The efficacy of error correction and various kinds of correction approaches is one of the key issues in second language writing faced by both teachers and researchers. The current paper reviews the definition of error...The efficacy of error correction and various kinds of correction approaches is one of the key issues in second language writing faced by both teachers and researchers. The current paper reviews the definition of error correction and examines the different views on whether error correction in L2 writing should be corrected. In particular, the paper discusses and analyses the three common correction methods: direct correction, peer feedback and indirect correction. Teachers are encouraged to weigh and analyze the advantages and disadvantages of these methods according to the current literature, employ the most beneficial error correction method in L2 writing, and adapt its suitability to their teaching context.展开更多
In this paper, an analogue correction method of errors （ACE） based on a complicated atmospheric model is further developed and applied to numerical weather prediction （NWP）. The analysis shows that the ACE can eff...In this paper, an analogue correction method of errors （ACE） based on a complicated atmospheric model is further developed and applied to numerical weather prediction （NWP）. The analysis shows that the ACE can effectively reduce model errors by combining the statistical analogue method with the dynamical model together in order that the information of plenty of historical data is utilized in the current complicated NWP model, Furthermore, in the ACE, the differences of the similarities between different historical analogues and the current initial state are considered as the weights for estimating model errors. The results of daily, decad and monthly prediction experiments on a complicated T63 atmospheric model show that the performance of the ACE by correcting model errors based on the estimation of the errors of 4 historical analogue predictions is not only better than that of the scheme of only introducing the correction of the errors of every single analogue prediction, but is also better than that of the T63 model.展开更多
In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration ...In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration with high fluctuation usually occurs. If these kinds of tool paths are directly used for machining, the feedrate and quality will be greatly reduced. Thus, generating continuous tool paths is strongly desired. This paper presents a new error-controllable method for generating continuous tool path. Different from the traditional method focusing on fitting the cutter locations, the proposed method realizes globally smoothing the tool path in an error-controllable way. Concretely, it does the smoothing by approaching the newly produced curve to the linear tool path by taking the tolerance requirement as a constraint. That is, the error between the desired tool path and the G01 commands are taken as a boundary condition to ensure the finally smoothed curve being within the given tolerance. Besides, to improve the smoothing ability in case of small corner angle, an improved local smoothing method is also proposed by symmetrically assigning the control points to the two adjacent linear segments with the constrains of tolerance and G3 continuity. Experiments on an open five-axis machine are developed to verify the advantages of the proposed methods.展开更多
Although there are some multi-sensor methods for measuring the straightness and tilt errors of a linear slideway, they need to be further improved in some aspects, such as suppressing measurement noise and reducing pr...Although there are some multi-sensor methods for measuring the straightness and tilt errors of a linear slideway, they need to be further improved in some aspects, such as suppressing measurement noise and reducing precondition.In this paper, a new four-sensor method with an improved measurement system is proposed to on-machine separate the straightness and tilt errors of a linear slideway from the sensor outputs, considering the influences of the reference surface profile and the zero-adjustment values. The improved system is achieved by adjusting a single sensor to di erent positions. Based on the system, a system of linear equations is built by fusing the sensor outputs to cancel out the e ects of the straightness and tilt errors. Three constraints are then derived and supplemented into the linear system to make the coe cient matrix full rank. To restrain the sensitivity of the solution of the linear system to the measurement noise in the sensor outputs, the Tikhonov regularization method is utilized. After the surface profile is obtained from the solution, the straightness and tilt errors are identified from the sensor outputs. To analyze the e ects of the measurement noise and the positioning errors of the sensor and the linear slideway, a series of computer simulations are carried out. An experiment is conducted for validation, showing good consistency. The new four-sensor method with the improved measurement system provides a new way to measure the straightness and tilt errors of a linear slideway, which can guarantee favorable propagations of the residuals induced by the noise and the positioning errors.展开更多
Human reliability analysis(HRA) is an expansion of man-machine engineering. It is also a new multidisciplinary based on behavioral science, cognitive science, information processing, system analysis and probability st...Human reliability analysis(HRA) is an expansion of man-machine engineering. It is also a new multidisciplinary based on behavioral science, cognitive science, information processing, system analysis and probability statistics in order to analyze, predict, reduce and prevent human errors. Firstly, the quantitative analysis model of HRA is proposed based on Markov process theory by using human error probability(HEP) and error correction cycle(ECC) as parameters. And human reliability evaluation criterion is built. Then, the HRA process considering error correction is proposed based on cognitive reliability and error analysis method(CREAM). Finally, according to the characteristics of armored vehicle system, common performance condition(CPC) in CREAM is improved.A reliability impact index is characterized by the overall contexts of tasks. Human reliability evaluation criterion of armored vehicle system is formulated. And the result of HRA is obtained based on the method presented in this paper. In addition, the relative weights are estimated by combining scale of 10/10—18/2 and analytical hierarchy process(AHP), and the triangular fuzzy number considering confidence factor and optimism index is adopted in order to reduce the subjectivity. The analysis results show that the method presented in this paper is reasonable and feasible. Meantime, the method can provide guidance for human reliability analysis of other weapon systems.展开更多
