We present a noncommutative version of the Ablowitz-Kaup-Newell-Segur （AKNS） equation hierarchy, which possesses the zero curvature representation. Furthermore, we derive the noncommutative AKNS equation from the no...We present a noncommutative version of the Ablowitz-Kaup-Newell-Segur （AKNS） equation hierarchy, which possesses the zero curvature representation. Furthermore, we derive the noncommutative AKNS equation from the noncommutative （anti-）self-dual Yang-Mills equation by reduction, which is an evidence for the noncommutative Ward conjecture. Finally, the integrable coupling system of the noncommutative AKNS equation hierarchy is constructed by using the Kronecker product.展开更多
Firstly, a vector loop algebra G3 is constructed, by use of it multi-component KN hierarchy is obtained. Further, by taking advantage of the extending vector loop algebras G6 and G9 of G3 the double integrable couplin...Firstly, a vector loop algebra G3 is constructed, by use of it multi-component KN hierarchy is obtained. Further, by taking advantage of the extending vector loop algebras G6 and G9 of G3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively. Finally, Hamiltonian structures of obtained system are given by quadratic-form identity.展开更多
Based on the matrix Lie super algebra and supertrace identity, the integrable super-Geng hierarchy with self-consistent is established. Furthermore, we establish the infinitely many conservation laws for the integrabl...Based on the matrix Lie super algebra and supertrace identity, the integrable super-Geng hierarchy with self-consistent is established. Furthermore, we establish the infinitely many conservation laws for the integrable super-Geng hierarchy. The methods derived by us can be generalized to other nonlinear equation hierarchies.展开更多
American Transcendentalism aroused New Englanders to individualism enlightenment. Kate Chopin' s The Awakening, un doubtedly voices female quest for identity. The novel was banned by the force of social convention...American Transcendentalism aroused New Englanders to individualism enlightenment. Kate Chopin' s The Awakening, un doubtedly voices female quest for identity. The novel was banned by the force of social conventions, for the sociological role it played in form of literature, negotiating female professional identity, social role identity and sexual identity. This treatise analyzes the awakening of women conscious regarding identity and contradiction it brings therefore with social conventions, and argues the inevitable fate of the sex to self-isolation and self-destruction is caused by the prudery conventions. It maintains to review the sociological function of the piece and reconstruct interdisciplinary perspective of literature and sociology, appeal harmony between two sexes.展开更多
In this paper, we introduce the supertrace identity and its applications. A new eight-dimensional Lie superalgebra is constructed and the super-Dirac hierarchy is derived. By the supertrace identity, we obtain the sup...In this paper, we introduce the supertrace identity and its applications. A new eight-dimensional Lie superalgebra is constructed and the super-Dirac hierarchy is derived. By the supertrace identity, we obtain the super-bi-Hamiltonian structure of the super-Dirac hierarchy.展开更多
The Hamiltonian structure of.the integrable couplings obtained by our method has not been solved. In this paper, the Hamiltonian structure of the KN hierarchy is obtained by making use of the quadratlc-form identity.
The author examines the differentiation of self-identity, school treatment, and academic struggle between two Asian American students in U.S. Midwest urban school environments. Using an interview study, the author foc...The author examines the differentiation of self-identity, school treatment, and academic struggle between two Asian American students in U.S. Midwest urban school environments. Using an interview study, the author focuses on understanding the students＇ perspectives in relation to the label of model minority. The purpose of the study is to investigate how social, academic, and economic factors affect these students, including different outcomes in terms of school achievement and self-identity formation. The findings aim to help urban educators approach complex factors regarding minority students＇ educational opportunities. Comprehensive results identified that： （1） The concept of model minority significantly affects Asian American students at all levels of daily life; （2） Urban schools continue reinforcing social reproduction and producing perceptions based on socioeconomic background and intersectional discrimination; （3） The evidence in the study shows that school environments do not aid students in valuing their cultural capital; （4） Students from different social classes present different linguistic and behavioral patterns; and （5） Social stratification significantly influences students＇ perspectives in response to the Asian stereotype, self-identity, and racial hierarchy in school and society.展开更多
Based on a kind of Lie a/gebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using th...Based on a kind of Lie a/gebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using the methods proposed by Ma and Gao. With the help of variational identity, we get the Hamiltonian structure of the hierarchy.展开更多
A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obt...A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obtained respectively under the framework of zero curvature equation, which is derived from the compatibility of the isospectral problems expressed by Hirota operators. At the same time, we obtain the Hamiltonian structure of the first hierarchy and the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.展开更多
文摘We present a noncommutative version of the Ablowitz-Kaup-Newell-Segur （AKNS） equation hierarchy, which possesses the zero curvature representation. Furthermore, we derive the noncommutative AKNS equation from the noncommutative （anti-）self-dual Yang-Mills equation by reduction, which is an evidence for the noncommutative Ward conjecture. Finally, the integrable coupling system of the noncommutative AKNS equation hierarchy is constructed by using the Kronecker product.
