Curriculum ideology and politics is the key to carry out the mission of educating people in colleges and universities in the new era.On the problem of integrating the linear algebra course into the ideological and pol...Curriculum ideology and politics is the key to carry out the mission of educating people in colleges and universities in the new era.On the problem of integrating the linear algebra course into the ideological and political education,it was expounded from four aspects:the necessity of integrating the course ideology and politics into the teaching of linear algebra,exploring curriculum ideological and political elements,the case design of integrating the course ideology and politics teaching,and the expected effect of integrating linear algebra courses into ideological and political education in the curriculum,in order to have the reference and help function to the educator.展开更多
Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivati...Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.展开更多
Let Mn be the algebra of all n × n complex matrices and gl（n, C） be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ ： gl（n, C） → gl（n, C） preserves solvability in both directions...Let Mn be the algebra of all n × n complex matrices and gl（n, C） be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ ： gl（n, C） → gl（n, C） preserves solvability in both directions if both φ and φ-1 map every solvable Lie subalgebra of gl（n, C） to some solvable Lie subalgebra. In this paper we classify the invertible linear maps preserving solvability on gl（n, C） in both directions. As a sequence, such maps coincide with the invertible linear maps preserving commutativity on Mn in both directions.展开更多
The application level of mathematics in each science discipline signs the level of development of this science. With the advancement of science and technology, especially the rapid development of computer technology, ...The application level of mathematics in each science discipline signs the level of development of this science. With the advancement of science and technology, especially the rapid development of computer technology, mathematics has permeated from natural scientific technology to agricultural construction, from economic activities to all areas of social life. Generally, when the actual problem requires us to provide quantitative results of analysis, forecasting, decision making, control and other aspects for real object under study, we are often inseparable from the application of mathematics. Mathematical modeling is the key to this process, whose purpose is to make mathematics applied to social and social services, and using mathematics to solve practical problems is through mathematical models. When using mathematical methods to solve some practical problems, we usually first transfer practical problems into mathematical language, and then abstract them into a mathematical model.展开更多
A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed. Then an algorithm of 3D object recognition using the linear Lie algebra models is presented. It is a ...A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed. Then an algorithm of 3D object recognition using the linear Lie algebra models is presented. It is a convenient recognition method for the objects which are symmetric about some axis. By using the presented algorithm, the representation matrices of the fibre or the base curve from only finite points of the linear Lie algebra model can be obtained. At last some recognition results of practicalities are given.展开更多
Let g be the general linear Lie algebra consisting of all n x n matrices over a field F and with the usual bracket operation {x, y} =xy - yx. An invertible map φ ： g →g is said to preserve staircase subalgebras if ...Let g be the general linear Lie algebra consisting of all n x n matrices over a field F and with the usual bracket operation {x, y} =xy - yx. An invertible map φ ： g →g is said to preserve staircase subalgebras if it maps every staircase subalgebra to some staircase subalgebra of the same dimension. In this paper, we devote to giving an explicit description on the invertible maps on g that preserve staircase subalgebras.展开更多
Linear algebra has a very important application in physics and technical disciplines. This article conducted a questionnaire survey on the factors that affect the effect of linear algebra learning;the questionnaire co...Linear algebra has a very important application in physics and technical disciplines. This article conducted a questionnaire survey on the factors that affect the effect of linear algebra learning;the questionnaire contains several aspects of learning attitude, learning interest, learning methods, teaching methods, etc.;based on recycling data, cross chi-square test and multiple logistic regression analysis </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">are </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">us</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ed</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> to obtain the factors that affect the effect of linear algebra learning. The research results show that: learning methods, learning attitudes, teaching methods and elementary algebra basics are the main factors that affect the learning effect of linear algebra;among them, there are positive correlations between teaching methods, learning methods, learning attitudes and learning effects;teaching methods, learning methods 3. The three principal components of learning attitude are positively correlated. Based on the research and analysis, the following conclusions are drawn: finding a suitable learning method for the college students and maintaining a positive learning attitude are effective means to improve the linear algebra learning effect of the college students;in teaching, it is recommended to advance with the times, the teaching content and teaching methods innovate to stimulate students’ interest in learning</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">,</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> thus improv</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ing</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the learning effect of college students’ linear algebra courses.展开更多
To find out what knowledge in linear algebra is essential to non-mathematics students, a reverse tracking method was used. Based on practical problems likely to encountered by students in subsequent engineering course...To find out what knowledge in linear algebra is essential to non-mathematics students, a reverse tracking method was used. Based on practical problems likely to encountered by students in subsequent engineering courses, the minimum contents required has been determined. Rules are proposed to meet the background of most freshman students. An application oriented, easy to understand, computer based text book “Applied Popular Linear Algebra with MATLAB” [1] was published.展开更多
