In this paper, using Lin＇s integral identity technique, we prove the optimal uniform convergence θ（Nx^-2ln^2Nx＋Ny^-2ln^2Ny） in the L^2-norm for singularly perturbed problems with parabolic layers. The error esti...In this paper, using Lin＇s integral identity technique, we prove the optimal uniform convergence θ（Nx^-2ln^2Nx＋Ny^-2ln^2Ny） in the L^2-norm for singularly perturbed problems with parabolic layers. The error estimate is achieved by bilinear finite elements on a Shishkin type mesh. Here Nx and Ny are the number of elements in the x- and y-directions, respectively. Numerical results are provided supporting our theoretical analysis.展开更多
A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems a...A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems and minimization of factor of safety in slope stability analysis. The new algorithm combines the global exploration ability of the GSA to converge rapidly to a near optimum solution. In addition, it uses the accurate local exploitation ability of the SQP to accelerate the search process and find an accurate solution. A set of five well-known benchmark optimization problems was used to validate the performance of the GSA-SQP as a global optimization algorithm and facilitate comparison with the classical GSA. In addition, the effectiveness of the proposed method for slope stability analysis was investigated using three ease studies of slope stability problems from the literature. The factor of safety of earth slopes was evaluated using the Morgenstern-Price method. The numerical experiments demonstrate that the hybrid algorithm converges faster to a significantly more accurate final solution for a variety of benchmark test functions and slope stability problems.展开更多
There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method...There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method to tackle the nonlinear eontact and large deformation problem in A Software on Large Deformation Analysis for Soft Rock Engineering at Great Depth was presented. In the software, based on Lagrange multiplier method and Coulomb friction law, kinematic constraints on contact boundaries were introduced in functional function, and the finite element equations was established for two incremental large deformation analyses models, polar decomposition model and additive decomposition model. For every incremental loading step, by searching for the contact points in the potential contact interfaces （the excavation boundaries）, the Lagrange multipliers, i.e., contact forces are cal- culated iteratively by Gauss-Seidel method, and justified through satisfy the inequalities of static constraint on contact boundaries. With the software, large deformation and frictional contact of a transport roadway were analyzed numerically by the two models. The numerical examples demonstrated the efficiency of the method used in the software.展开更多
The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was const...The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was constructed. The stability factor formulation by the upper bound theorem leads to a classical nonlinear programming problem, when the external work rate and internal energy dissipation were solved, and the constraint condition of the programming problem was given. The upper bound optimization problem can be solved efficiently by applying a nonlinear SQP algorithm, and stability factor was obtained, which agrees well with previous achievements.展开更多
The flow of an Oldroyd 8-constant fluid between coaxial cylinders with variable viscosity is considered.The heat transfer analysis is also taken into account.An analytical solution of the non-linear problem is obtaine...The flow of an Oldroyd 8-constant fluid between coaxial cylinders with variable viscosity is considered.The heat transfer analysis is also taken into account.An analytical solution of the non-linear problem is obtained usinghomotopy analysis method.The behavior of pertinent parameters is analyzed and depicted through graphs.展开更多
Many applications in computational science and engineering require the computation of eigenvalues and vectors of dense symmetric or Hermitian matrices. For example, in DFT （density functional theory） calculations on...Many applications in computational science and engineering require the computation of eigenvalues and vectors of dense symmetric or Hermitian matrices. For example, in DFT （density functional theory） calculations on modern supercomputers 10% to 30% of the eigenvalues and eigenvectors of huge dense matrices have to be calculated. Therefore, performance and parallel scaling of the used eigensolvers is of upmost interest. In this article different routines of the linear algebra packages ScaLAPACK and Elemental for parallel solution of the symmetric eigenvalue problem are compared concerning their performance on the BlueGene/P supercomputer. Parameters for performance optimization are adjusted for the different data distribution methods used in the two libraries. It is found that for all test cases the new library Elemental which uses a two-dimensional element by element distribution of the matrices to the processors shows better performance than the old ScaLAPACK library which uses a block-cyclic distribution.展开更多
The paper uses the proportion of zero-return days model to analyze stock market synchronous behaviors for 11 sample counties. It is found that the zero-return measure of stock synchronicity is higher for some emerging...The paper uses the proportion of zero-return days model to analyze stock market synchronous behaviors for 11 sample counties. It is found that the zero-return measure of stock synchronicity is higher for some emerging economies than the developed economies though the result is not statistically significant. In addition, panel data analysis indicates somewhat positive and negative correlation between the zero-return measures with the explanatory variables. The findings raise question about the reliability of the proportion of zero-return days measure and its capability to capture stock market synchronous behavior.展开更多
