We propose an information theory based objective function for measuring the statistics independent of source signals. Then, we develop a learlling algorithm for blind separation of nonstationary signals by minimizing ...We propose an information theory based objective function for measuring the statistics independent of source signals. Then, we develop a learlling algorithm for blind separation of nonstationary signals by minimizing the objective function, in which the property of nonstationary and direct architecture neural network is applied. The analysis demonstrates the equiralence of two neural architectures in some special cases. The computer simulation shows the validity of the proposed algorithm. We give the performance surface of the object function at the last of the paper.展开更多
A source enumeration method based on diagonal loading of eigenvalues and constructing second-order statistics is proposed,for the case that the antenna array observed signals are overlapped with spatial colored noise,...A source enumeration method based on diagonal loading of eigenvalues and constructing second-order statistics is proposed,for the case that the antenna array observed signals are overlapped with spatial colored noise,and the number of antennas compared with the number of snapshots meet the requirement of general asymptotic regime.Firstly,the sample covariance matrix of the observed signals is obtained,the eigenvalues of the sample covariance matrix can be acquired by eigenvalue decomposition,and the eigenvalues are diagonally loaded,and a new formula for calculating the diagonal loading is presented.Based on the diagonal loaded eigenvalues,the difference values are calculated for the adjacent eigenvalues after diagonal loading,and the statistical variance of the difference values is calculated.On this basis,the second-order statistics of the difference values are constructed,and when the second-order statistics are minimized,the corresponding number of sources is estimated.The proposed method has wide applicability,which is suitable for both general asymptotic regime and classical asymptotic system,and is suitable for both white Gaussian noise environment and colored noise environment.The method makes up for the lack of source enumeration methods in the case of general asymptotic system and colored noise.展开更多
We present an adaptive algorithm for blind identification and equalization of single-input multiple-output （SIMO） FIR channels with second-order statistics. We first reformulate the blind channel identification prob...We present an adaptive algorithm for blind identification and equalization of single-input multiple-output （SIMO） FIR channels with second-order statistics. We first reformulate the blind channel identification problem into a low-rank matrix approximation solution based on the QR decomposition of the received data matrix. Then, a fast recursive algorithm is developed based on the bi-iterative least squares （Bi-LS） subspace tracking method. The new algorithm requires only a computational complexity of O（md2） at each iteration, or even as low as O（md） if only equalization is necessary, where m is the dimension of the received data vector （or the row rank of channel matrix） and d is the dimension of the signal subspace （or the column rank of channel matrix）. To overcome the shortcoming of the back substitution, an inverse QR iteration algorithm for subspace tracking and channel equalization is also developed. The inverse QR iteration algorithm is well suited for the parallel implementation in the systolic array. Simulation results are presented to illustrate the effectiveness of the proposed algorithms for the channel identification and equalization.展开更多
The lottery has long captivated the imagination of players worldwide, offering the tantalizing possibility of life-changing wins. While winning the lottery is largely a matter of chance, as lottery drawings are typica...The lottery has long captivated the imagination of players worldwide, offering the tantalizing possibility of life-changing wins. While winning the lottery is largely a matter of chance, as lottery drawings are typically random and unpredictable. Some people use the lottery terminal randomly generates numbers for them, some players choose numbers that hold personal significance to them, such as birthdays, anniversaries, or other important dates, some enthusiasts have turned to statistical analysis as a means to analyze past winning numbers identify patterns or frequencies. In this paper, we use order statistics to estimate the probability of specific order of numbers or number combinations being drawn in future drawings.展开更多
To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregress...To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.展开更多
Objective: To explore the application effect of CBL combined with rain classroom teaching method in medical statistics courses. Methods: The undergraduate students of medical imaging technology in 2019 and 2020 in a u...Objective: To explore the application effect of CBL combined with rain classroom teaching method in medical statistics courses. Methods: The undergraduate students of medical imaging technology in 2019 and 2020 in a university were selected as the research objects. A cluster sampling method was used to select 79 undergraduate students from 2019 in the control group and 75 undergraduate students from 2020 in the experimental group. Traditional teaching method and CBL combined with rain classroom teaching method was used in the control group and experimental group respectively. The final examination scores of the two groups were compared. In experimental group, the correlation between the average score in the rain classroom and the final examination score was tested, and the teaching effect was evaluated. Results: The average score of final examination in experimental group and control group was 79.13 ± 10.32 points and 71.54 ± 14.752 points, respectively, which had a statistically significant difference (Z = 2.586, P = 0.012);the final examination scores of the students in the experimental group were positively correlated with the average scores of the rain classroom (r = 0.372, P = 0.001), and the proportion of satisfaction in the experimental group was 94.7%. Conclusion: The CBL combined with rain classroom teaching method can improve the teaching effectiveness of medical statistics courses.展开更多