With the increasingly widespread application of linear algebra theory, and in its opposite direction is not enough emphasis, linear algebra, several important points： matrix, determinant, linear equations, linear tra...With the increasingly widespread application of linear algebra theory, and in its opposite direction is not enough emphasis, linear algebra, several important points： matrix, determinant, linear equations, linear transformations, matrix keratosis and other anti-deepening understanding of the basics and improve the comprehensive ability to solve problems.展开更多
In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE ar...In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE are presented. We also propose numerical algorithms to develop sharper solution bounds. The obtained bounds can give a supplement to those appeared in the literature. 展开更多
This paper presents a systematic comparison of the curriculum design and application orientation of the linear algebra curriculum in our country and abroad.It explains mainly differences in course objectives,teaching ...This paper presents a systematic comparison of the curriculum design and application orientation of the linear algebra curriculum in our country and abroad.It explains mainly differences in course objectives,teaching content,approaches,and feedback mechanisms,reflecting divergent understandings of the discipline’s value within distinct educational ecosystems.Forward-looking and practical conclusions are proposed across five main directions:optimizing course structure,strengthening practical components,deepening interdisciplinary integration,building faculty capacity,and developing teaching resources.The aim is to provide strong conceptual help and realistic guidance for getting real progress in linear algebra education in China.展开更多
This paper studies the robust stochastic stabilization and robust H∞ control for linear time-delay systems with both Markovian jump parameters and unknown norm-bounded parameter uncertainties. This problem can be sol...This paper studies the robust stochastic stabilization and robust H∞ control for linear time-delay systems with both Markovian jump parameters and unknown norm-bounded parameter uncertainties. This problem can be solved on the basis of stochastic Lyapunov approach and linear matrix inequality (LMI) technique. Sufficient conditions for the existence of stochastic stabilization and robust H∞ state feedback controller are presented in terms of a set of solutions of coupled LMIs. Finally, a numerical example is included to demonstrate the practicability of the proposed methods.展开更多
This project uses knowledge of neural network to analyze if the person under study is analyzed to be Parkinson disease patient or not. Binary classification is constructed based on the multi-feature database. A decisi...This project uses knowledge of neural network to analyze if the person under study is analyzed to be Parkinson disease patient or not. Binary classification is constructed based on the multi-feature database. A decision boundary is clearly plotted to separate patient with and without Parkinson disease. Results show that over 80% accuracy could be obtained with the preliminary results. Future efforts could be performed to construct more complicated neural network to improve the accuracy.展开更多
A surface model called the fibre bundle model is proposed. This model represents a surface locally as a direct product of two curves： a base curve and a fibre curve. We introduce the fibre bundle model and then obtai...A surface model called the fibre bundle model is proposed. This model represents a surface locally as a direct product of two curves： a base curve and a fibre curve. We introduce the fibre bundle model and then obtain the Gaussian curvatures and the mean curvatures of a certain kind of fibre bundle surface models using 1-parameter groups of a linear Lie algebra as fibres. Some examples are given to verify our results.展开更多
In this article, we will explore the applications of linear ordinary differential equations (linear ODEs) in Physics and other branches of mathematics, and dig into the matrix method for solving linear ODEs. Although ...In this article, we will explore the applications of linear ordinary differential equations (linear ODEs) in Physics and other branches of mathematics, and dig into the matrix method for solving linear ODEs. Although linear ODEs have a comparatively easy form, they are effective in solving certain physical and geometrical problems. We will begin by introducing fundamental knowledge in Linear Algebra and proving the existence and uniqueness of solution for ODEs. Then, we will concentrate on finding the solutions for ODEs and introducing the matrix method for solving linear ODEs. Eventually, we will apply the conclusions we’ve gathered from the previous parts into solving problems concerning Physics and differential curves. The matrix method is of great importance in doing higher dimensional computations, as it allows multiple variables to be calculated at the same time, thus reducing the complexity.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
This paper gives and proofs a theorem, for any matrix A, do elementary column operations, change it to a matrix which is partitioned to two blocks which left one is column full rank and right one is zero matrix. That ...This paper gives and proofs a theorem, for any matrix A, do elementary column operations, change it to a matrix which is partitioned to two blocks which left one is column full rank and right one is zero matrix. That is, use a invertible matrix P to let AP = （B,O）, O is zero matrix with n-r columns, r and n is rank and column number of A, so the P＇s right n-r columns is just the basis of the null space of the matrix A. On the basis of the theorem, lots of problems of linear algebra can be resolved and lots of theorems can be proofed by elementary column operations. Perhaps the textbooks used in universities will have a lot of change with the result of the paper. This result is first found by author in 2010.12.8 in http：//www.paper.edu.cn/index.php/default/releasepaper/content/201012-232, but is not formal published.展开更多
文摘Curriculum ideology and politics is the key to carry out the mission of educating people in colleges and universities in the new era.On the problem of integrating the linear algebra course into the ideological and political education,it was expounded from four aspects:the necessity of integrating the course ideology and politics into the teaching of linear algebra,exploring curriculum ideological and political elements,the case design of integrating the course ideology and politics teaching,and the expected effect of integrating linear algebra courses into ideological and political education in the curriculum,in order to have the reference and help function to the educator.
