-DC-recycle)are essential components in chemical processes.This paper proposes a method to establish a normal operating zone(NOZ)model to represent allowable variations of the CSTR-DC-recycle chemical processes.The NOZ is a geometric space containing all safe operating points of the CSTR-DC-recycle chemical processes,so that it is an effective model for process monitoring.The novelty of the proposed method is to establish the NOZ model based on boundary points.The boundary points make it possible to capture the actual geometric space irrespective of the space shape.In contrast,existing methods represent the NOZ of processes by fixed mathematical models such as ellipsoidal and convex-hull models;they are not suitable for the CSTR-DC-recycle chemical processes whose NOZs cannot be exactly defined by fixed mathematical structures.Simulated case studies based on Aspen Hysys software are given to illustrate the proposed method.
基金Projects(51274083,51074062)supported by the National Natural Science Foundation of China
文摘Microstructure, precipitate and magnetic characteristic of fmal products with different normalizing cooling processes for Fe-3.2%Si low-temperature hot-rolled grain-oriented silicon steel were analyzed and compared with the hot-rolled plate by optical microscopy （OM）, transmission electron microscopy （TEM）, and energy dispersive spectrometry （EDS）. The results show that, the surface microstructure is uniform, the proportion of recrystallization in matrix increases, and the banding textures are narrowed; the precipitates, whose quantity in normalized plate is more than that in hot-rolled plate greatly, are mainly A1N, MnS, composite precipitates （Cu,Mn）S and so on. Normalizing technology with a temperature of 1120 ℃, holding for 3 min, and a two-stage cooling is a most advantaged method to obtain oriented silicon steel with sharper Goss texture and higher magnetic properties, owing to the uniform surface microstructures and the obvious inhomogeneity of microstructures along the thickness. The normalizing technology with the two-stage cooling is the optimum process, which can generate more fine precipitates dispersed over the matrix, and be beneficial for finished products to get higher magnetic properties.
基金the National Science,Research and Innovation Fund(NSRF)King Mongkuts University of Technology North Bangkok under contract no.KMUTNB-FF-68-B-08.
文摘This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is an autoregressive model of order p,representing a time series with dependencies on its p previous values.Additionally,the study evaluates the accuracy of both explicit and numerical integral equation(NIE)solutions for AR(p)using the TEWMA control chart,focusing on the absolute percentage relative error.The results indicate that the explicit and approximate solutions are in close agreement.Furthermore,the study investigates the performance of exponentially weighted moving average(EWMA)and TEWMA control charts in detecting changes in the process,using the relative mean index(RMI)as a measure.The findings demonstrate that the TEWMA control chart outperforms the EWMA control chart in detecting process changes,especially when the value ofλis sufficiently large.In addition,an analysis using historical data from the SET index between January 2024 and May 2024 and historical data of global annual plastic production,the results of both data sets also emphasize the superior performance of the TEWMA control chart.
文摘Statistical Quality Control （SQC） is used to analyze and monitor quality characteristic measurements of normal neonatal weight in a maternity clinic in Banjarmasin in this paper. The objective of this study is to assist medical practitioners in observing pregnant women to deliver their babies with normal weight. It is also assumed that pregnant women who delivered their babies in the clinic have been monitored during their nine-month pregnancy. Thus, they can manage their own pregnancy to deliver normal weight babies. The use of Statistical Process Control （SPC） tools, such as frequency histogram, probability plot, and the implementation of Shewhart, R, and S control charts as primary techniques, are presented to display the monitoring aspects of the process. In addition, Process Capability Analysis （PCA） is performed to ensure that the process outcomes are capable of meeting certain requirements or specifications. The Process Capability Ratio （PCR） for the process is also presented. This analysis is an essential part of an overall quality improvement program.
文摘A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance condition.We obtain the well-posedness using nonlinear semigroup theory arguments.Moreover,the exponential stability result of the solution is shown by using the energy method to produce a suitable Lyapunov function.
基金This paper is supported by the National Natural Science Foundation ofChina (No .40371107) .
文摘In order to evaluate radiometric normalization techniques, two image normalization algorithms for absolute radiometric correction of Landsat imagery were quantitatively compared in this paper, which are the Illumination Correction Model proposed by Markham and Irish and the Illumination and Atmospheric Correction Model developed by the Remote Sensing and GIS Laboratory of the Utah State University. Relative noise, correlation coefficient and slope value were used as the criteria for the evaluation and comparison, which were derived from pseudo-invarlant features identified from multitemporal Landsat image pairs of Xiamen （厦门） and Fuzhou （福州） areas, both located in the eastern Fujian （福建） Province of China. Compared with the unnormalized image, the radiometric differences between the normalized multitemporal images were significantly reduced when the seasons of multitemporal images were different. However, there was no significant difference between the normalized and unnorrealized images with a similar seasonal condition. Furthermore, the correction results of two algorithms are similar when the images are relatively clear with a uniform atmospheric condition. Therefore, the radiometric normalization procedures should be carried out if the multitemporal images have a significant seasonal difference.
文摘The paper deals with the estimation of parameters of multidimensional diffusion processes that are discretely observed. We construct estimator of the parameters based on the minimum Hellinger distance method. This method is based on the minimization of the Hellinger distance between the density of the invariant distribution of the diffusion process and a nonparametric estimator of this density. We give conditions which ensure the existence of an invariant measure that admits density with respect to the Lebesgue measure and the strong mixing property with exponential rate for the Markov process. Under this condition, we define an estimator of the density based on kernel function and study his properties (almost sure convergence and asymptotic normality). After, using the estimator of the density, we construct the minimum Hellinger distance estimator of the parameters of the diffusion process and establish the almost sure convergence and the asymptotic normality of this estimator. To illustrate the properties of the estimator of the parameters, we apply the method to two examples of multidimensional diffusion processes.
