In this paper, the minimal residual （MRES） method for solving nonsymmetric equation systems was improved, the recurrence relation was deduced between the approximate solutions of the linear equation system Ax = b, a...In this paper, the minimal residual （MRES） method for solving nonsymmetric equation systems was improved, the recurrence relation was deduced between the approximate solutions of the linear equation system Ax = b, and a more effective method was presented, which can reduce the operational count and the storage.展开更多
Triply periodic minimal surface(TPMS)-based bone implants are an innovative approach in orthopedic implantology,offering customized solutions for bone defect repair and regeneration.This review comprehensively examine...Triply periodic minimal surface(TPMS)-based bone implants are an innovative approach in orthopedic implantology,offering customized solutions for bone defect repair and regeneration.This review comprehensively examines the current research landscape of TPMS-based bone implants,addressing key challenges and proposing future directions.It explores design strategies aimed at optimizing mechanical strength and enhancing biological integration,with a particular emphasis on TPMS structures.These design strategies include graded,hierarchical,and hybrid designs,each contributing to the overall functionality and performance of the implants.This review also highlights state-of-the-art fabrication technologies,particularly advancements in additive manufacturing(AM)techniques for creating metal-based,polymer-based,and ceramic-based bone implants.The ability to precisely control the architecture of TPMS structures using AM techniques is crucial for tailoring the mechanical and biological properties of such implants.Furthermore,this review critically evaluates the biological performance of TPMS implants,focusing on their potential to promote bone ingrowth and regeneration.Key factors,such as mechanical properties,permeability,and biocompatibility,are examined to determine the effectiveness of these implants in clinical applications.By synthesizing existing knowledge and proposing innovative research directions,this review underscores the transformative potential of TPMS-based bone implants in orthopedic surgery.The objective is to improve clinical outcomes and enhance patient care through advanced implant designs and manufacturing techniques.展开更多
Management of the complex anal fistula represents a perennial challenge to surgeons.Conventional approaches often upset the balance between recurrence prevention and continence preservation with their high failure rat...Management of the complex anal fistula represents a perennial challenge to surgeons.Conventional approaches often upset the balance between recurrence prevention and continence preservation with their high failure rates and significant associated morbidity.The emergence of minimally invasive treatment in recent years,however,offers a promising paradigm shift.Regenerative solutions like autologous stem cell therapy or fistula plugs with extracellular and synthetic matrices represent new frontiers in anal fistula treatment,harnessing physiological regenerative capacities and avoiding the traditional postoperative burden of open wounds,drains,or setons in situ.Together with novel techniques like fistula laser closure,video-assisted fistula treatment,or over-the-scope clip burgeoning over the last decade,these state-of-the-art approaches have been touted for their total sphincter-sparing nature,preserving functional outcomes and quality of life.Despite gaining much scientific and clinical momentum,do these newer modalities live up to their promise?This review aims to critically appraise the latest evidence surrounding minimally invasive approaches,providing up-todate insights into the constantly evolving landscape of anal fistula management.Further long-term and comparative studies will nevertheless be needed to supplement the significantly heterogenous,retrospective analyses consolidated.展开更多
Thermodynamic analysis was applied to study combined partial oxidation and carbon dioxide reforming of methane in view of carbon formation. The equilibrium calculations employing the Gibbs energy minimization were per...Thermodynamic analysis was applied to study combined partial oxidation and carbon dioxide reforming of methane in view of carbon formation. The equilibrium calculations employing the Gibbs energy minimization were performed upon wide ranges of pressure （1-25 atm）, temperature （600-1300 K）, carbon dioxide to methane ratio （0-2） and oxygen to methane ratio （0-1）. The thermodynamic results were compared with the results obtained over a Ru supported catalyst. The results revealed that by increasing the reaction pressure methane conversion decreased. Also it was found that the atmospheric pressure is the preferable pressure for both dry reforming and partial oxidation of methane and increasing the temperature caused increases in both activity of carbon and conversion of methane. The results clearly showed that the addition of O2 to the feed mixture could lead to a reduction of carbon deposition.展开更多
In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimizati...In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimization problems,then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system.The existence and uniqueness of the solution for the linear system are also proved.Experimental results show the efficiency of the proposed approach,and its application in 1 G blending curve construction is also presented.展开更多
