在数学史上一个重现的主题是成果的文化背景.无论相信与否,社会背景是有争议的[1].一方面,背景一定是重要的,因为数学基于人类的经验[2];另一方面,社会无法左右数学,因为数学是纯粹的思想.后一个观点经专家通过他们的著作了解过去而得...在数学史上一个重现的主题是成果的文化背景.无论相信与否,社会背景是有争议的[1].一方面,背景一定是重要的,因为数学基于人类的经验[2];另一方面,社会无法左右数学,因为数学是纯粹的思想.后一个观点经专家通过他们的著作了解过去而得到加强:把著名想法的“遗产”[3]归因于过去,但用最新的术语表达,使这些想法显得是一成不变的.Roger Hart的《线性代数学的中国根源(The Chinese Roots of Linear Algebra)》将引起生动的讨论,因为许多关于数学遗产的书籍几乎没有提到中国.展开更多
A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton＇s method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots ...A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton＇s method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton and Newton-type methods. The results show that the proposed method has some more advantages than others. It enriches the methods to find the roots of non-linear equations and it is important in both theory and application.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
In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treat...In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treated. The methods are proved to be quadratically convergent provided the w eak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative meth ods with a variable parameter are developed.展开更多
An algebraic method is proposed to solve a new (2+1)-dimensional Calogero KdV equation and explicitly construct a series of exact solutions including rational solutions, triangular solutions, exponential solution, lin...An algebraic method is proposed to solve a new (2+1)-dimensional Calogero KdV equation and explicitly construct a series of exact solutions including rational solutions, triangular solutions, exponential solution, line soliton solutions, and doubly periodic wave solutions.展开更多
A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence nea...A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton＇s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.展开更多
An improved algorithm for symbolic computations of polynomial-type conservation laws (PCLaws) of ageneral polynomial nonlinear system is presented.The algorithm is implemented in Maple and can be successfully usedfor ...An improved algorithm for symbolic computations of polynomial-type conservation laws (PCLaws) of ageneral polynomial nonlinear system is presented.The algorithm is implemented in Maple and can be successfully usedfor high-dimensional models.Furthermore,the algorithm discards the restriction to evolution equations.The programcan also be used to determine the preferences for a given parameterized nonlinear systems.The code is tested on severalknown nonlinear equations from the soliton theory.展开更多
In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical...In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical modeling and solving and model of evaluation and promotion of the two links, put forward the ＂bystander＂ and ＂the authorities＂ this two characters, and points out that excellent mathematical modeling participants should have ＂from a bystander to the authorities＂ and ＂from the authorities to return to bystanders＂ two-way role transformation ability. Great situation in mathematics teaching, by means of the mathematical modeling formed in the development of the teachers, as well as the teaching thought, teaching experience and achievements, the onward march of mathematical experiment should be faster than mathematical modeling. Our research provides the new paradigm for the math development which will be meaningful.展开更多
In this paper, we categorify the algebra Uq（sl2） with the same approach as in [A. Lauda, Adv. Math. （2010）, arXiv：math.QA/0803.3662; M. Khovanov, Comm. Algebra 11 （2001） 5033]. The algebra U =Uq（sl2） is obtai...In this paper, we categorify the algebra Uq（sl2） with the same approach as in [A. Lauda, Adv. Math. （2010）, arXiv：math.QA/0803.3662; M. Khovanov, Comm. Algebra 11 （2001） 5033]. The algebra U =Uq（sl2） is obtained from Uq（sl2） by adjoining a collection of orthogonal idempotents 1λ,λ ∈ P, in which P is the weight lattice of Uq（sl2）. Under such construction the algebra U is decomposed into a direct sum λ∈p 1λ,U1λ. We set the collection of λ∈ P as the objects of the category U, 1-morphisms from λ to λ′ are given by 1λ,U1λ, and 2-morphisms are constructed by some semilinear form defined on U. Hence we get a 2-category u from the algebra Uq（sl2）.展开更多
