Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely...Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.展开更多
Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence ap- proaches a constant -0.515 when the Reynolds number is very high, ...Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence ap- proaches a constant -0.515 when the Reynolds number is very high, which is in agree- ment with the DNS (direct numerical simulation) result of Vincent and Meneguzzi (1991).展开更多
Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades...Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （EM） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.展开更多
The turbulence governed by the Navier-Stokes equation is paramount in many physical processes.However,it has been considered as a challenging problem due to its inherent nonlinearity,non-equilibrium,and complexity.Her...The turbulence governed by the Navier-Stokes equation is paramount in many physical processes.However,it has been considered as a challenging problem due to its inherent nonlinearity,non-equilibrium,and complexity.Herein,we review the connections between the velocity derivative skewness Sk and the non-equilibrium properties of turbulence.Sk,a reasonable candidate for describing the non-equilibrium turbulence,which varies during the non-equilibrium procedure.A lot of experimental or numerical evidences have shown that the perturbation of energy spectrum,which associated with the excitation of large scales,results in an obvious variation of Sk,and Sk is a negative value in this rapid energy decay process.The variation of positive Sk is closely related to the perturbation of transfer spectrum,and this corresponds to the backward energy transfer process.In addition,the skewness characterizes the production(or reduction)rate of enstrophy due to vortex stretching(or compression).Using the transport equation of turbulent energy dissipation rate and enstrophy,it is possible to establish a theoretical connection between skewness and the non-equilibrium turbulence.It is expected that this work could trigger the rapid advancement of the future studies of non-equilibrium turbulence,and also the improvement of turbulence models.展开更多
The skewness of subsurface temperature anomaly in the equatorial Pacific Ocean shows a significant asymmetry between the east and west.A positive temperature skewness appears in the equatorial eastern Pacific,while th...The skewness of subsurface temperature anomaly in the equatorial Pacific Ocean shows a significant asymmetry between the east and west.A positive temperature skewness appears in the equatorial eastern Pacific,while the temperature skewness in the western and central Pacific is primarily negative.There is also an asymmetry of the temperature skewness above and below the climatological mean thermocline in the central and western Pacific.A positive skewness appears below the thermocline,but the skewness is negative above the thermocline.The distinctive vertical asymmetry of the temperature skewness is argued to be attributed to the asymmetric temperature response to upward and downward thermocline displacement in the presence of the observed upper-ocean vertical thermal structure.Because of positive(negative) second derivative of temperature with respect to depth below(above) the thermocline,an upward and a downward shift of the thermocline with equal displacement would lead to a negative temperature skewness above the thermocline but a positive skewness below the thermocline.In the far eastern equatorial Pacific,the thermocline is close to the base of the mixed layer,the shape of the upper-ocean vertical temperature profile cannot be kept.Positive skewness appears in both below the thermocline and above the thermocline in the far eastern basin.Over the central and eastern Pacific,the anomalies of the subsurface waters tend to entrain into the surface mixed layer(by climatological mean upwelling) and then affect the SST.Hence,the positive(negative) subsurface skewness in the far eastern(central) Pacific may favor positive(negative) SST skewness,which is consistent with the observational fact that more La Nia(El Nio) occur in the central(eastern) Pacific.The present result implies a possible new paradigm for El Nio and La Nia amplitude asymmetry in the eastern Pacific.展开更多
In the digital world,a wide range of handwritten and printed documents should be converted to digital format using a variety of tools,including mobile phones and scanners.Unfortunately,this is not an optimal procedure...In the digital world,a wide range of handwritten and printed documents should be converted to digital format using a variety of tools,including mobile phones and scanners.Unfortunately,this is not an optimal procedure,and the entire document image might be degraded.Imperfect conversion effects due to noise,motion blur,and skew distortion can lead to significant impact on the accuracy and effectiveness of document image segmentation and analysis in Optical Character Recognition(OCR)systems.In Document Image Analysis Systems(DIAS),skew estimation of images is a crucial step.In this