Segmentation of three-dimensional(3D) complicated structures is of great importance for many real applications.In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmenta...Segmentation of three-dimensional(3D) complicated structures is of great importance for many real applications.In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model.Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations.Instead,the minimum cut on a special designed graph need to be computed.The method is tested on data with complicated structures.It is rather stable with respect to initial value and the algorithm is nearly parameter free.Experiments show that it can solve large problems much faster than traditional approaches.展开更多
The downward continuation of potential fields is a process of calculating their values in a lower plane based on those of a certain plane.This technology is not only a data processing method for resource exploration b...The downward continuation of potential fields is a process of calculating their values in a lower plane based on those of a certain plane.This technology is not only a data processing method for resource exploration but also plays an extremely important role in military applications.However,the downward continuation of potential fields is a typical linear inverse problem that is ill-posed.Generalized minimal residuals(GMRES)is an eff ective solution to ill-posed inverse problems,but it is unstable under the condition wherein the GMRES is directly applied in the calculation process.Moreover,the long-term behavior of its iterative computation is a disordered,divergent result.Therefore,to obtain stable solutions,GMRES is applied to solve the normal equations of the downward continuation of potential fields;it is also used to prequalify for occasional interruptions in the operation process by adding the damping coefficient,thus strengthening the stability conditions of the equations of residual minimization.Finally,the stable downward continuation of the potential fields method is proposed.As indicated by the theoretical data and the measured testing data,the method proposed in this paper has the advantages of high-precision and excellent stability.Furthermore,compared with the Tikhonov iteration method,the proposed method avoids the need to choose regularization parameters.展开更多
A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general g...A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general global minimiizing algorithm is employed as a subroutine of the algorithm. The method is expected to tackle a large class of nonsmooth constrained minimization problem.展开更多
We analyze three commonly used energy functions in solving Plateau-Mesh Prob- lem, that is, Dirichlet, area, and the discrete mean curvature（DMC）. They all possess unique advantages compared to others, but their dra...We analyze three commonly used energy functions in solving Plateau-Mesh Prob- lem, that is, Dirichlet, area, and the discrete mean curvature（DMC）. They all possess unique advantages compared to others, but their drawbacks restrict their usages individually. Our algo- rithm combines the three steps together to make full use of their features. At first the Dirichlet energy is optimized for faster approximation with better topology. Then the area energy is used to come close to the constrained domain. Finally the DMC energy is engaged to achieve a better converging step. Results show that our method can work under a rather noisy initial mesh, which is even topologically different from the final result.展开更多
This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programmin...This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programming and convex theory,the generalized directional derivative of the general multicommodity minimal cost flow problems is derived.The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.展开更多
Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected ...Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.展开更多
The learning curve in minimally invasive colorectal surgery is a constant subject of discussion in the literature.Discordant data likely reflects the varying degrees of each surgeon’s experience in colorectal,laparos...The learning curve in minimally invasive colorectal surgery is a constant subject of discussion in the literature.Discordant data likely reflects the varying degrees of each surgeon’s experience in colorectal,laparoscopic or robotic surgery.Several factors are necessary for a successful minimally invasive colorectal surgery training program,including:Compliance with oncological outcomes;dissection along the embryological planes;constant presence of an expert tutor;periodic discussion of the morbidity and mortality rate;and creation of a dedicated,expert team.展开更多
We solve the Duffin-Kemmer-Petiau （DKP） equation with a non-minimal vector Yukawa potential in （1＋1）- dimensional spa^e-time for spin-1 particles. The Nikiforov Uvarov method is used in the calculations, and the ...We solve the Duffin-Kemmer-Petiau （DKP） equation with a non-minimal vector Yukawa potential in （1＋1）- dimensional spa^e-time for spin-1 particles. The Nikiforov Uvarov method is used in the calculations, and the eigen- functions as well as the energy eigenvalues are obtained in a proper Pekeris-type approximation.展开更多
In this paper,we improve object functions and constraint conditions of genetic algorithms (GAs) applied in PRCs identification of water networks.This identification method can increase calculation efficiency,but can n...In this paper,we improve object functions and constraint conditions of genetic algorithms (GAs) applied in PRCs identification of water networks.This identification method can increase calculation efficiency,but can not solve an identification problem with infinitely many solutions well.Then we propose PRCs identification based on the minimal norm method,which satisfies observability conditions and has advantages of high computing efficiency and short time consumption.The two identification methods are applied in a water network,and their identification results are compared under the same conditions.From the results,we know that PRCs identification based on the minimal norm method has advantages of higher computing efficiency,shorter time consumption and higher precision.展开更多
Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studi...Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.展开更多
A strategy for water and wastewater minimization is developed for continuous water utilization systems involving fixed flowrate(non-mass-transfer-based)operations,based on the fictitious operations that is introduced ...A strategy for water and wastewater minimization is developed for continuous water utilization systems involving fixed flowrate(non-mass-transfer-based)operations,based on the fictitious operations that is introduced to represent the water losing and/or generating operations and a modified concentration interval analysis(MCIA) technique.This strategy is a simple,nongraphical,and noniterative procedure and is suitable for the quick yields of targets and the identification of pinch point location.Moreover,on the basis of the target method,a heuristic-based approach is also presented to generate water utilization networks,which could be demonstrated to be optimum ones. The proposed approaches are illustrated with example problems.展开更多
Current minimization programs do not permit full control over different aspects of minimization algorithm such as distance or probability measures and may not allow for unequal allocation ratios. This article describe...Current minimization programs do not permit full control over different aspects of minimization algorithm such as distance or probability measures and may not allow for unequal allocation ratios. This article describes the implementation of “MinimPy” an open-source minimization program in Python programming language, which provides full customizetion of minimization features. MinimPy supports naive and biased coin minimization together with various new and classic distance measures. Data syncing is provided to facilitate minimization of multicenter trial over the network. MinimPy can easily be modified to fit special needs of clinical trials and in particular change it to a pure web application, though it currently supports network syncing of data in multi-center trials using network repositories.展开更多
Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization p...Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.展开更多
An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution o...An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution of systems of linear or nonlinear equations by fixed-point iterative methods, and are simply the required solutions. In most cases of interest, however, these sequences converge to their limits extremely slowly. One practical way to make the sequences converge more quickly is to apply to them vector extrapolation methods. Two types of methods exist in the literature: polynomial type methods and epsilon algorithms. In most applications, the polynomial type methods have proved to be superior convergence accelerators. Three polynomial type methods are known, and these are the minimal polynomial extrapolation (MPE), the reduced rank extrapolation (RRE), and the modified minimal polynomial extrapolation (MMPE). In this work, we develop yet another polynomial type method, which is based on the singular value decomposition, as well as the ideas that lead to MPE. We denote this new method by SVD-MPE. We also design a numerically stable algorithm for its implementation, whose computational cost and storage requirements are minimal. Finally, we illustrate the use of SVD-MPE with numerical examples.展开更多
文摘In this paper, the minimal residual （MRES） method for solving nonsymmetric equation systems was improved, the recurrence relation was deduced between the approximate solutions of the linear equation system Ax = b, and a more effective method was presented, which can reduce the operational count and the storage.
基金funded by the National Natural Science Foundation of China(No.52275343)the Natural Science Foundation of Zhejiang Province(No.LY23E050003)+1 种基金Ningbo Youth Science and Technology Innovation Leading Talent Project(No.2023QL021)Smart Medicine and Engineering Interdisciplinary Innovation Project of Ningbo University(No.ZHYG001).
文摘Triply periodic minimal surface(TPMS)-based bone implants are an innovative approach in orthopedic implantology,offering customized solutions for bone defect repair and regeneration.This review comprehensively examines the current research landscape of TPMS-based bone implants,addressing key challenges and proposing future directions.It explores design strategies aimed at optimizing mechanical strength and enhancing biological integration,with a particular emphasis on TPMS structures.These design strategies include graded,hierarchical,and hybrid designs,each contributing to the overall functionality and performance of the implants.This review also highlights state-of-the-art fabrication technologies,particularly advancements in additive manufacturing(AM)techniques for creating metal-based,polymer-based,and ceramic-based bone implants.The ability to precisely control the architecture of TPMS structures using AM techniques is crucial for tailoring the mechanical and biological properties of such implants.Furthermore,this review critically evaluates the biological performance of TPMS implants,focusing on their potential to promote bone ingrowth and regeneration.Key factors,such as mechanical properties,permeability,and biocompatibility,are examined to determine the effectiveness of these implants in clinical applications.By synthesizing existing knowledge and proposing innovative research directions,this review underscores the transformative potential of TPMS-based bone implants in orthopedic surgery.The objective is to improve clinical outcomes and enhance patient care through advanced implant designs and manufacturing techniques.