In this paper,it is shown that the homoclinic orbits exist in iterated functional systems.so do the solitary wave structures.Moreover,Harr father wavelet,Mexican Cap wavelet,and other closed form wavelets have this so...In this paper,it is shown that the homoclinic orbits exist in iterated functional systems.so do the solitary wave structures.Moreover,Harr father wavelet,Mexican Cap wavelet,and other closed form wavelets have this solitary wave structure,too So wavelet is a certain kind of solitary wave.展开更多
1.引言拟阵(matroid)理论是独立性的一个组合学理论,它起源于线性代数学和图论,并祖发现与其他许多领域皆有深刻联系.在线性代数学,图论,匹配理论,域的扩张理论和径理论(the theory of routing)及其他学科中,存在独立性的自然观念拟阵...1.引言拟阵(matroid)理论是独立性的一个组合学理论,它起源于线性代数学和图论,并祖发现与其他许多领域皆有深刻联系.在线性代数学,图论,匹配理论,域的扩张理论和径理论(the theory of routing)及其他学科中,存在独立性的自然观念拟阵抓住了这些观念共有的组合本质.展开更多
Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) =...Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.展开更多
It is shown that an n × n matrix of continuous linear maps from a pro-C^＊-algebra A to L（H）, which verifies the condition of complete positivity, is of the form [V^＊TijФ（·）V]^n i,where Ф is a represe...It is shown that an n × n matrix of continuous linear maps from a pro-C^＊-algebra A to L（H）, which verifies the condition of complete positivity, is of the form [V^＊TijФ（·）V]^n i,where Ф is a representation of A on a Hilbert space K, V is a bounded linear operator from H to K, and j=1,[Tij]^n i,j=1 is a positive element in the C^＊-algebra of all n×n matrices over the commutant of Ф（A） in L（K）. This generalizes a result of C. Y.Suen in Proc. Amer. Math. Soc., 112（3）, 1991, 709-712. Also, a covariant version of this construction is given.展开更多
This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic im...This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified func- tions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the ＂continuity＂ of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known l-resilient functions modified by Tu-Deng and Tang- Carlet-Tang functions.展开更多
Jimbo-Miwa(JM) equation is one of the famous(3+1)-dimensional conditionally integrable nonlinear dynamical systems. It is pointed out that JM equation and its generalized form possess some types of interesting nonline...Jimbo-Miwa(JM) equation is one of the famous(3+1)-dimensional conditionally integrable nonlinear dynamical systems. It is pointed out that JM equation and its generalized form possess some types of interesting nonlinear excitations such as the algebraic lump-type line solitons, the lumpoff-type half line solitons, and segment solitons.展开更多
Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S^(*n)T S^n}is convergent...Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S^(*n)T S^n}is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H.In this paper,we study the asymptotic T_u-Toeplitzness of weighted composition operators on the Hardy space H^2,where u is a nonconstant inner function.展开更多
文摘在数学史上一个重现的主题是成果的文化背景.无论相信与否,社会背景是有争议的[1].一方面,背景一定是重要的,因为数学基于人类的经验[2];另一方面,社会无法左右数学,因为数学是纯粹的思想.后一个观点经专家通过他们的著作了解过去而得到加强:把著名想法的“遗产”[3]归因于过去,但用最新的术语表达,使这些想法显得是一成不变的.Roger Hart的《线性代数学的中国根源(The Chinese Roots of Linear Algebra)》将引起生动的讨论,因为许多关于数学遗产的书籍几乎没有提到中国.
基金Foundation item： Supported by the National Science Foundation of China（10701066） Supported by the National Foundation of the Education Department of Henan Province（2008A110022）
文摘A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton＇s method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton and Newton-type methods. The results show that the proposed method has some more advantages than others. It enriches the methods to find the roots of non-linear equations and it is important in both theory and application.
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.
文摘In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treated. The methods are proved to be quadratically convergent provided the w eak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative meth ods with a variable parameter are developed.
文摘An algebraic method is proposed to solve a new (2+1)-dimensional Calogero KdV equation and explicitly construct a series of exact solutions including rational solutions, triangular solutions, exponential solution, line soliton solutions, and doubly periodic wave solutions.
基金Foundation item： Supported by the National Science Foundation of China（10701066）
文摘A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton＇s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.