基金the Specialized Research Fund for the Doctoral Program of Higher Education, China Ministry of Education (No.20030003039).
文摘This paper investigates Carrier Frequency Offset (CFO) estimation in the uplink of the Orthogonal Frequency-Division Multiple Access (OFDMA) systems with the interleaved subcarrier assignment. CFOs between the transmitters and the uplink receiver will destroy orthogonality among different subcarriers, hence resulting in inter-carrier interference and multiuser interference. A two-stage frequency offset estimation algorithm based on subspace processing is proposed. The main advantage of the proposed method is that it can obtain the CFOs of all users simultaneously using only one OFDMA block. Compared with the previously known methods, it not only has a relatively low implementation complexity but is also suitable for random subchannel assignment.
基金National Natural Science Foundation of China(1047112610671176).
文摘In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions.
文摘P. M. Djuric, etc.(1992) researched on the segmentation of nonstationary stochastic process into piecewise stationary stochastic process by Bayesian criterion ,and gave a dynamic equation about the number of segments, their boundaries and AR model orders for each segment, but did not give detailed solution for the equation. Because the solution for the equation is very complex, this paper investigates the solution, derives some recursive relations, simplifies the problem ,saves computation time and goes further into the segmentation of nonstationary stochastic process into piecewise stationary stochastic process.
文摘This paper describes the preparation and properties of TiN_x-SiO_2 double-layered antireflective(AR) coatings that were applied with print process. The coating material was analyzed and TiN_x was used instead of TiO_2 as high refractive material. The influence of solution concentration on AR property was studied. The testing result shows that the coatings using print process are featured with excellent mechanical property and the AR property is comparable to American Southwall AR product. It is expected that the study would promote the industrialization progress in AR coatings.
基金National Natural Science Foundation of China(1067117610771192).
文摘Let variables in the {X, Xn, n ≥ 1} be a sequence of strictly stationary φ-mixing positive random domain of attraction of the normal law. Under some suitable conditions the principle for self-normalized products of partial sums is obtained.
文摘The Linear Gaussian white noise process is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution N (0, σ2 ) . Hence, if X1, x2, …, Xn is a realization of such an iid sequence, this paper studies in detail the covariance structure of X1d, X2d, …, Xnd, d=1, 2, …. By this study, it is shown that: 1) all powers of a Linear Gaussian White Noise Process are iid but, not normally distributed and 2) the higher moments (variance and kurtosis) of Xtd, d=2, 3, … can be used to distinguish between the Linear Gaussian white noise process and other processes with similar covariance structure.
文摘Seismological Bureau of Sichuan Province, Chengdu 610041, China2) Center for Analysis and Prediction, State Seismological Bureau, Beijing 100036, China3) Observation Center for Prediction of Earthquakes and Volcanic Eruptions, Faculty of Sciences, Tohoku University, Sendai 98077, Japan
基金Sponsored by New Century Excellent Talent Support Project (NCET-04-0545)
文摘An algorithm of broadband minimum variance distortionless response(MVDR) based on the frequency energy normalization is proposed.First,every narrowband frequency component of the broadband signal is normalized by the total narrowband energy of all array elements,and the narrowband power is calculated by MVDR.Finally,final spatial energy spectrum can be obtained by averaging or summing all results of every narrowband frequency bin.Any prior-information about the noise or the signal is unnecessary for the proposed method in this paper.The processing gain of the proposed method compared to the conventional broadband MVDR can be obtained as long as the amplitude fluctuation of the array noise frequency spectrum is severer than that of the target signal.The validity of the method is validated by the optimal signal detection theory.Simulation and real data are used to validate the performance of the method.Analysis results show that about 4 dB processing gain compared to the general broadband MVDR can be reached by the proposed method.
文摘The linear Gaussian white noise process (LGWNP) is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution . Some processes, such as the simple bilinear white noise process (SBWNP), have the same covariance structure like the LGWNP. How can these two processes be distinguished and/or compared? If is a realization of the SBWNP. This paper studies in detail the covariance structure of . It is shown from this study that;1) the covariance structure of is non-normal with distribution equivalent to the linear ARMA(2, 1) model;2) the covariance structure of is iid;3) the variance of can be used for comparison of SBWNP and LGWNP.
文摘According to the current understanding, electromagnetic interaction is invariable under time reversal. However, the proof of time reversal symmetry in quantum theory of field has not considered the effects of high order perturbation normalizations. It is proved in the paper that when the renormalization effect of third order vertex angles process is taken into account, the symmetry of time reversal will be violated in electromagnetic interaction process. Because the magnitude order of symmetry violation is about 10–5, but the precision of current experiments on time reversal in particle physics is about 10–3, this kind of symmetry violation can not be found. The result reveals the micro-origin of asymmetry of time reversal and can be used to solve the famous irreversibility paradox in the evolution processes of macro- material systems.
基金Characteristic Innovation Projects of Ordinary Universities of Guangdong Province,China(No.2022KTSCX150)Zhaoqing Education Development Institute Project,China(No.ZQJYY2021144)Zhaoqing College Quality Project and Teaching Reform Project,China(Nos.zlgc202003 and zlgc202112)。
文摘The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.