paper,a novel,fast,and reliable skew detection algorithm based on the Radon Transform and Curve Length Fitness Function(CLF),so-called Radon CLF,was proposed.The Radon CLF model aims to take advantage of the properties of Radon spaces.The Radon CLF explores the dominating angle more effectively for a 1D signal than it does for a 2D input image due to an innovative fitness function formulation for a projected signal of the Radon space.Several significant performance indicators,including Mean Square Error(MSE),Mean Absolute Error(MAE),Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Measure(SSIM),Accuracy,and run-time,were taken into consideration when assessing the performance of our model.In addition,a new dataset named DSI5000 was constructed to assess the accuracy of the CLF model.Both two-dimensional image signal and the Radon space have been used in our simulations to compare the noise effect.Obtained results show that the proposed method is more effective than other approaches already in use,with an accuracy of roughly 99.87%and a run-time of 0.048(s).The introduced model is far more accurate and timeefficient than current approaches in detecting image skew.展开更多
Large torque can be output by the single gimbal control momentum gyroscope (SGCMG) based on the principle of the gyroscopic precession. However, the singularity is a major obstacle to successfully implement the task o...Large torque can be output by the single gimbal control momentum gyroscope (SGCMG) based on the principle of the gyroscopic precession. However, the singularity is a major obstacle to successfully implement the task of the attitude control. The singularity can be avoided by the additional variable flywheel speed of variable speed control moment gyroscopes (VSCMG). Unfortunately, some kind of singularity cannot be effectively avoided. Consequently, the output toque can be only supported by the reaction torque of the flywheel when the singularity is encountered, and the consume power that is determined by the flywheel speed and reaction torque can be greatly increased when the flywheel spin rate over one thousand revolutions per minute. In this paper, the pyramid configuration with variable skew angle of the VSCMG is considered. A new steering law for the VSCMG with variable skew angle is proposed. The singularity that cannot be avoided by the varying flywheel speed can be effectively avoided with assisting of varying the skew angle. Consequently, the requirement of flywheel torque can be reduced. At last, the optimizing VSCMG with variable skew angle can be cast as a multi-objective function with multi-constraints. The particle swarm optimization method is used to solve the optimizing problem. In summary, the VSCMG with variable skew angle can be redesigned with considering of the singularity avoidance and minimizing system power.展开更多
基金supported by the National Natural Science Foundation of China(12131015,12071422).
文摘Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.
基金The project supported by the National Basic Research Program "Non-linear Science"
文摘Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence ap- proaches a constant -0.515 when the Reynolds number is very high, which is in agree- ment with the DNS (direct numerical simulation) result of Vincent and Meneguzzi (1991).
基金Supported by the National Natural Science Foundation of China(11261025,11561075)the Natural Science Foundation of Yunnan Province(2016FB005)the Program for Middle-aged Backbone Teacher,Yunnan University
文摘Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （EM） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.
基金Project supported by the National Natural Science Foundation of China(Grant No.11772032)the Science Foundation of North University of China(Grant No.11026829).
文摘The turbulence governed by the Navier-Stokes equation is paramount in many physical processes.However,it has been considered as a challenging problem due to its inherent nonlinearity,non-equilibrium,and complexity.Herein,we review the connections between the velocity derivative skewness Sk and the non-equilibrium properties of turbulence.Sk,a reasonable candidate for describing the non-equilibrium turbulence,which varies during the non-equilibrium procedure.A lot of experimental or numerical evidences have shown that the perturbation of energy spectrum,which associated with the excitation of large scales,results in an obvious variation of Sk,and Sk is a negative value in this rapid energy decay process.The variation of positive Sk is closely related to the perturbation of transfer spectrum,and this corresponds to the backward energy transfer process.In addition,the skewness characterizes the production(or reduction)rate of enstrophy due to vortex stretching(or compression).Using the transport equation of turbulent energy dissipation rate and enstrophy,it is possible to establish a theoretical connection between skewness and the non-equilibrium turbulence.It is expected that this work could trigger the rapid advancement of the future studies of non-equilibrium turbulence,and also the improvement of turbulence models.