文摘Management of the complex anal fistula represents a perennial challenge to surgeons.Conventional approaches often upset the balance between recurrence prevention and continence preservation with their high failure rates and significant associated morbidity.The emergence of minimally invasive treatment in recent years,however,offers a promising paradigm shift.Regenerative solutions like autologous stem cell therapy or fistula plugs with extracellular and synthetic matrices represent new frontiers in anal fistula treatment,harnessing physiological regenerative capacities and avoiding the traditional postoperative burden of open wounds,drains,or setons in situ.Together with novel techniques like fistula laser closure,video-assisted fistula treatment,or over-the-scope clip burgeoning over the last decade,these state-of-the-art approaches have been touted for their total sphincter-sparing nature,preserving functional outcomes and quality of life.Despite gaining much scientific and clinical momentum,do these newer modalities live up to their promise?This review aims to critically appraise the latest evidence surrounding minimally invasive approaches,providing up-todate insights into the constantly evolving landscape of anal fistula management.Further long-term and comparative studies will nevertheless be needed to supplement the significantly heterogenous,retrospective analyses consolidated.
基金supported by University of Kashan(Grant No.158426/5)
文摘Thermodynamic analysis was applied to study combined partial oxidation and carbon dioxide reforming of methane in view of carbon formation. The equilibrium calculations employing the Gibbs energy minimization were performed upon wide ranges of pressure （1-25 atm）, temperature （600-1300 K）, carbon dioxide to methane ratio （0-2） and oxygen to methane ratio （0-1）. The thermodynamic results were compared with the results obtained over a Ru supported catalyst. The results revealed that by increasing the reaction pressure methane conversion decreased. Also it was found that the atmospheric pressure is the preferable pressure for both dry reforming and partial oxidation of methane and increasing the temperature caused increases in both activity of carbon and conversion of methane. The results clearly showed that the addition of O2 to the feed mixture could lead to a reduction of carbon deposition.
基金Thanks for the reviewers’comments to improve the paper.This research was supported by the National Nature Science Foundation of China under Grant Nos.61772163,61761136010,61472111,Zhejiang Provincial Natural Science Foundation of China under Grant Nos.LR16F020003,LQ16F020005.
文摘In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimization problems,then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system.The existence and uniqueness of the solution for the linear system are also proved.Experimental results show the efficiency of the proposed approach,and its application in 1 G blending curve construction is also presented.
基金support from the Centre for Integrated Petroleum Research(CIPR),University of Bergen, Norway,and Singapore MOE Grant T207B2202NRF2007IDMIDM002-010
文摘Segmentation of three-dimensional(3D) complicated structures is of great importance for many real applications.In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model.Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations.Instead,the minimum cut on a special designed graph need to be computed.The method is tested on data with complicated structures.It is rather stable with respect to initial value and the algorithm is nearly parameter free.Experiments show that it can solve large problems much faster than traditional approaches.
基金This research is supported by the National Key Research and Development Program of China under Grant No.2018YFC1505401the Key Research and Development Projects of the Sichuan Science and Technology Department under Grant Nos.2019YFG0460,2020YFG0303,and 2021YJ0031+1 种基金the Technology Research and Development Program of China Railway Group Limited under Grant No.CZ01-Key Point-05the Fundamental Research Funds for the Central Universities under Grant No.2682021GF019.
文摘The downward continuation of potential fields is a process of calculating their values in a lower plane based on those of a certain plane.This technology is not only a data processing method for resource exploration but also plays an extremely important role in military applications.However,the downward continuation of potential fields is a typical linear inverse problem that is ill-posed.Generalized minimal residuals(GMRES)is an eff ective solution to ill-posed inverse problems,but it is unstable under the condition wherein the GMRES is directly applied in the calculation process.Moreover,the long-term behavior of its iterative computation is a disordered,divergent result.Therefore,to obtain stable solutions,GMRES is applied to solve the normal equations of the downward continuation of potential fields;it is also used to prequalify for occasional interruptions in the operation process by adding the damping coefficient,thus strengthening the stability conditions of the equations of residual minimization.Finally,the stable downward continuation of the potential fields method is proposed.As indicated by the theoretical data and the measured testing data,the method proposed in this paper has the advantages of high-precision and excellent stability.Furthermore,compared with the Tikhonov iteration method,the proposed method avoids the need to choose regularization parameters.
文摘A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general global minimiizing algorithm is employed as a subroutine of the algorithm. The method is expected to tackle a large class of nonsmooth constrained minimization problem.
基金Supported by the National Natural Science Foundation of China(11371320)Zhejiang Natural Science Foundation(LZ14A010002)+1 种基金Foundation of Science and Technology Department of Zhejiang Province(2013C31084)Scientific Research Fund of Zhejiang Provincial Education Department(Y201431077 and Y201329420)
文摘We analyze three commonly used energy functions in solving Plateau-Mesh Prob- lem, that is, Dirichlet, area, and the discrete mean curvature（DMC）. They all possess unique advantages compared to others, but their drawbacks restrict their usages individually. Our algo- rithm combines the three steps together to make full use of their features. At first the Dirichlet energy is optimized for faster approximation with better topology. Then the area energy is used to come close to the constrained domain. Finally the DMC energy is engaged to achieve a better converging step. Results show that our method can work under a rather noisy initial mesh, which is even topologically different from the final result.