The Bureau of Statistics has demonstrated a forward-looking strategic approach in its economic census.By leveraging dual innovations in technology and management,and incorporating modern technologies such as big data,...The Bureau of Statistics has demonstrated a forward-looking strategic approach in its economic census.By leveraging dual innovations in technology and management,and incorporating modern technologies such as big data,cloud computing,and the Internet of Things,it has deepened the reform of the census methodology.Additionally,the Bureau has built a multi-dimensional collaborative network that enhances international cooperation,departmental coordination,and public participation.This approach not only addresses the limitations of traditional statistical methods in a complex economic environment but also improves data quality and census efficiency,providing an accurate and reliable foundation for national economic decision-making.展开更多
In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ...In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.展开更多
To cultivate talents with an exploratory spirit and practical skills in the era of information technology,it is imperative to reform teaching methods and approaches.In the teaching process of the Probability and Stati...To cultivate talents with an exploratory spirit and practical skills in the era of information technology,it is imperative to reform teaching methods and approaches.In the teaching process of the Probability and Statistics course,an application-oriented blended teaching model combining problem-based learning and small private online course was explored.By organizing and implementing online and offline teaching activities based on problem-based learning,a multidimensional process-oriented learning assessment system was established.Practice has shown that this model can effectively enhance classroom teaching effectiveness,benefiting the improvement of students’overall skills and mathematical literacy.展开更多
With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses...With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors.Its critical role in cultivating students’thinking skills and improving their problem-solving skills is self-evident.Course ideological and political education construction is an important link in college talent training work.Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality.At present,the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems,mainly manifested in the lack of attention paid by teachers to course ideological and political education,insufficient exploitation of ideological and political elements,and the simplification of ideological and political education implementation methods.In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching,we should strengthen the construction of teacher teams,improve teachers’ability to carry out course ideological and political education,integrate educational resources,develop educational resources for ideological and political education,and innovate teaching methods to improve the overall effect of ideological and political education integration.展开更多
A method to remove stripes from remote sensing images is proposed based on statistics and a new image enhancement method.The overall processing steps for improving the quality of remote sensing images are introduced t...A method to remove stripes from remote sensing images is proposed based on statistics and a new image enhancement method.The overall processing steps for improving the quality of remote sensing images are introduced to provide a general baseline.Due to the differences in satellite sensors when producing images,subtle but inherent stripes can appear at the stitching positions between the sensors.These stitchingstripes cannot be eliminated by conventional relative radiometric calibration.The inherent stitching stripes cause difficulties in downstream tasks such as the segmentation,classification and interpretation of remote sensing images.Therefore,a method to remove the stripes based on statistics and a new image enhancement approach are proposed in this paper.First,the inconsistency in grayscales around stripes is eliminated with the statistical method.Second,the pixels within stripes are weighted and averaged based on updated pixel values to enhance the uniformity of the overall image radiation quality.Finally,the details of the images are highlighted by a new image enhancement method,which makes the whole image clearer.Comprehensive experiments are performed,and the results indicate that the proposed method outperforms the baseline approach in terms of visual quality and radiation correction accuracy.展开更多
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ...Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.展开更多
This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is...This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.展开更多