First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setti...First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.展开更多
That is a global issue to preserve and increase the value of pension funds, also has caused widespread concern of the governments around the world. China＇s basic pension funds are also facing the severe problem. In t...That is a global issue to preserve and increase the value of pension funds, also has caused widespread concern of the governments around the world. China＇s basic pension funds are also facing the severe problem. In this background, The State Council issued ＂the Measures for the Administration of Investment in Basic Pension Insurance Funds＂, Basic Pension Funds into Capital Markers finally＂ have laws to go by ＂. To explore the basic pension funds into the market has a realistic social significance. Based on the SWOT analysis method, make a detailed analysis of the pension market from four aspects, put forward some views and hope that these opinions can provide reference for the sustainable development of China＇s basic pension fund system.展开更多
Decision-making of investors at the stock exchange can be based on the fundamental indicators of stocks, on the technical indicators, or can exist as a combination of these two methods. The paper gives emphasis to the...Decision-making of investors at the stock exchange can be based on the fundamental indicators of stocks, on the technical indicators, or can exist as a combination of these two methods. The paper gives emphasis to the domain of technical analysis. In the broader sense the technical analysis enables the dynamics of the expected future values of the shares estimation. This can be performed on the basis of the data on historical trends of the revenues, profits and other indicators from the balance sheet, but also on the basis of historical data on changes in the values of the shares. Companies generally belong to the different sectors that have different presumptions of development resulting from the global market trends, technology and other characteristic. Processing of historical data values of the outstanding shares of the Zagreb Stock Exchange （ZSE） is origination of this research. Investors are interested to know the estimation of future returns for the stocks as well as the size of the risk associated with the expected returns. Research task in this paper is finding the optimal portfolio at the ZSE based on the concept of dominant portfolio by Markowitz approach. The portfolio is created by solving non-linear programming problem using the common software tools. The results of obtained optimal portfolios contain relevant conclusions about the specifics of the shares as well as the characteristics of the industrial sectors but also provide a further knowledge about diverse sectors treatment at the stock exchange in a multi-year period.展开更多
In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly app...In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly approximated.At each iteration,we construct a quadratic interpolation model of the objective function around the current iterate.The new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust region.The filter technique is used to ensure the feasibility and optimality of the iterative sequence.Global convergence of the proposed algorithm is proved under some suitable assumptions.展开更多
A problem of a hierarchy structure optimization is considered.Hierarchical structures arewidely used in the Analytic Hierarchy Process,conjoint analysis,and various other methods of multiplecriteria decision making.Th...A problem of a hierarchy structure optimization is considered.Hierarchical structures arewidely used in the Analytic Hierarchy Process,conjoint analysis,and various other methods of multiplecriteria decision making.The problem consists in finding a structure that needs a minimum number ofpair comparisons for a given total number of the alternatives.For an optimal hierarchy,the minimumefforts are needed for eliciting data and synthesizing the local preferences across the hierarchy to getthe global priorities or utilities.Special estimation techniques are developed and numerical simulationsperformed.Analytical and numerical results suggest optimal ways of priority evaluations for practicalmanagerial decisions in a complex environment.展开更多
The guide-weight method is introduced to solve the topology optimization problems of thermoelastic structures in this paper.First,the solid isotropic microstructure with penalization(SIMP)with different penalty factor...The guide-weight method is introduced to solve the topology optimization problems of thermoelastic structures in this paper.First,the solid isotropic microstructure with penalization(SIMP)with different penalty factors is selected as a material interpolation model for the thermal and mechanical fields.The general criteria of the guide-weight method is then presented.Two types of iteration formulas of the guide-weight method are applied to the topology optimization of thermoelastic structures,one of which is to minimize the mean compliance of the structure with material constraint,whereas the other one is to minimize the total weight with displacement constraint.For each type of problem,sensitivity analysis is conducted based on SIMP model.Finally,four classical 2-dimensional numerical examples and a 3-dimensional numerical example considering the thermal field are selected to perform calculation.The factors that affect the optimal topology are discussed,and the performance of the guide-weight method is tested.The results show that the guide-weight method has the advantages of simple iterative formula,fast convergence and relatively clear topology result.展开更多
文摘In this paper, using Lin＇s integral identity technique, we prove the optimal uniform convergence θ（Nx^-2ln^2Nx＋Ny^-2ln^2Ny） in the L^2-norm for singularly perturbed problems with parabolic layers. The error estimate is achieved by bilinear finite elements on a Shishkin type mesh. Here Nx and Ny are the number of elements in the x- and y-directions, respectively. Numerical results are provided supporting our theoretical analysis.