基金Supported by the National Basic Research Program of China (973 Program)(No 2007CB816005)the National Natural Science Foundation of China (No 40706003)+1 种基金International S&T Cooperation Project of the Ministry of Science and Technology of China (No2009DFA21430)the COPES in China (GYHY200706005)
文摘The skewness of subsurface temperature anomaly in the equatorial Pacific Ocean shows a significant asymmetry between the east and west.A positive temperature skewness appears in the equatorial eastern Pacific,while the temperature skewness in the western and central Pacific is primarily negative.There is also an asymmetry of the temperature skewness above and below the climatological mean thermocline in the central and western Pacific.A positive skewness appears below the thermocline,but the skewness is negative above the thermocline.The distinctive vertical asymmetry of the temperature skewness is argued to be attributed to the asymmetric temperature response to upward and downward thermocline displacement in the presence of the observed upper-ocean vertical thermal structure.Because of positive(negative) second derivative of temperature with respect to depth below(above) the thermocline,an upward and a downward shift of the thermocline with equal displacement would lead to a negative temperature skewness above the thermocline but a positive skewness below the thermocline.In the far eastern equatorial Pacific,the thermocline is close to the base of the mixed layer,the shape of the upper-ocean vertical temperature profile cannot be kept.Positive skewness appears in both below the thermocline and above the thermocline in the far eastern basin.Over the central and eastern Pacific,the anomalies of the subsurface waters tend to entrain into the surface mixed layer(by climatological mean upwelling) and then affect the SST.Hence,the positive(negative) subsurface skewness in the far eastern(central) Pacific may favor positive(negative) SST skewness,which is consistent with the observational fact that more La Nia(El Nio) occur in the central(eastern) Pacific.The present result implies a possible new paradigm for El Nio and La Nia amplitude asymmetry in the eastern Pacific.
文摘In the digital world,a wide range of handwritten and printed documents should be converted to digital format using a variety of tools,including mobile phones and scanners.Unfortunately,this is not an optimal procedure,and the entire document image might be degraded.Imperfect conversion effects due to noise,motion blur,and skew distortion can lead to significant impact on the accuracy and effectiveness of document image segmentation and analysis in Optical Character Recognition(OCR)systems.In Document Image Analysis Systems(DIAS),skew estimation of images is a crucial step.In this paper,a novel,fast,and reliable skew detection algorithm based on the Radon Transform and Curve Length Fitness Function(CLF),so-called Radon CLF,was proposed.The Radon CLF model aims to take advantage of the properties of Radon spaces.The Radon CLF explores the dominating angle more effectively for a 1D signal than it does for a 2D input image due to an innovative fitness function formulation for a projected signal of the Radon space.Several significant performance indicators,including Mean Square Error(MSE),Mean Absolute Error(MAE),Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Measure(SSIM),Accuracy,and run-time,were taken into consideration when assessing the performance of our model.In addition,a new dataset named DSI5000 was constructed to assess the accuracy of the CLF model.Both two-dimensional image signal and the Radon space have been used in our simulations to compare the noise effect.Obtained results show that the proposed method is more effective than other approaches already in use,with an accuracy of roughly 99.87%and a run-time of 0.048(s).The introduced model is far more accurate and timeefficient than current approaches in detecting image skew.
文摘Large torque can be output by the single gimbal control momentum gyroscope (SGCMG) based on the principle of the gyroscopic precession. However, the singularity is a major obstacle to successfully implement the task of the attitude control. The singularity can be avoided by the additional variable flywheel speed of variable speed control moment gyroscopes (VSCMG). Unfortunately, some kind of singularity cannot be effectively avoided. Consequently, the output toque can be only supported by the reaction torque of the flywheel when the singularity is encountered, and the consume power that is determined by the flywheel speed and reaction torque can be greatly increased when the flywheel spin rate over one thousand revolutions per minute. In this paper, the pyramid configuration with variable skew angle of the VSCMG is considered. A new steering law for the VSCMG with variable skew angle is proposed. The singularity that cannot be avoided by the varying flywheel speed can be effectively avoided with assisting of varying the skew angle. Consequently, the requirement of flywheel torque can be reduced. At last, the optimizing VSCMG with variable skew angle can be cast as a multi-objective function with multi-constraints. The particle swarm optimization method is used to solve the optimizing problem. In summary, the VSCMG with variable skew angle can be redesigned with considering of the singularity avoidance and minimizing system power.