The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for e...The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.展开更多
Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the resul...Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on ＂The Guide to the Expression of Uncertainty in Measurement（GUM）＂. In order to compute spatial straightness error（SSE） accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization（QPSO） is proposed to solve the minimum zone SSE and Monte Carlo Method（MCM） is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function（PDF） for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine（CMM） is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.展开更多
Human error(HE) is the most important factor influencing on structural safety because its effect often exceeds the random deviation.Large numbers of facts have shown that structural failures may be caused by the gross...Human error(HE) is the most important factor influencing on structural safety because its effect often exceeds the random deviation.Large numbers of facts have shown that structural failures may be caused by the gross error due to HE.So it is essential to analyze HE in construction.The crucial work of human error analysis(HEA) is the estimation of human error probability(HEP) in construction.The method for estimating HEP,analytic hierarchy process and failure likelihood index method(AHP-FLIM),is introduced in this paper.The method also uses the process of expert judgment within the failure likelihood index method(FLIM).A numerical example shows the effectiveness of the methods proposed.展开更多
Error estimates of Galerkin method for Kuramoto-Sivashingsky (K-S) equation in space dimension ≥3 are derived in the paper. These results furnish strong evidence for the computation of the solutions.
In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is establ...In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is established .for Halley’s iteration in Banach spaces.展开更多
To overcome the shortcoming that the traditional minimum error threshold method can obtain satisfactory image segmentation results only when the object and background of the image strictly obey a certain type of proba...To overcome the shortcoming that the traditional minimum error threshold method can obtain satisfactory image segmentation results only when the object and background of the image strictly obey a certain type of probability distribution,one proposes the regularized minimum error threshold method and treats the traditional minimum error threshold method as its special case.Then one constructs the discrete probability distribution by using the separation between segmentation threshold and the average gray-scale values of the object and background of the image so as to compute the information energy of the probability distribution.The impact of the regularized parameter selection on the optimal segmentation threshold of the regularized minimum error threshold method is investigated.To verify the effectiveness of the proposed regularized minimum error threshold method,one selects typical grey-scale images and performs segmentation tests.The segmentation results obtained by the regularized minimum error threshold method are compared with those obtained with the traditional minimum error threshold method.The segmentation results and their analysis show that the regularized minimum error threshold method is feasible and produces more satisfactory segmentation results than the minimum error threshold method.It does not exert much impact on object acquisition in case of the addition of a certain noise to an image.Therefore,the method can meet the requirements for extracting a real object in the noisy environment.展开更多
We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utiliz...We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.展开更多
To enhance the integrity, an analytic method （AM） which has less execution time is proposed to calculate the user differential range error （UDRE） used by the user to detect the potential risk. An ephemeris and clo...To enhance the integrity, an analytic method （AM） which has less execution time is proposed to calculate the user differential range error （UDRE） used by the user to detect the potential risk. An ephemeris and clock correction calculation method is introduced first. It shows that the most important thing of computing UDRE is to find the worst user location （WUL） in the service volume. Then, a UDRE algorithm using AM is described to solve this problem. By using the covariance matrix of the error vector, the searching of WUL is converted to an analytic geometry problem. The location of WUL can be obtained directly by mathematical derivation. Experiments are conducted to compare the performance between the proposed AM algorithm and the exhaustive grid search （EGS） method used in the master station. The results show that the correctness of the AM algorithm can be proved by the EGS method and the AM algorithm can reduce the calculation time by more than 90%. The computational complexity of this proposed algorithm is better than that of EGS. Thereby this algorithm is more suitable for computing UDRE at the master station.展开更多
In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimati...In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.展开更多
<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the...<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>展开更多
