In this paper,we consider a block-structured convex optimization model,where in the objective the block variables are nonseparable and they are further linearly coupled in the constraint.For the 2-block case,we propos...In this paper,we consider a block-structured convex optimization model,where in the objective the block variables are nonseparable and they are further linearly coupled in the constraint.For the 2-block case,we propose a number of first-order algorithms to solve this model.First,the alternating direction method of multipliers(ADMM)is extended,assuming that it is easy to optimize the augmented Lagrangian function with one block of variables at each time while fixing the other block.We prove that O(1/t)iteration complexity bound holds under suitable conditions,where t is the number of iterations.If the subroutines of the ADMM cannot be implemented,then we propose new alternative algorithms to be called alternating proximal gradient method of multipliers,alternating gradient projection method of multipliers,and the hybrids thereof.Under suitable conditions,the O(1/t)iteration complexity bound is shown to hold for all the newly proposed algorithms.Finally,we extend the analysis for the ADMM to the general multi-block case.展开更多
This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are...This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.展开更多
The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear...The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.展开更多
The best-fit equations of linear and non-linear forms of the two widely used kinetic models,namely pseudo-first-order and pseudo-second-order equations,were compared in this study.The experimental kinetics of methylen...The best-fit equations of linear and non-linear forms of the two widely used kinetic models,namely pseudo-first-order and pseudo-second-order equations,were compared in this study.The experimental kinetics of methylene blue adsorption on activated carbon was used for this research.Both the correlation coefficient(R2)and the normalized standard deviationΔq(%)were employed as error analysis methods to determine the best-fitting equations.The results show that the non-linear forms of pseudo-first-order and pseudo-second-order models were more suitable than the linear forms for fitting the experimental data.The experimental kinetics may have been distorted by linearization of the linear kinetic equations,and thus,the non-linear forms of kinetic equations should be primarily used to obtain the adsorption parameters.In addition,theΔq(%)method for error analysis may be better to determine the best-fitting model in this case.展开更多
The production-oriented approach （POA） has been developed over a decade. It is driven by the need to improve English classroom instruction for university students in China （Wen, 2016）. It is also motivated by the ...The production-oriented approach （POA） has been developed over a decade. It is driven by the need to improve English classroom instruction for university students in China （Wen, 2016）. It is also motivated by the aspiration to enhance the quality of foreign language education in other similar pedagogical contexts outside China. A volume of research has been done by Wen Qiufang and her research team, to formulate the theory of POA and to test its effectiveness in classroom pedagogy （e.g. Wen, 2016, 2015; Yang, 2015; Zhang, 2015）. At the moment, the POA is still at an early stage of theory building and almost all empirical research is done in the Chinese context. In order to improve the quality of this theory and to make it intelligible to the international academic community, a one-day symposium was held in Beijing Foreign Studies University on May 15, 2017. The symposium was entitled ＇The first international forum on innovative foreign language education in China： Appraisal of the POA＇. In the forum, leading experts in applied linguistics were invited to discuss the strengths and weaknesses of the POA and the directions for its future development. The symposium was the first attempt for the POA research team to discuss its latest work with international scholars. This Viewpoint section collects the responses of four experts who participated in the symposium, listed in alphabetical order. The collection of articles covers three topics related to the POA： its pedagogical application, its use for teacher training, and its research. Alister Cumming is Professor Emeritus and the former Head of the Centre for Educational Research on Languages and Literacies, University of Toronto, Canada. His article focuses primarily on POA research as an exemplary case of design-based research. Rod Ellis is Research Professor in the School of Education at Curtin University, Australia. He discusses POA in terms of pedagogy, teacher training and research, with both critiques and constructive suggestions. Paul Kei M展开更多
Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact.In some practical problems,we can only obtain approximate values of the objective function and i...Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact.In some practical problems,we can only obtain approximate values of the objective function and its gradient.It is necessary to design optimization algorithms that can utilize inexact first-order information.In this paper,we propose an adaptive regularized quasi-Newton method to solve such problems.Under some mild conditions,we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method.Detailed implementations of our method,including the subspace technique to reduce the amount of computation,are presented.Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method,which can utilize the inexact first-order information effectively.展开更多
Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna...Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.展开更多
Theoretical investigation of the phase equilibria of the Fe-Ni alloy has been performed by combining the FLAPW total energy calculations and the Cluster Variation Method through the Cluster Expansion Method. The calcu...Theoretical investigation of the phase equilibria of the Fe-Ni alloy has been performed by combining the FLAPW total energy calculations and the Cluster Variation Method through the Cluster Expansion Method. The calculations have proved the stabilization of the LIE phase at 1：3 stoichiometry, which is in agreement with the experimental result, and predicted the existence of L1 0 as a stable phase below 550 K; this L1 0 phase has been missing in the conventional phase diagram. The calculations are extended to the Fe-rich region that is characterized by a wide range phase separation and has drawn considerable attention because of the intriguing Invar property associated with a Fe concentration of 65%. To reveal the origin of the phase separation, a P-V curve in an entire concentration range is derived by the second derivative of free energy functional of the disordered phase with respect to the volume. The calculation confirmed that the phase separation is caused by the breakdown of the mechanical-stability criterion. The newly calculated phase separation line combined with the L1 0 and L12Eorder-disordered phase boundaries provides phase equilibria in the wider concentration range of the system. Furthermore, a coefficient of thermal expansion （CTE） is attempted by incorporating the thermal vibration effect through harmonic approximation of the Debye-Gruneisen model. The Invar behavior has been reproduced, and the origin of this anomalous volume change has been discussed.展开更多
文摘In this paper,we consider a block-structured convex optimization model,where in the objective the block variables are nonseparable and they are further linearly coupled in the constraint.For the 2-block case,we propose a number of first-order algorithms to solve this model.First,the alternating direction method of multipliers(ADMM)is extended,assuming that it is easy to optimize the augmented Lagrangian function with one block of variables at each time while fixing the other block.We prove that O(1/t)iteration complexity bound holds under suitable conditions,where t is the number of iterations.If the subroutines of the ADMM cannot be implemented,then we propose new alternative algorithms to be called alternating proximal gradient method of multipliers,alternating gradient projection method of multipliers,and the hybrids thereof.Under suitable conditions,the O(1/t)iteration complexity bound is shown to hold for all the newly proposed algorithms.Finally,we extend the analysis for the ADMM to the general multi-block case.