In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.I...In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.It is shown that the first crossing point and the last exit time are asymptotically independent and dependent for weakly and strongly dependent cases,respectively.The asymptotic relations between the first crossing point and the last exit time for stationary weakly and strongly dependent Gaussian sequences are also obtained.展开更多
In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are usi...In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.展开更多
This paper discusses a statistical second-order two-scale（SSOTS） analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials.Firstly,the microscopic configur...This paper discusses a statistical second-order two-scale（SSOTS） analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials.Firstly,the microscopic configuration for the structure with random distribution is briefly characterized.Secondly,the SSOTS formulae for computing the heat transfer problem are derived successively by means of the construction way for each cell.Then,the statistical prediction algorithm based on the proposed two-scale model is described in detail.Finally,some numerical experiments are proposed,which show that the SSOTS method developed in this paper is effective for predicting the heat transfer performance of porous materials and demonstrating its significant applications in actual engineering computation.展开更多
Based on the second order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth integrated local horizontal momentum components are derived by use of the charact...Based on the second order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave number spectrum of ocean waves. As an illustrative example, a fully developed wind generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.展开更多
This paper contributes a sophisticated statistical method for the assessment of performance in routing protocols salient Mobile Ad Hoc Network(MANET)routing protocols:Destination Sequenced Distance Vector(DSDV),Ad hoc...This paper contributes a sophisticated statistical method for the assessment of performance in routing protocols salient Mobile Ad Hoc Network(MANET)routing protocols:Destination Sequenced Distance Vector(DSDV),Ad hoc On-Demand Distance Vector(AODV),Dynamic Source Routing(DSR),and Zone Routing Protocol(ZRP).In this paper,the evaluation will be carried out using complete sets of statistical tests such as Kruskal-Wallis,Mann-Whitney,and Friedman.It articulates a systematic evaluation of how the performance of the previous protocols varies with the number of nodes and the mobility patterns.The study is premised upon the Quality of Service(QoS)metrics of throughput,packet delivery ratio,and end-to-end delay to gain an adequate understanding of the operational efficiency of each protocol under different network scenarios.The findings explained significant differences in the performance of different routing protocols;as a result,decisions for the selection and optimization of routing protocols can be taken effectively according to different network requirements.This paper is a step forward in the general understanding of the routing dynamics of MANETs and contributes significantly to the strategic deployment of robust and efficient network infrastructures.展开更多
This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2<sup>nd</sup>-BERRU-PMD. The attribute “2<sup>nd</sup>” indicates that this met...This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2<sup>nd</sup>-BERRU-PMD. The attribute “2<sup>nd</sup>” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2<sup>nd</sup>-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2<sup>nd</sup>-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.展开更多
文摘We propose an information theory based objective function for measuring the statistics independent of source signals. Then, we develop a learlling algorithm for blind separation of nonstationary signals by minimizing the objective function, in which the property of nonstationary and direct architecture neural network is applied. The analysis demonstrates the equiralence of two neural architectures in some special cases. The computer simulation shows the validity of the proposed algorithm. We give the performance surface of the object function at the last of the paper.
基金supported by the Natural Science Foundation of China(61801480)。
文摘A source enumeration method based on diagonal loading of eigenvalues and constructing second-order statistics is proposed,for the case that the antenna array observed signals are overlapped with spatial colored noise,and the number of antennas compared with the number of snapshots meet the requirement of general asymptotic regime.Firstly,the sample covariance matrix of the observed signals is obtained,the eigenvalues of the sample covariance matrix can be acquired by eigenvalue decomposition,and the eigenvalues are diagonally loaded,and a new formula for calculating the diagonal loading is presented.Based on the diagonal loaded eigenvalues,the difference values are calculated for the adjacent eigenvalues after diagonal loading,and the statistical variance of the difference values is calculated.On this basis,the second-order statistics of the difference values are constructed,and when the second-order statistics are minimized,the corresponding number of sources is estimated.The proposed method has wide applicability,which is suitable for both general asymptotic regime and classical asymptotic system,and is suitable for both white Gaussian noise environment and colored noise environment.The method makes up for the lack of source enumeration methods in the case of general asymptotic system and colored noise.