A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution...A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution are first discussed, and then a posteriori error estimator based on the NGME method is derived.展开更多
This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the p...This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context.展开更多
Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system....Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.展开更多
An error processing method is presented based on optimization theory and microcomputer technique which can be successfully used in the cycloidal gear measurement on three dimensional coordinates measuring machine (CMM...An error processing method is presented based on optimization theory and microcomputer technique which can be successfully used in the cycloidal gear measurement on three dimensional coordinates measuring machine (CMM). In the procedure, the minimum quadratic sum of the normal deviation is used as the object function and the equidistant curve is dealed with instead of the teeth profile. CMM is a high accurate measuring machine which can provide a way to evaluate the accuracy of the cycloidal gear completely.展开更多
The efficiency of an optimization method for acoustic emission/microseismic（AE/MS） source location is determined by the compatibility of its error definition with the errors contained in the input data.This compatib...The efficiency of an optimization method for acoustic emission/microseismic（AE/MS） source location is determined by the compatibility of its error definition with the errors contained in the input data.This compatibility can be examined in terms of the distribution of station residuals.For an ideal distribution,the input error is held at the station where it takes place as the station residual and the error is not permitted to spread to other stations.A comparison study of two optimization methods,namely the least squares method and the absolute value method,shows that the distribution with this character constrains the input errors and minimizes their impact,which explains the much more robust performance by the absolute value method in dealing with large and isolated input errors.When the errors in the input data are systematic and/or extreme in that the basic data structure is altered by these errors,none of the optimization methods are able to function.The only means to resolve this problem is the early detection and correction of these errors through a data screening process.An efficient data screening process is of primary importance for AE/MS source location.In addition to its critical role in dealing with those systematic and extreme errors,data screening creates a favorable environment for applying optimization methods.展开更多
文摘The efficacy of error correction and various kinds of correction approaches is one of the key issues in second language writing faced by both teachers and researchers. The current paper reviews the definition of error correction and examines the different views on whether error correction in L2 writing should be corrected. In particular, the paper discusses and analyses the three common correction methods: direct correction, peer feedback and indirect correction. Teachers are encouraged to weigh and analyze the advantages and disadvantages of these methods according to the current literature, employ the most beneficial error correction method in L2 writing, and adapt its suitability to their teaching context.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 40575036 and 40325015）.Acknowledgement The authors thank Drs Zhang Pei-Qun and Bao Ming very much for their valuable comments on the present paper.
文摘In this paper, an analogue correction method of errors （ACE） based on a complicated atmospheric model is further developed and applied to numerical weather prediction （NWP）. The analysis shows that the ACE can effectively reduce model errors by combining the statistical analogue method with the dynamical model together in order that the information of plenty of historical data is utilized in the current complicated NWP model, Furthermore, in the ACE, the differences of the similarities between different historical analogues and the current initial state are considered as the weights for estimating model errors. The results of daily, decad and monthly prediction experiments on a complicated T63 atmospheric model show that the performance of the ACE by correcting model errors based on the estimation of the errors of 4 historical analogue predictions is not only better than that of the scheme of only introducing the correction of the errors of every single analogue prediction, but is also better than that of the T63 model.
基金supported by the National Natural Science Foundation of China under Grant Nos.51675440 and 11620101002National Key Research and Development Program of China under Grant No.2017YFB1102800the Fundamental Research Funds for the Central Universities under Grant No.3102018gxc025
文摘In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration with high fluctuation usually occurs. If these kinds of tool paths are directly used for machining, the feedrate and quality will be greatly reduced. Thus, generating continuous tool paths is strongly desired. This paper presents a new error-controllable method for generating continuous tool path. Different from the traditional method focusing on fitting the cutter locations, the proposed method realizes globally smoothing the tool path in an error-controllable way. Concretely, it does the smoothing by approaching the newly produced curve to the linear tool path by taking the tolerance requirement as a constraint. That is, the error between the desired tool path and the G01 commands are taken as a boundary condition to ensure the finally smoothed curve being within the given tolerance. Besides, to improve the smoothing ability in case of small corner angle, an improved local smoothing method is also proposed by symmetrically assigning the control points to the two adjacent linear segments with the constrains of tolerance and G3 continuity. Experiments on an open five-axis machine are developed to verify the advantages of the proposed methods.
