Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of...Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.展开更多
Cantilever casting concrete arch bridge using form traveller has a broad application prospect.However,it is difficult to obtain reasonable initial cable force in construction stage.In this study,stress balance and inf...Cantilever casting concrete arch bridge using form traveller has a broad application prospect.However,it is difficult to obtain reasonable initial cable force in construction stage.In this study,stress balance and influence matrix methods were developed to determine the initial cable force of cantilever casting concrete arch bridge.The stress balance equation and influence matrix of arch rib critical section were established,and the buckle cable force range was determined by the allowable stress of arch rib critical section.Then a group of buckle cable forces were selected and substituted into the stress balance equation,and the reasonable initial buckle cable force was determined through iteration.Based on the principle of force balance,the initial anchor cable force was determined.In an engineering application example,it is shown that the stress balance and influence matrix methods for the determination of initial cable force are feasible and reliable.The initial cable forces of arch rib segments only need to be adjusted once in the corresponding construction process,which improves the working efficiency and reduces the construction risk.It is found that the methods have great advantages for determining initial cable force in cantilever casting construction process of concrete arch bridge.展开更多
The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the p...The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the purposes of calculation.The results from the kernels are summed according to an expression characteristic of KEM to obtain the full molecule energy.A generalization of the kernel expansion to density matrices provides the full molecule density matrix and orbitals.In this study,the kernel expansion for the density matrix is examined in the context of density functional theory(DFT) Kohn-Sham(KS) calculations.A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined,and is then converted into a normalizedprojector by using the Clinton algorithm.Such normalized projectors are factorizable into linear combination of atomic orbitals(LCAO) matrices that deliver full-molecule Kohn-Sham molecular orbitals in the atomic orbital basis.Both straightforward KEM energies and energies from a normalized,idempotent density matrix obtained from a density matrix kernel expansion to which the Clinton algorithm has been applied are compared to reference energies obtained from calculations on the full system without any kernel expansion.Calculations were performed both for a simple proof-of-concept system consisting of three atoms in a linear configuration and for a water cluster consisting of twelve water molecules.In the case of the proof-of-concept system,calculations were performed using the STO-3 G and6-31 G(d,p) bases over a range of atomic separations,some very far from equilibrium.The water cluster was calculated in the 6-31 G(d,p) basis at an equilibrium geometry.The normalized projector density energies are more accurate than the straightforward KEM energy results in nearly all cases.In the case of the water cluster,the energy of the normalized projector is approximately four times more accurate than the straightforward KEM energy result.The KS density matrices of this study are applicable to quantum crystallography.展开更多
In consideration of the problem that the effect of conduit structure on water hammer has been ignored in the classical theory,the Poisson coupling between the fluid and the pipeline was studied and a fourteen-equation...In consideration of the problem that the effect of conduit structure on water hammer has been ignored in the classical theory,the Poisson coupling between the fluid and the pipeline was studied and a fourteen-equation mathematical model of fluid-structure interaction(FSI)was developed.Then,the transfer matrix method(TMM)was used to calculate the modal frequency,modal shape and frequency response.The results were compared with that in experiment to verify the correctness of the TMM and the results show that the fluid-structure coupling has a greater impact on the modal frequencies than the modal shape.Finally,the influence on the response spectrum of different damping ratios was studied and the results show that the natural frequency under different damping ratios has changed little but there is a big difference for the pressure spectrum.With the decreasing of damping ratio,the damping of the system on frequency spectrum is more and more significant and the dispersion and dissipation is more and more apparent.Therefore the appropriate damping ratio should be selected to minimize the effects of the vibration of the FSI.The results provide references for the theory research of FSI in the transient process.展开更多
A vicious script detection method based on statistic is proposed by analyzing the vicious script in the hypertext markup language(HTML).We utilize the judgment matrix approach which is one of the subjective weighting ...A vicious script detection method based on statistic is proposed by analyzing the vicious script in the hypertext markup language(HTML).We utilize the judgment matrix approach which is one of the subjective weighting approaches to set the different weights for various statistic methods.Then we make use of the weighted geometric method to perfect the statistic results.Experimental results show the validity of this method.展开更多