基金Supported by the National Basic Research Program of China (Grant No. 2008CB317109)the National Natural Science Foundation of China(Grant No. 60572054)+1 种基金the Foundation of Authors of National Excellent Doctoral Dissertation (Grant No. 200239)the Scientific Research Foundation for Returned Scholars, Ministry of Education of China
文摘We present an adaptive algorithm for blind identification and equalization of single-input multiple-output （SIMO） FIR channels with second-order statistics. We first reformulate the blind channel identification problem into a low-rank matrix approximation solution based on the QR decomposition of the received data matrix. Then, a fast recursive algorithm is developed based on the bi-iterative least squares （Bi-LS） subspace tracking method. The new algorithm requires only a computational complexity of O（md2） at each iteration, or even as low as O（md） if only equalization is necessary, where m is the dimension of the received data vector （or the row rank of channel matrix） and d is the dimension of the signal subspace （or the column rank of channel matrix）. To overcome the shortcoming of the back substitution, an inverse QR iteration algorithm for subspace tracking and channel equalization is also developed. The inverse QR iteration algorithm is well suited for the parallel implementation in the systolic array. Simulation results are presented to illustrate the effectiveness of the proposed algorithms for the channel identification and equalization.
文摘The lottery has long captivated the imagination of players worldwide, offering the tantalizing possibility of life-changing wins. While winning the lottery is largely a matter of chance, as lottery drawings are typically random and unpredictable. Some people use the lottery terminal randomly generates numbers for them, some players choose numbers that hold personal significance to them, such as birthdays, anniversaries, or other important dates, some enthusiasts have turned to statistical analysis as a means to analyze past winning numbers identify patterns or frequencies. In this paper, we use order statistics to estimate the probability of specific order of numbers or number combinations being drawn in future drawings.
基金The National Key Research and Development Program of China under contract No.2023YFC3107701the National Natural Science Foundation of China under contract No.42375143.
文摘To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.
文摘Objective: To explore the application effect of CBL combined with rain classroom teaching method in medical statistics courses. Methods: The undergraduate students of medical imaging technology in 2019 and 2020 in a university were selected as the research objects. A cluster sampling method was used to select 79 undergraduate students from 2019 in the control group and 75 undergraduate students from 2020 in the experimental group. Traditional teaching method and CBL combined with rain classroom teaching method was used in the control group and experimental group respectively. The final examination scores of the two groups were compared. In experimental group, the correlation between the average score in the rain classroom and the final examination score was tested, and the teaching effect was evaluated. Results: The average score of final examination in experimental group and control group was 79.13 ± 10.32 points and 71.54 ± 14.752 points, respectively, which had a statistically significant difference (Z = 2.586, P = 0.012);the final examination scores of the students in the experimental group were positively correlated with the average scores of the rain classroom (r = 0.372, P = 0.001), and the proportion of satisfaction in the experimental group was 94.7%. Conclusion: The CBL combined with rain classroom teaching method can improve the teaching effectiveness of medical statistics courses.
文摘The Bureau of Statistics has demonstrated a forward-looking strategic approach in its economic census.By leveraging dual innovations in technology and management,and incorporating modern technologies such as big data,cloud computing,and the Internet of Things,it has deepened the reform of the census methodology.Additionally,the Bureau has built a multi-dimensional collaborative network that enhances international cooperation,departmental coordination,and public participation.This approach not only addresses the limitations of traditional statistical methods in a complex economic environment but also improves data quality and census efficiency,providing an accurate and reliable foundation for national economic decision-making.
文摘In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
基金2023 Quality Engineering Project of Guangzhou City Polytechnic“Research on Process Assessment Mode of‘Probability Theory and Mathematical Statistics’Course Based on Application Ability Cultivation”(JY230140)2024 Quality Engineering Project of Guangzhou City Polytechnic“Exploration and Practice of Teaching Model Based on PBL+SPOC+Flipped Classroom in‘Probability Theory and Mathematical Statistics’”(J1124030)。
文摘To cultivate talents with an exploratory spirit and practical skills in the era of information technology,it is imperative to reform teaching methods and approaches.In the teaching process of the Probability and Statistics course,an application-oriented blended teaching model combining problem-based learning and small private online course was explored.By organizing and implementing online and offline teaching activities based on problem-based learning,a multidimensional process-oriented learning assessment system was established.Practice has shown that this model can effectively enhance classroom teaching effectiveness,benefiting the improvement of students’overall skills and mathematical literacy.