文摘A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems and minimization of factor of safety in slope stability analysis. The new algorithm combines the global exploration ability of the GSA to converge rapidly to a near optimum solution. In addition, it uses the accurate local exploitation ability of the SQP to accelerate the search process and find an accurate solution. A set of five well-known benchmark optimization problems was used to validate the performance of the GSA-SQP as a global optimization algorithm and facilitate comparison with the classical GSA. In addition, the effectiveness of the proposed method for slope stability analysis was investigated using three ease studies of slope stability problems from the literature. The factor of safety of earth slopes was evaluated using the Morgenstern-Price method. The numerical experiments demonstrate that the hybrid algorithm converges faster to a significantly more accurate final solution for a variety of benchmark test functions and slope stability problems.
基金subsidized by special funds for the National Basic Research Program of China (No.2002cb412708)supported by the Opening Funds of the State Key Laboratory of Hydroscience and Engineering of China (No.sklhse-2007-D-02)
文摘There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method to tackle the nonlinear eontact and large deformation problem in A Software on Large Deformation Analysis for Soft Rock Engineering at Great Depth was presented. In the software, based on Lagrange multiplier method and Coulomb friction law, kinematic constraints on contact boundaries were introduced in functional function, and the finite element equations was established for two incremental large deformation analyses models, polar decomposition model and additive decomposition model. For every incremental loading step, by searching for the contact points in the potential contact interfaces （the excavation boundaries）, the Lagrange multipliers, i.e., contact forces are cal- culated iteratively by Gauss-Seidel method, and justified through satisfy the inequalities of static constraint on contact boundaries. With the software, large deformation and frictional contact of a transport roadway were analyzed numerically by the two models. The numerical examples demonstrated the efficiency of the method used in the software.
基金Project(2013CB036004)supported by the National Basic Research Program of ChinaProject(51178468)supported by the National Natural Science Foundation of China
文摘The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was constructed. The stability factor formulation by the upper bound theorem leads to a classical nonlinear programming problem, when the external work rate and internal energy dissipation were solved, and the constraint condition of the programming problem was given. The upper bound optimization problem can be solved efficiently by applying a nonlinear SQP algorithm, and stability factor was obtained, which agrees well with previous achievements.
文摘The flow of an Oldroyd 8-constant fluid between coaxial cylinders with variable viscosity is considered.The heat transfer analysis is also taken into account.An analytical solution of the non-linear problem is obtained usinghomotopy analysis method.The behavior of pertinent parameters is analyzed and depicted through graphs.
文摘Many applications in computational science and engineering require the computation of eigenvalues and vectors of dense symmetric or Hermitian matrices. For example, in DFT （density functional theory） calculations on modern supercomputers 10% to 30% of the eigenvalues and eigenvectors of huge dense matrices have to be calculated. Therefore, performance and parallel scaling of the used eigensolvers is of upmost interest. In this article different routines of the linear algebra packages ScaLAPACK and Elemental for parallel solution of the symmetric eigenvalue problem are compared concerning their performance on the BlueGene/P supercomputer. Parameters for performance optimization are adjusted for the different data distribution methods used in the two libraries. It is found that for all test cases the new library Elemental which uses a two-dimensional element by element distribution of the matrices to the processors shows better performance than the old ScaLAPACK library which uses a block-cyclic distribution.