Driven by the challenge of integrating large amount of experimental data, classification technique emerges as one of the major and popular tools in computational biology and bioinformatics research. Machine learning m...Driven by the challenge of integrating large amount of experimental data, classification technique emerges as one of the major and popular tools in computational biology and bioinformatics research. Machine learning methods, especially kernel methods with Support Vector Machines （SVMs） are very popular and effective tools. In the perspective of kernel matrix, a technique namely Eigen- matrix translation has been introduced for protein data classification. The Eigen-matrix translation strategy has a lot of nice properties which deserve more exploration. This paper investigates the major role of Eigen-matrix translation in classification. The authors propose that its importance lies in the dimension reduction of predictor attributes within the data set. This is very important when the dimension of features is huge. The authors show by numerical experiments on real biological data sets that the proposed framework is crucial and effective in improving classification accuracy. This can therefore serve as a novel perspective for future research in dimension reduction problems.展开更多
生态环境修复方案的可行性论证与修复效果评价是生态环境修复工程的重要内容,对生态环境修复工程的设计及建设具有重要指导意义。目的为确定生态环境修复方案可行性和修复的综合效果,以盘石头水库为例,对该水库生态修复方案进行综合评...生态环境修复方案的可行性论证与修复效果评价是生态环境修复工程的重要内容,对生态环境修复工程的设计及建设具有重要指导意义。目的为确定生态环境修复方案可行性和修复的综合效果,以盘石头水库为例,对该水库生态修复方案进行综合评价研究。方法首先,参照OECD(Organization for Economic Cooperation and Development)模型,构建由生态效益、景观效益、社会效益、维护管理共4个准则层和18个评价子指标组成的盘石头水库生态环境修复方案可行性和修复效果评价体系;其次,通过最优传递矩阵对层次分析法的权重计算进行改进,对构建的评价指标体系进行权重的计算;最后,将改进AHP与模糊综合评价方法相结合,对盘石头水库生态修复方案进行综合评价。结果结果表明,在盘石头水库生态环境修复方案中最重要的准则层指标是生态效益;在选取的18个评价子指标中,物种多样性、观赏价值、改善城市形象和降低灾害这4个指标的权重较大;所评价的鹤壁市盘石头水库生态环境修复方案的修复效果为优,方案可行。结论模糊-改进AHP法为生态环境修复及其方案可行性的评价提供了一种新的、更有效的方法。展开更多
研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导...研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导线离散迭代和开阔边界迭代两阶段自动迭代边界元算法(automatic iterative boundary element method,AIBEM),并结合实例阐述了全域法和区域分解法两种多层介质问题系数矩阵生成方法。研究结果表明,边界环内生成的系数矩阵存在误差均衡协调问题,对复杂模型需合理选择各线段离散单元数及开阔边界尺寸,通过AIBEM可以获得经济的离散参数,有效避免矩阵奇异性,并提高收敛稳定性。将计算结果与有限元法、解析法、传输线法、矩量法进行了对比分析,证实了算法的可靠性。展开更多
基金Supported by the National Natural Science Foundation of China(12001395)the special fund for Science and Technology Innovation Teams of Shanxi Province(202204051002018)+1 种基金Research Project Supported by Shanxi Scholarship Council of China(2022-169)Graduate Education Innovation Project of Taiyuan Normal University(SYYJSYC-2314)。
文摘Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.
基金Projects(51478049,51778068)supported by the National Natural Science Foundation of ChinaProject(14JJ2075,2019JJ40301)supported by the Hunan Natural Science Foundation of China+1 种基金Project(17A010)supported by the Scientific Research Fund of Hunan Provincial Education Department of ChinaProject(2017GK4034)supported by the Major Technological Achievements Transformation Program of Hunan Strategic Emerging Industries of China
文摘Cantilever casting concrete arch bridge using form traveller has a broad application prospect.However,it is difficult to obtain reasonable initial cable force in construction stage.In this study,stress balance and influence matrix methods were developed to determine the initial cable force of cantilever casting concrete arch bridge.The stress balance equation and influence matrix of arch rib critical section were established,and the buckle cable force range was determined by the allowable stress of arch rib critical section.Then a group of buckle cable forces were selected and substituted into the stress balance equation,and the reasonable initial buckle cable force was determined through iteration.Based on the principle of force balance,the initial anchor cable force was determined.In an engineering application example,it is shown that the stress balance and influence matrix methods for the determination of initial cable force are feasible and reliable.The initial cable forces of arch rib segments only need to be adjusted once in the corresponding construction process,which improves the working efficiency and reduces the construction risk.It is found that the methods have great advantages for determining initial cable force in cantilever casting construction process of concrete arch bridge.
文摘The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the purposes of calculation.The results from the kernels are summed according to an expression characteristic of KEM to obtain the full molecule energy.A generalization of the kernel expansion to density matrices provides the full molecule density matrix and orbitals.In this study,the kernel expansion for the density matrix is examined in the context of density functional theory(DFT) Kohn-Sham(KS) calculations.A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined,and is then converted into a normalizedprojector by using the Clinton algorithm.Such normalized projectors are factorizable into linear combination of atomic orbitals(LCAO) matrices that deliver full-molecule Kohn-Sham molecular orbitals in the atomic orbital basis.Both straightforward KEM energies and energies from a normalized,idempotent density matrix obtained from a density matrix kernel expansion to which the Clinton algorithm has been applied are compared to reference energies obtained from calculations on the full system without any kernel expansion.Calculations were performed both for a simple proof-of-concept system consisting of three atoms in a linear configuration and for a water cluster consisting of twelve water molecules.In the case of the proof-of-concept system,calculations were performed using the STO-3 G and6-31 G(d,p) bases over a range of atomic separations,some very far from equilibrium.The water cluster was calculated in the 6-31 G(d,p) basis at an equilibrium geometry.The normalized projector density energies are more accurate than the straightforward KEM energy results in nearly all cases.In the case of the water cluster,the energy of the normalized projector is approximately four times more accurate than the straightforward KEM energy result.The KS density matrices of this study are applicable to quantum crystallography.