基金Supported by National Natural Science Foundation of China(Grant No.51435006)
文摘Although there are some multi-sensor methods for measuring the straightness and tilt errors of a linear slideway, they need to be further improved in some aspects, such as suppressing measurement noise and reducing precondition.In this paper, a new four-sensor method with an improved measurement system is proposed to on-machine separate the straightness and tilt errors of a linear slideway from the sensor outputs, considering the influences of the reference surface profile and the zero-adjustment values. The improved system is achieved by adjusting a single sensor to di erent positions. Based on the system, a system of linear equations is built by fusing the sensor outputs to cancel out the e ects of the straightness and tilt errors. Three constraints are then derived and supplemented into the linear system to make the coe cient matrix full rank. To restrain the sensitivity of the solution of the linear system to the measurement noise in the sensor outputs, the Tikhonov regularization method is utilized. After the surface profile is obtained from the solution, the straightness and tilt errors are identified from the sensor outputs. To analyze the e ects of the measurement noise and the positioning errors of the sensor and the linear slideway, a series of computer simulations are carried out. An experiment is conducted for validation, showing good consistency. The new four-sensor method with the improved measurement system provides a new way to measure the straightness and tilt errors of a linear slideway, which can guarantee favorable propagations of the residuals induced by the noise and the positioning errors.
基金the Technical Basis Projects of China’s Ministry of Industry and Information Technology(No.ZQ092012B003)
文摘Human reliability analysis(HRA) is an expansion of man-machine engineering. It is also a new multidisciplinary based on behavioral science, cognitive science, information processing, system analysis and probability statistics in order to analyze, predict, reduce and prevent human errors. Firstly, the quantitative analysis model of HRA is proposed based on Markov process theory by using human error probability(HEP) and error correction cycle(ECC) as parameters. And human reliability evaluation criterion is built. Then, the HRA process considering error correction is proposed based on cognitive reliability and error analysis method(CREAM). Finally, according to the characteristics of armored vehicle system, common performance condition(CPC) in CREAM is improved.A reliability impact index is characterized by the overall contexts of tasks. Human reliability evaluation criterion of armored vehicle system is formulated. And the result of HRA is obtained based on the method presented in this paper. In addition, the relative weights are estimated by combining scale of 10/10—18/2 and analytical hierarchy process(AHP), and the triangular fuzzy number considering confidence factor and optimism index is adopted in order to reduce the subjectivity. The analysis results show that the method presented in this paper is reasonable and feasible. Meantime, the method can provide guidance for human reliability analysis of other weapon systems.
基金supported by National Natural Science Foundation of China(Grant Nos. 50775190No.51275425)+2 种基金Spring Sunshine Plan of Ministry of Education of China(Grant No. 10202258)Talent Introduction of Xihua UniversityChina(Grant No. Z1220217)
文摘The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.
基金supported by National Natural Science Foundation of China (Grant No. 51075198)Jiangsu Provincial Natural Science Foundation of China (Grant No. BK2010479)+2 种基金Innovation Research of Nanjing Institute of Technology, China (Grant No. CKJ20100008)Jiangsu Provincial Foundation of 333 Talents Engineering of ChinaJiangsu Provincial Foundation of Six Talented Peak of China
文摘Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on ＂The Guide to the Expression of Uncertainty in Measurement（GUM）＂. In order to compute spatial straightness error（SSE） accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization（QPSO） is proposed to solve the minimum zone SSE and Monte Carlo Method（MCM） is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function（PDF） for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine（CMM） is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.
文摘Human error(HE) is the most important factor influencing on structural safety because its effect often exceeds the random deviation.Large numbers of facts have shown that structural failures may be caused by the gross error due to HE.So it is essential to analyze HE in construction.The crucial work of human error analysis(HEA) is the estimation of human error probability(HEP) in construction.The method for estimating HEP,analytic hierarchy process and failure likelihood index method(AHP-FLIM),is introduced in this paper.The method also uses the process of expert judgment within the failure likelihood index method(FLIM).A numerical example shows the effectiveness of the methods proposed.