基金2023 General Project of Philosophy and Social Science Research in Universities of Jiangsu Province“Exploration and Practice of Mixed Teaching Model Oriented by Curriculum Ideology and Politics in the Course of Probability Theory and Mathematical Statistics”(2023SJYB1499)。
文摘With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors.Its critical role in cultivating students’thinking skills and improving their problem-solving skills is self-evident.Course ideological and political education construction is an important link in college talent training work.Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality.At present,the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems,mainly manifested in the lack of attention paid by teachers to course ideological and political education,insufficient exploitation of ideological and political elements,and the simplification of ideological and political education implementation methods.In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching,we should strengthen the construction of teacher teams,improve teachers’ability to carry out course ideological and political education,integrate educational resources,develop educational resources for ideological and political education,and innovate teaching methods to improve the overall effect of ideological and political education integration.
文摘A method to remove stripes from remote sensing images is proposed based on statistics and a new image enhancement method.The overall processing steps for improving the quality of remote sensing images are introduced to provide a general baseline.Due to the differences in satellite sensors when producing images,subtle but inherent stripes can appear at the stitching positions between the sensors.These stitchingstripes cannot be eliminated by conventional relative radiometric calibration.The inherent stitching stripes cause difficulties in downstream tasks such as the segmentation,classification and interpretation of remote sensing images.Therefore,a method to remove the stripes based on statistics and a new image enhancement approach are proposed in this paper.First,the inconsistency in grayscales around stripes is eliminated with the statistical method.Second,the pixels within stripes are weighted and averaged based on updated pixel values to enhance the uniformity of the overall image radiation quality.Finally,the details of the images are highlighted by a new image enhancement method,which makes the whole image clearer.Comprehensive experiments are performed,and the results indicate that the proposed method outperforms the baseline approach in terms of visual quality and radiation correction accuracy.
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.
基金Project supported by the Executive Agency for Higher Education Research Development and Innovation Funding of Romania(No.PN-III-P4-PCE-2021-0993)。
文摘This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.
基金Supported by the National Natural Science Foundation of China(11501250)Zhejiang Provincial Natural Science Foundation of China(LY18A010020)Innovation of Jiaxing City:a program to support the talented persons。
文摘In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.It is shown that the first crossing point and the last exit time are asymptotically independent and dependent for weakly and strongly dependent cases,respectively.The asymptotic relations between the first crossing point and the last exit time for stationary weakly and strongly dependent Gaussian sequences are also obtained.
文摘In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.
基金Project supported by the China Postdoctoral Science Foundation(Grant Nos.2015M580256 and 2016T90276)
文摘This paper discusses a statistical second-order two-scale（SSOTS） analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials.Firstly,the microscopic configuration for the structure with random distribution is briefly characterized.Secondly,the SSOTS formulae for computing the heat transfer problem are derived successively by means of the construction way for each cell.Then,the statistical prediction algorithm based on the proposed two-scale model is described in detail.Finally,some numerical experiments are proposed,which show that the SSOTS method developed in this paper is effective for predicting the heat transfer performance of porous materials and demonstrating its significant applications in actual engineering computation.
文摘Based on the second order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave number spectrum of ocean waves. As an illustrative example, a fully developed wind generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.
基金supported by Northern Border University,Arar,KSA,through the Project Number“NBU-FFR-2024-2248-02”.
文摘This paper contributes a sophisticated statistical method for the assessment of performance in routing protocols salient Mobile Ad Hoc Network(MANET)routing protocols:Destination Sequenced Distance Vector(DSDV),Ad hoc On-Demand Distance Vector(AODV),Dynamic Source Routing(DSR),and Zone Routing Protocol(ZRP).In this paper,the evaluation will be carried out using complete sets of statistical tests such as Kruskal-Wallis,Mann-Whitney,and Friedman.It articulates a systematic evaluation of how the performance of the previous protocols varies with the number of nodes and the mobility patterns.The study is premised upon the Quality of Service(QoS)metrics of throughput,packet delivery ratio,and end-to-end delay to gain an adequate understanding of the operational efficiency of each protocol under different network scenarios.The findings explained significant differences in the performance of different routing protocols;as a result,decisions for the selection and optimization of routing protocols can be taken effectively according to different network requirements.This paper is a step forward in the general understanding of the routing dynamics of MANETs and contributes significantly to the strategic deployment of robust and efficient network infrastructures.
文摘This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2<sup>nd</sup>-BERRU-PMD. The attribute “2<sup>nd</sup>” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2<sup>nd</sup>-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2<sup>nd</sup>-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.