基金supported by the National Natural Science Foundation of China(11101084,11071040)the Fujian Province Nature Science Foundation of China(2013J01005)
文摘Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.
基金The NSF (2009J05005) of Fujian Provincea Key Project of Fujian Provincial Universities-Information Technology Research Based on Mathematics
文摘Let Mn be the algebra of all n × n complex matrices and gl（n, C） be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ ： gl（n, C） → gl（n, C） preserves solvability in both directions if both φ and φ-1 map every solvable Lie subalgebra of gl（n, C） to some solvable Lie subalgebra. In this paper we classify the invertible linear maps preserving solvability on gl（n, C） in both directions. As a sequence, such maps coincide with the invertible linear maps preserving commutativity on Mn in both directions.
文摘The application level of mathematics in each science discipline signs the level of development of this science. With the advancement of science and technology, especially the rapid development of computer technology, mathematics has permeated from natural scientific technology to agricultural construction, from economic activities to all areas of social life. Generally, when the actual problem requires us to provide quantitative results of analysis, forecasting, decision making, control and other aspects for real object under study, we are often inseparable from the application of mathematics. Mathematical modeling is the key to this process, whose purpose is to make mathematics applied to social and social services, and using mathematics to solve practical problems is through mathematical models. When using mathematical methods to solve some practical problems, we usually first transfer practical problems into mathematical language, and then abstract them into a mathematical model.
基金Sponsored by the Ministry of Education Foundation of China(5220308)
文摘A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed. Then an algorithm of 3D object recognition using the linear Lie algebra models is presented. It is a convenient recognition method for the objects which are symmetric about some axis. By using the presented algorithm, the representation matrices of the fibre or the base curve from only finite points of the linear Lie algebra model can be obtained. At last some recognition results of practicalities are given.
基金The NSF (11126121) of ChinaPh.D.Fund (B2010-93) of Henan Polytechnic University+1 种基金Natural Science Research Program (112300410120) of Science and Technology Department of Henan ProvinceNatural Science Research Program (2011B110016) of Education Department of Henan Province
文摘Let g be the general linear Lie algebra consisting of all n x n matrices over a field F and with the usual bracket operation {x, y} =xy - yx. An invertible map φ ： g →g is said to preserve staircase subalgebras if it maps every staircase subalgebra to some staircase subalgebra of the same dimension. In this paper, we devote to giving an explicit description on the invertible maps on g that preserve staircase subalgebras.
文摘Linear algebra has a very important application in physics and technical disciplines. This article conducted a questionnaire survey on the factors that affect the effect of linear algebra learning;the questionnaire contains several aspects of learning attitude, learning interest, learning methods, teaching methods, etc.;based on recycling data, cross chi-square test and multiple logistic regression analysis </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">are </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">us</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ed</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> to obtain the factors that affect the effect of linear algebra learning. The research results show that: learning methods, learning attitudes, teaching methods and elementary algebra basics are the main factors that affect the learning effect of linear algebra;among them, there are positive correlations between teaching methods, learning methods, learning attitudes and learning effects;teaching methods, learning methods 3. The three principal components of learning attitude are positively correlated. Based on the research and analysis, the following conclusions are drawn: finding a suitable learning method for the college students and maintaining a positive learning attitude are effective means to improve the linear algebra learning effect of the college students;in teaching, it is recommended to advance with the times, the teaching content and teaching methods innovate to stimulate students’ interest in learning</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">,</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> thus improv</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ing</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the learning effect of college students’ linear algebra courses.