基金supported by the National Natural Science Foundation of China(Grant Nos.52109144,52025094 and 52222905).
文摘This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.
基金supported by the National Natural Science Foundation of China (No.10662003)Educational Commission of Guangxi Province of China (No.200807MS109)
文摘The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.
基金the Research Scheme of Education Department of Zhejiang Province,China(No.Y200806037).
文摘The best-fit equations of linear and non-linear forms of the two widely used kinetic models,namely pseudo-first-order and pseudo-second-order equations,were compared in this study.The experimental kinetics of methylene blue adsorption on activated carbon was used for this research.Both the correlation coefficient(R2)and the normalized standard deviationΔq(%)were employed as error analysis methods to determine the best-fitting equations.The results show that the non-linear forms of pseudo-first-order and pseudo-second-order models were more suitable than the linear forms for fitting the experimental data.The experimental kinetics may have been distorted by linearization of the linear kinetic equations,and thus,the non-linear forms of kinetic equations should be primarily used to obtain the adsorption parameters.In addition,theΔq(%)method for error analysis may be better to determine the best-fitting model in this case.
文摘The production-oriented approach （POA） has been developed over a decade. It is driven by the need to improve English classroom instruction for university students in China （Wen, 2016）. It is also motivated by the aspiration to enhance the quality of foreign language education in other similar pedagogical contexts outside China. A volume of research has been done by Wen Qiufang and her research team, to formulate the theory of POA and to test its effectiveness in classroom pedagogy （e.g. Wen, 2016, 2015; Yang, 2015; Zhang, 2015）. At the moment, the POA is still at an early stage of theory building and almost all empirical research is done in the Chinese context. In order to improve the quality of this theory and to make it intelligible to the international academic community, a one-day symposium was held in Beijing Foreign Studies University on May 15, 2017. The symposium was entitled ＇The first international forum on innovative foreign language education in China： Appraisal of the POA＇. In the forum, leading experts in applied linguistics were invited to discuss the strengths and weaknesses of the POA and the directions for its future development. The symposium was the first attempt for the POA research team to discuss its latest work with international scholars. This Viewpoint section collects the responses of four experts who participated in the symposium, listed in alphabetical order. The collection of articles covers three topics related to the POA： its pedagogical application, its use for teacher training, and its research. Alister Cumming is Professor Emeritus and the former Head of the Centre for Educational Research on Languages and Literacies, University of Toronto, Canada. His article focuses primarily on POA research as an exemplary case of design-based research. Rod Ellis is Research Professor in the School of Education at Curtin University, Australia. He discusses POA in terms of pedagogy, teacher training and research, with both critiques and constructive suggestions. Paul Kei M
基金supported by the National Natural Science Foundation of China(Grant No.NSFC-11971118).
文摘Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact.In some practical problems,we can only obtain approximate values of the objective function and its gradient.It is necessary to design optimization algorithms that can utilize inexact first-order information.In this paper,we propose an adaptive regularized quasi-Newton method to solve such problems.Under some mild conditions,we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method.Detailed implementations of our method,including the subspace technique to reduce the amount of computation,are presented.Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method,which can utilize the inexact first-order information effectively.
文摘Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.
文摘Theoretical investigation of the phase equilibria of the Fe-Ni alloy has been performed by combining the FLAPW total energy calculations and the Cluster Variation Method through the Cluster Expansion Method. The calculations have proved the stabilization of the LIE phase at 1：3 stoichiometry, which is in agreement with the experimental result, and predicted the existence of L1 0 as a stable phase below 550 K; this L1 0 phase has been missing in the conventional phase diagram. The calculations are extended to the Fe-rich region that is characterized by a wide range phase separation and has drawn considerable attention because of the intriguing Invar property associated with a Fe concentration of 65%. To reveal the origin of the phase separation, a P-V curve in an entire concentration range is derived by the second derivative of free energy functional of the disordered phase with respect to the volume. The calculation confirmed that the phase separation is caused by the breakdown of the mechanical-stability criterion. The newly calculated phase separation line combined with the L1 0 and L12Eorder-disordered phase boundaries provides phase equilibria in the wider concentration range of the system. Furthermore, a coefficient of thermal expansion （CTE） is attempted by incorporating the thermal vibration effect through harmonic approximation of the Debye-Gruneisen model. The Invar behavior has been reproduced, and the origin of this anomalous volume change has been discussed.