文摘The paper uses the proportion of zero-return days model to analyze stock market synchronous behaviors for 11 sample counties. It is found that the zero-return measure of stock synchronicity is higher for some emerging economies than the developed economies though the result is not statistically significant. In addition, panel data analysis indicates somewhat positive and negative correlation between the zero-return measures with the explanatory variables. The findings raise question about the reliability of the proportion of zero-return days measure and its capability to capture stock market synchronous behavior.
文摘First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.
文摘That is a global issue to preserve and increase the value of pension funds, also has caused widespread concern of the governments around the world. China＇s basic pension funds are also facing the severe problem. In this background, The State Council issued ＂the Measures for the Administration of Investment in Basic Pension Insurance Funds＂, Basic Pension Funds into Capital Markers finally＂ have laws to go by ＂. To explore the basic pension funds into the market has a realistic social significance. Based on the SWOT analysis method, make a detailed analysis of the pension market from four aspects, put forward some views and hope that these opinions can provide reference for the sustainable development of China＇s basic pension fund system.
文摘Decision-making of investors at the stock exchange can be based on the fundamental indicators of stocks, on the technical indicators, or can exist as a combination of these two methods. The paper gives emphasis to the domain of technical analysis. In the broader sense the technical analysis enables the dynamics of the expected future values of the shares estimation. This can be performed on the basis of the data on historical trends of the revenues, profits and other indicators from the balance sheet, but also on the basis of historical data on changes in the values of the shares. Companies generally belong to the different sectors that have different presumptions of development resulting from the global market trends, technology and other characteristic. Processing of historical data values of the outstanding shares of the Zagreb Stock Exchange （ZSE） is origination of this research. Investors are interested to know the estimation of future returns for the stocks as well as the size of the risk associated with the expected returns. Research task in this paper is finding the optimal portfolio at the ZSE based on the concept of dominant portfolio by Markowitz approach. The portfolio is created by solving non-linear programming problem using the common software tools. The results of obtained optimal portfolios contain relevant conclusions about the specifics of the shares as well as the characteristics of the industrial sectors but also provide a further knowledge about diverse sectors treatment at the stock exchange in a multi-year period.
基金supported by National Natural Science Foundation of China (Grant Nos. 11071122 and 11171159)the Specialized Research Fund of Doctoral Program of Higher Education of China (Grant No. 20103207110002)
文摘In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly approximated.At each iteration,we construct a quadratic interpolation model of the objective function around the current iterate.The new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust region.The filter technique is used to ensure the feasibility and optimality of the iterative sequence.Global convergence of the proposed algorithm is proved under some suitable assumptions.
文摘A problem of a hierarchy structure optimization is considered.Hierarchical structures arewidely used in the Analytic Hierarchy Process,conjoint analysis,and various other methods of multiplecriteria decision making.The problem consists in finding a structure that needs a minimum number ofpair comparisons for a given total number of the alternatives.For an optimal hierarchy,the minimumefforts are needed for eliciting data and synthesizing the local preferences across the hierarchy to getthe global priorities or utilities.Special estimation techniques are developed and numerical simulationsperformed.Analytical and numerical results suggest optimal ways of priority evaluations for practicalmanagerial decisions in a complex environment.
基金supported by the National Natural Science Foundation of China(Grant No.51375251)the National Basic Research Program("973"Program)(Grant No.2013CB035400)of China
文摘The guide-weight method is introduced to solve the topology optimization problems of thermoelastic structures in this paper.First,the solid isotropic microstructure with penalization(SIMP)with different penalty factors is selected as a material interpolation model for the thermal and mechanical fields.The general criteria of the guide-weight method is then presented.Two types of iteration formulas of the guide-weight method are applied to the topology optimization of thermoelastic structures,one of which is to minimize the mean compliance of the structure with material constraint,whereas the other one is to minimize the total weight with displacement constraint.For each type of problem,sensitivity analysis is conducted based on SIMP model.Finally,four classical 2-dimensional numerical examples and a 3-dimensional numerical example considering the thermal field are selected to perform calculation.The factors that affect the optimal topology are discussed,and the performance of the guide-weight method is tested.The results show that the guide-weight method has the advantages of simple iterative formula,fast convergence and relatively clear topology result.