基金the Scientific Fund of Education Department of Zhejiang Province of China under Grant No.20070979the National Natural Science Foundations of China under Grant Nos.10675065,90503006,and 10735030+1 种基金the State Basic Research Program of China (973 Program) under Grant No.2007CB814800the K.C.Wong Magna Fund in Ningbo University
文摘An improved algorithm for symbolic computations of polynomial-type conservation laws (PCLaws) of ageneral polynomial nonlinear system is presented.The algorithm is implemented in Maple and can be successfully usedfor high-dimensional models.Furthermore,the algorithm discards the restriction to evolution equations.The programcan also be used to determine the preferences for a given parameterized nonlinear systems.The code is tested on severalknown nonlinear equations from the soliton theory.
文摘In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical modeling and solving and model of evaluation and promotion of the two links, put forward the ＂bystander＂ and ＂the authorities＂ this two characters, and points out that excellent mathematical modeling participants should have ＂from a bystander to the authorities＂ and ＂from the authorities to return to bystanders＂ two-way role transformation ability. Great situation in mathematics teaching, by means of the mathematical modeling formed in the development of the teachers, as well as the teaching thought, teaching experience and achievements, the onward march of mathematical experiment should be faster than mathematical modeling. Our research provides the new paradigm for the math development which will be meaningful.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10975102, 10871135, 11031005, and 10871227
文摘In this paper, we categorify the algebra Uq（sl2） with the same approach as in [A. Lauda, Adv. Math. （2010）, arXiv：math.QA/0803.3662; M. Khovanov, Comm. Algebra 11 （2001） 5033]. The algebra U =Uq（sl2） is obtained from Uq（sl2） by adjoining a collection of orthogonal idempotents 1λ,λ ∈ P, in which P is the weight lattice of Uq（sl2）. Under such construction the algebra U is decomposed into a direct sum λ∈p 1λ,U1λ. We set the collection of λ∈ P as the objects of the category U, 1-morphisms from λ to λ′ are given by 1λ,U1λ, and 2-morphisms are constructed by some semilinear form defined on U. Hence we get a 2-category u from the algebra Uq（sl2）.
基金The project supported by National Natural Science Foundation of China under Grant Nos.40045016 and No.40175016
文摘In this paper,it is shown that the homoclinic orbits exist in iterated functional systems.so do the solitary wave structures.Moreover,Harr father wavelet,Mexican Cap wavelet,and other closed form wavelets have this solitary wave structure,too So wavelet is a certain kind of solitary wave.
基金supported by the National Natural Science Foundation of China(No.11526123,No.11401273)the Natural Science Foundation of Shandong Province of China(No.ZR2015PA010)
文摘Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.
基金Project supported by the grant CNCSIS (Romanian National Council for Research in High Education)-code A 1065/2006.
文摘It is shown that an n × n matrix of continuous linear maps from a pro-C^＊-algebra A to L（H）, which verifies the condition of complete positivity, is of the form [V^＊TijФ（·）V]^n i,where Ф is a representation of A on a Hilbert space K, V is a bounded linear operator from H to K, and j=1,[Tij]^n i,j=1 is a positive element in the C^＊-algebra of all n×n matrices over the commutant of Ф（A） in L（K）. This generalizes a result of C. Y.Suen in Proc. Amer. Math. Soc., 112（3）, 1991, 709-712. Also, a covariant version of this construction is given.
基金supported by the National Key Basic Research Program of China under Grant No.2013CB834203the National Natural Science Foundation of China under Grant Nos.61472417 and 61472120the Research Council of Norway
文摘This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified func- tions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the ＂continuity＂ of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known l-resilient functions modified by Tu-Deng and Tang- Carlet-Tang functions.
基金Supported by National Natural Science Foundation of China under Grant No.11435005Ningbo Natural Science Foundation(No.2015A610159)+1 种基金granted by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No.xkzwl1502sponsored by K.C.Wong Magna Fund in Ningbo University
文摘Jimbo-Miwa(JM) equation is one of the famous(3+1)-dimensional conditionally integrable nonlinear dynamical systems. It is pointed out that JM equation and its generalized form possess some types of interesting nonlinear excitations such as the algebraic lump-type line solitons, the lumpoff-type half line solitons, and segment solitons.
基金supported by Hankuk University of Foreign Studies Research Fund
文摘Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S^(*n)T S^n}is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H.In this paper,we study the asymptotic T_u-Toeplitzness of weighted composition operators on the Hardy space H^2,where u is a nonconstant inner function.