文摘Error estimates of Galerkin method for Kuramoto-Sivashingsky (K-S) equation in space dimension ≥3 are derived in the paper. These results furnish strong evidence for the computation of the solutions.
基金Jointly supported by China Major Key Project for Basic Researcher and Provincial Natrual Science Foundation.
文摘In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is established .for Halley’s iteration in Banach spaces.
基金supported by the National Natural Science Foundations of China(Nos.61136002,61472324)the Natural Science Foundation of Shanxi Province(No.2014JM8331)
文摘To overcome the shortcoming that the traditional minimum error threshold method can obtain satisfactory image segmentation results only when the object and background of the image strictly obey a certain type of probability distribution,one proposes the regularized minimum error threshold method and treats the traditional minimum error threshold method as its special case.Then one constructs the discrete probability distribution by using the separation between segmentation threshold and the average gray-scale values of the object and background of the image so as to compute the information energy of the probability distribution.The impact of the regularized parameter selection on the optimal segmentation threshold of the regularized minimum error threshold method is investigated.To verify the effectiveness of the proposed regularized minimum error threshold method,one selects typical grey-scale images and performs segmentation tests.The segmentation results obtained by the regularized minimum error threshold method are compared with those obtained with the traditional minimum error threshold method.The segmentation results and their analysis show that the regularized minimum error threshold method is feasible and produces more satisfactory segmentation results than the minimum error threshold method.It does not exert much impact on object acquisition in case of the addition of a certain noise to an image.Therefore,the method can meet the requirements for extracting a real object in the noisy environment.
基金The NNSF (10371137 and 10201034) of Chinathe Foundation (20030558008) of Doctoral Program of National Higher Education, Guangdong Provincial Natural Science Foundation (1011170) of China and the Advanced Research Foundation of Zhongshan UniversityThe US National Science Foundation (9973427 and 0312113)NSF (10371122) of China and the Chinese Academy of Sciences under the program of "Hundred Distinguished Young Chinese Scientists."
文摘We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.
文摘To enhance the integrity, an analytic method （AM） which has less execution time is proposed to calculate the user differential range error （UDRE） used by the user to detect the potential risk. An ephemeris and clock correction calculation method is introduced first. It shows that the most important thing of computing UDRE is to find the worst user location （WUL） in the service volume. Then, a UDRE algorithm using AM is described to solve this problem. By using the covariance matrix of the error vector, the searching of WUL is converted to an analytic geometry problem. The location of WUL can be obtained directly by mathematical derivation. Experiments are conducted to compare the performance between the proposed AM algorithm and the exhaustive grid search （EGS） method used in the master station. The results show that the correctness of the AM algorithm can be proved by the EGS method and the AM algorithm can reduce the calculation time by more than 90%. The computational complexity of this proposed algorithm is better than that of EGS. Thereby this algorithm is more suitable for computing UDRE at the master station.
文摘In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.
文摘<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>
文摘A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution are first discussed, and then a posteriori error estimator based on the NGME method is derived.
文摘This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context.
基金The NNSF.MTYF(10126029)of China and the YF of Shandong University.
文摘Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.
文摘An error processing method is presented based on optimization theory and microcomputer technique which can be successfully used in the cycloidal gear measurement on three dimensional coordinates measuring machine (CMM). In the procedure, the minimum quadratic sum of the normal deviation is used as the object function and the equidistant curve is dealed with instead of the teeth profile. CMM is a high accurate measuring machine which can provide a way to evaluate the accuracy of the cycloidal gear completely.
文摘The efficiency of an optimization method for acoustic emission/microseismic（AE/MS） source location is determined by the compatibility of its error definition with the errors contained in the input data.This compatibility can be examined in terms of the distribution of station residuals.For an ideal distribution,the input error is held at the station where it takes place as the station residual and the error is not permitted to spread to other stations.A comparison study of two optimization methods,namely the least squares method and the absolute value method,shows that the distribution with this character constrains the input errors and minimizes their impact,which explains the much more robust performance by the absolute value method in dealing with large and isolated input errors.When the errors in the input data are systematic and/or extreme in that the basic data structure is altered by these errors,none of the optimization methods are able to function.The only means to resolve this problem is the early detection and correction of these errors through a data screening process.An efficient data screening process is of primary importance for AE/MS source location.In addition to its critical role in dealing with those systematic and extreme errors,data screening creates a favorable environment for applying optimization methods.