文摘To find out what knowledge in linear algebra is essential to non-mathematics students, a reverse tracking method was used. Based on practical problems likely to encountered by students in subsequent engineering courses, the minimum contents required has been determined. Rules are proposed to meet the background of most freshman students. An application oriented, easy to understand, computer based text book “Applied Popular Linear Algebra with MATLAB” [1] was published.
文摘With the increasingly widespread application of linear algebra theory, and in its opposite direction is not enough emphasis, linear algebra, several important points： matrix, determinant, linear equations, linear transformations, matrix keratosis and other anti-deepening understanding of the basics and improve the comprehensive ability to solve problems.
文摘In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE are presented. We also propose numerical algorithms to develop sharper solution bounds. The obtained bounds can give a supplement to those appeared in the literature.
文摘This paper presents a systematic comparison of the curriculum design and application orientation of the linear algebra curriculum in our country and abroad.It explains mainly differences in course objectives,teaching content,approaches,and feedback mechanisms,reflecting divergent understandings of the discipline’s value within distinct educational ecosystems.Forward-looking and practical conclusions are proposed across five main directions:optimizing course structure,strengthening practical components,deepening interdisciplinary integration,building faculty capacity,and developing teaching resources.The aim is to provide strong conceptual help and realistic guidance for getting real progress in linear algebra education in China.
文摘This paper studies the robust stochastic stabilization and robust H∞ control for linear time-delay systems with both Markovian jump parameters and unknown norm-bounded parameter uncertainties. This problem can be solved on the basis of stochastic Lyapunov approach and linear matrix inequality (LMI) technique. Sufficient conditions for the existence of stochastic stabilization and robust H∞ state feedback controller are presented in terms of a set of solutions of coupled LMIs. Finally, a numerical example is included to demonstrate the practicability of the proposed methods.
文摘This project uses knowledge of neural network to analyze if the person under study is analyzed to be Parkinson disease patient or not. Binary classification is constructed based on the multi-feature database. A decision boundary is clearly plotted to separate patient with and without Parkinson disease. Results show that over 80% accuracy could be obtained with the preliminary results. Future efforts could be performed to construct more complicated neural network to improve the accuracy.
基金supported by National Natural Science Foundation of China(61174053)National Key Basic Research Program of China(2014CB845301/2/3)+3 种基金Fundamental Research Funds for the Central Universities(2014ZP0021)Cultivation Fund of the Key Scientific and Technical Innovation Project,Ministry of Education of China(708069)partially by Key Laboratory of Autonomous Systems and Networked Control,Ministry of EducationKey Laboratory of Surface Functional Structure Manufacturing of Guangdong Higher Education Institutes
文摘A surface model called the fibre bundle model is proposed. This model represents a surface locally as a direct product of two curves： a base curve and a fibre curve. We introduce the fibre bundle model and then obtain the Gaussian curvatures and the mean curvatures of a certain kind of fibre bundle surface models using 1-parameter groups of a linear Lie algebra as fibres. Some examples are given to verify our results.
文摘In this article, we will explore the applications of linear ordinary differential equations (linear ODEs) in Physics and other branches of mathematics, and dig into the matrix method for solving linear ODEs. Although linear ODEs have a comparatively easy form, they are effective in solving certain physical and geometrical problems. We will begin by introducing fundamental knowledge in Linear Algebra and proving the existence and uniqueness of solution for ODEs. Then, we will concentrate on finding the solutions for ODEs and introducing the matrix method for solving linear ODEs. Eventually, we will apply the conclusions we’ve gathered from the previous parts into solving problems concerning Physics and differential curves. The matrix method is of great importance in doing higher dimensional computations, as it allows multiple variables to be calculated at the same time, thus reducing the complexity.
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This paper gives and proofs a theorem, for any matrix A, do elementary column operations, change it to a matrix which is partitioned to two blocks which left one is column full rank and right one is zero matrix. That is, use a invertible matrix P to let AP = （B,O）, O is zero matrix with n-r columns, r and n is rank and column number of A, so the P＇s right n-r columns is just the basis of the null space of the matrix A. On the basis of the theorem, lots of problems of linear algebra can be resolved and lots of theorems can be proofed by elementary column operations. Perhaps the textbooks used in universities will have a lot of change with the result of the paper. This result is first found by author in 2010.12.8 in http：//www.paper.edu.cn/index.php/default/releasepaper/content/201012-232, but is not formal published.