基金the National Natural Science Foundation of China ( 1 0 4 71 0 94) ,the ScienceFoundation of Shanghai Technical Sciences Committee ( 0 2 ZA1 40 70 ) and the Science Foundation ofShanghai Education Committee( 0 2 DK0 6)
文摘This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programming and convex theory,the generalized directional derivative of the general multicommodity minimal cost flow problems is derived.The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.
基金supported by Research Grant from the Kajima Foundation,JST CREST Grant No.JPMJCR1911,JapanJSPS KAKENHI(Nos.17K06633,21K04351).
文摘Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.
文摘The learning curve in minimally invasive colorectal surgery is a constant subject of discussion in the literature.Discordant data likely reflects the varying degrees of each surgeon’s experience in colorectal,laparoscopic or robotic surgery.Several factors are necessary for a successful minimally invasive colorectal surgery training program,including:Compliance with oncological outcomes;dissection along the embryological planes;constant presence of an expert tutor;periodic discussion of the morbidity and mortality rate;and creation of a dedicated,expert team.
文摘We solve the Duffin-Kemmer-Petiau （DKP） equation with a non-minimal vector Yukawa potential in （1＋1）- dimensional spa^e-time for spin-1 particles. The Nikiforov Uvarov method is used in the calculations, and the eigen- functions as well as the energy eigenvalues are obtained in a proper Pekeris-type approximation.
基金Sponsored by the National"Eleventh-five"Tackle Key Problem Program-China Science and Technology Support Project(Grant No.2006BAJ01A04)
文摘In this paper,we improve object functions and constraint conditions of genetic algorithms (GAs) applied in PRCs identification of water networks.This identification method can increase calculation efficiency,but can not solve an identification problem with infinitely many solutions well.Then we propose PRCs identification based on the minimal norm method,which satisfies observability conditions and has advantages of high computing efficiency and short time consumption.The two identification methods are applied in a water network,and their identification results are compared under the same conditions.From the results,we know that PRCs identification based on the minimal norm method has advantages of higher computing efficiency,shorter time consumption and higher precision.
文摘Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.
文摘A strategy for water and wastewater minimization is developed for continuous water utilization systems involving fixed flowrate(non-mass-transfer-based)operations,based on the fictitious operations that is introduced to represent the water losing and/or generating operations and a modified concentration interval analysis(MCIA) technique.This strategy is a simple,nongraphical,and noniterative procedure and is suitable for the quick yields of targets and the identification of pinch point location.Moreover,on the basis of the target method,a heuristic-based approach is also presented to generate water utilization networks,which could be demonstrated to be optimum ones. The proposed approaches are illustrated with example problems.
文摘Current minimization programs do not permit full control over different aspects of minimization algorithm such as distance or probability measures and may not allow for unequal allocation ratios. This article describes the implementation of “MinimPy” an open-source minimization program in Python programming language, which provides full customizetion of minimization features. MinimPy supports naive and biased coin minimization together with various new and classic distance measures. Data syncing is provided to facilitate minimization of multicenter trial over the network. MinimPy can easily be modified to fit special needs of clinical trials and in particular change it to a pure web application, though it currently supports network syncing of data in multi-center trials using network repositories.
文摘Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.
文摘An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution of systems of linear or nonlinear equations by fixed-point iterative methods, and are simply the required solutions. In most cases of interest, however, these sequences converge to their limits extremely slowly. One practical way to make the sequences converge more quickly is to apply to them vector extrapolation methods. Two types of methods exist in the literature: polynomial type methods and epsilon algorithms. In most applications, the polynomial type methods have proved to be superior convergence accelerators. Three polynomial type methods are known, and these are the minimal polynomial extrapolation (MPE), the reduced rank extrapolation (RRE), and the modified minimal polynomial extrapolation (MMPE). In this work, we develop yet another polynomial type method, which is based on the singular value decomposition, as well as the ideas that lead to MPE. We denote this new method by SVD-MPE. We also design a numerically stable algorithm for its implementation, whose computational cost and storage requirements are minimal. Finally, we illustrate the use of SVD-MPE with numerical examples.