文摘In consideration of the problem that the effect of conduit structure on water hammer has been ignored in the classical theory,the Poisson coupling between the fluid and the pipeline was studied and a fourteen-equation mathematical model of fluid-structure interaction(FSI)was developed.Then,the transfer matrix method(TMM)was used to calculate the modal frequency,modal shape and frequency response.The results were compared with that in experiment to verify the correctness of the TMM and the results show that the fluid-structure coupling has a greater impact on the modal frequencies than the modal shape.Finally,the influence on the response spectrum of different damping ratios was studied and the results show that the natural frequency under different damping ratios has changed little but there is a big difference for the pressure spectrum.With the decreasing of damping ratio,the damping of the system on frequency spectrum is more and more significant and the dispersion and dissipation is more and more apparent.Therefore the appropriate damping ratio should be selected to minimize the effects of the vibration of the FSI.The results provide references for the theory research of FSI in the transient process.
基金Sponsored by the National 242 Information Security Project (2005A10 )and( 2007F40)the National Defence Basic Scientific Research Project(C1120060497)
文摘A vicious script detection method based on statistic is proposed by analyzing the vicious script in the hypertext markup language(HTML).We utilize the judgment matrix approach which is one of the subjective weighting approaches to set the different weights for various statistic methods.Then we make use of the weighted geometric method to perfect the statistic results.Experimental results show the validity of this method.
基金supported by Research Grants Council of Hong Kong under Grant No.17301214HKU CERG Grants,Fundamental Research Funds for the Central Universities+2 种基金the Research Funds of Renmin University of ChinaHung Hing Ying Physical Research Grantthe Natural Science Foundation of China under Grant No.11271144
文摘Driven by the challenge of integrating large amount of experimental data, classification technique emerges as one of the major and popular tools in computational biology and bioinformatics research. Machine learning methods, especially kernel methods with Support Vector Machines （SVMs） are very popular and effective tools. In the perspective of kernel matrix, a technique namely Eigen- matrix translation has been introduced for protein data classification. The Eigen-matrix translation strategy has a lot of nice properties which deserve more exploration. This paper investigates the major role of Eigen-matrix translation in classification. The authors propose that its importance lies in the dimension reduction of predictor attributes within the data set. This is very important when the dimension of features is huge. The authors show by numerical experiments on real biological data sets that the proposed framework is crucial and effective in improving classification accuracy. This can therefore serve as a novel perspective for future research in dimension reduction problems.
文摘生态环境修复方案的可行性论证与修复效果评价是生态环境修复工程的重要内容,对生态环境修复工程的设计及建设具有重要指导意义。目的为确定生态环境修复方案可行性和修复的综合效果,以盘石头水库为例,对该水库生态修复方案进行综合评价研究。方法首先,参照OECD(Organization for Economic Cooperation and Development)模型,构建由生态效益、景观效益、社会效益、维护管理共4个准则层和18个评价子指标组成的盘石头水库生态环境修复方案可行性和修复效果评价体系;其次,通过最优传递矩阵对层次分析法的权重计算进行改进,对构建的评价指标体系进行权重的计算;最后,将改进AHP与模糊综合评价方法相结合,对盘石头水库生态修复方案进行综合评价。结果结果表明,在盘石头水库生态环境修复方案中最重要的准则层指标是生态效益;在选取的18个评价子指标中,物种多样性、观赏价值、改善城市形象和降低灾害这4个指标的权重较大;所评价的鹤壁市盘石头水库生态环境修复方案的修复效果为优,方案可行。结论模糊-改进AHP法为生态环境修复及其方案可行性的评价提供了一种新的、更有效的方法。
文摘研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导线离散迭代和开阔边界迭代两阶段自动迭代边界元算法(automatic iterative boundary element method,AIBEM),并结合实例阐述了全域法和区域分解法两种多层介质问题系数矩阵生成方法。研究结果表明,边界环内生成的系数矩阵存在误差均衡协调问题,对复杂模型需合理选择各线段离散单元数及开阔边界尺寸,通过AIBEM可以获得经济的离散参数,有效避免矩阵奇异性,并提高收敛稳定性。将计算结果与有限元法、解析法、传输线法、矩量法进行了对比分析,证实了算法的可靠性。