文摘Firstly, a vector loop algebra G3 is constructed, by use of it multi-component KN hierarchy is obtained. Further, by taking advantage of the extending vector loop algebras G6 and G9 of G3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively. Finally, Hamiltonian structures of obtained system are given by quadratic-form identity.
基金Supported by the National Natural Science Foundation of China（11271008, 61072147, 11547175） Supported by the Science and Technology Department of Henan Province（152300410230）+1 种基金 Supported by the Key Scientific Research Projects of Henan Province（16A110026） Supported by the Education Department of Henan Province（13All0101）
文摘Based on the matrix Lie super algebra and supertrace identity, the integrable super-Geng hierarchy with self-consistent is established. Furthermore, we establish the infinitely many conservation laws for the integrable super-Geng hierarchy. The methods derived by us can be generalized to other nonlinear equation hierarchies.
文摘American Transcendentalism aroused New Englanders to individualism enlightenment. Kate Chopin' s The Awakening, un doubtedly voices female quest for identity. The novel was banned by the force of social conventions, for the sociological role it played in form of literature, negotiating female professional identity, social role identity and sexual identity. This treatise analyzes the awakening of women conscious regarding identity and contradiction it brings therefore with social conventions, and argues the inevitable fate of the sex to self-isolation and self-destruction is caused by the prudery conventions. It maintains to review the sociological function of the piece and reconstruct interdisciplinary perspective of literature and sociology, appeal harmony between two sexes.
基金supported by the Joint Foundation of NSFC-Guangdong of China(No.U1133001/L03)
文摘In this paper, we introduce the supertrace identity and its applications. A new eight-dimensional Lie superalgebra is constructed and the super-Dirac hierarchy is derived. By the supertrace identity, we obtain the super-bi-Hamiltonian structure of the super-Dirac hierarchy.
基金The project supported by National Natural Science Foundation of China under Grant No. 10471139
文摘The Hamiltonian structure of.the integrable couplings obtained by our method has not been solved. In this paper, the Hamiltonian structure of the KN hierarchy is obtained by making use of the quadratlc-form identity.
文摘The author examines the differentiation of self-identity, school treatment, and academic struggle between two Asian American students in U.S. Midwest urban school environments. Using an interview study, the author focuses on understanding the students＇ perspectives in relation to the label of model minority. The purpose of the study is to investigate how social, academic, and economic factors affect these students, including different outcomes in terms of school achievement and self-identity formation. The findings aim to help urban educators approach complex factors regarding minority students＇ educational opportunities. Comprehensive results identified that： （1） The concept of model minority significantly affects Asian American students at all levels of daily life; （2） Urban schools continue reinforcing social reproduction and producing perceptions based on socioeconomic background and intersectional discrimination; （3） The evidence in the study shows that school environments do not aid students in valuing their cultural capital; （4） Students from different social classes present different linguistic and behavioral patterns; and （5） Social stratification significantly influences students＇ perspectives in response to the Asian stereotype, self-identity, and racial hierarchy in school and society.
基金Supported by the Natural Science Foundation of China under Grant Nos.11271008,61072147,11071159the Shanghai Leading Academic Discipline Project under Grant No.J50101the Shanghai Univ.Leading Academic Discipline Project(A.13-0101-12-004)
文摘Based on a kind of Lie a/gebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using the methods proposed by Ma and Gao. With the help of variational identity, we get the Hamiltonian structure of the hierarchy.
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1410800the Science Foundation of Key Laboratory of Mathematics Mechanization under Grant No.KLMM0806
文摘A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obtained respectively under the framework of zero curvature equation, which is derived from the compatibility of the isospectral problems expressed by Hirota operators. At the same time, we obtain the Hamiltonian structure of the first hierarchy and the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.
