Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the ...In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the BSE property then A has so.We also establish the converse of this result,whenever X is discrete and A has the BSE-norm property.Furthermore,we prove the same result for the BSE property of type I.Finally,we prove that C0(X,A)has the BSE-norm property if and only if A has so.展开更多
We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations...We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.展开更多
Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implicat...Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implication algebra is discussed. Also, the concept of filter is proposed with some basic properties being studied.展开更多
This paper investigates the high order differential neighbourhoods of holomorphic mappings from S-1 x S-1 to a vector space and gives a new extension of the high-order Virasoro algebra.
The following problem in an OBA （ordered Banach algebra） has been studied by various authors： If a and b are positiveelements in an OBA such that 0 ≤ α ≤ b and ifb has a certain property, under what conditions d...The following problem in an OBA （ordered Banach algebra） has been studied by various authors： If a and b are positiveelements in an OBA such that 0 ≤ α ≤ b and ifb has a certain property, under what conditions does a inherit that property？ This will be referred to as the domination problem. In this paper we will introduce absolute value ｜.｜ in an OBA and obtain results for the domination problem under the more general inequality ｜α｜ ≤｜b｜. We will show that these results are applicable to positive operators on a Banach lattice. Furthermore, it will be demonstrated that some known results for the domination problem in OBAs continue to hold true if 0 ≤ α≤ b is replaced by ｜a｜≤｜b｜.展开更多
In this paper, we study the relation of the algebraic properties of the higher-order Courant bracket and Dorfman bracket on the direct sum bundle TM⊕∧<sup>p</sup>T*M for an m-dimensional smooth mani...In this paper, we study the relation of the algebraic properties of the higher-order Courant bracket and Dorfman bracket on the direct sum bundle TM⊕∧<sup>p</sup>T*M for an m-dimensional smooth manifold M, and a Lie 2-algebra which is a “categorified” version of a Lie algebra. We prove that the higher-order Courant algebroids give rise to a semistrict Lie 2-algebra, and we prove that the higher-order Dorfman algebroids give rise to a hemistrict Lie 2-algebra. Consequently, there is an isomorphism from the higher-order Courant algebroids to the higher-order Dorfman algebroids as Lie 2-algebras homomorphism.展开更多
Some new properties of lattice filters are presented based on the order-preserving mapping and lattice homomorphism, and two necessary and sufficient conditions for lattice filters under the chain type are given. Then...Some new properties of lattice filters are presented based on the order-preserving mapping and lattice homomorphism, and two necessary and sufficient conditions for lattice filters under the chain type are given. Then, the relations between lattice filter and lattice implication algebras （LIAs）, i. e., the relations between lattice filter and LIA-filters, and the related properties are investigated. In addition, three necessary and sufficient conditions for LIA-filters are discussed. The obtained results may serve as some theoretical supports to lattice-valued logical system.展开更多
This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employi...This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays.展开更多
Orders of magnitude reasoning in artificial intelligence (AI) and qualitative algebra are discussed and applied in selecting shield in this paper. It includes basic quantitative calculation, qualitative constraint and...Orders of magnitude reasoning in artificial intelligence (AI) and qualitative algebra are discussed and applied in selecting shield in this paper. It includes basic quantitative calculation, qualitative constraint and principle of orders of magitude reasoning. The method has potential prospects in dealing with the engineering problems.展开更多
Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the...Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the adjoint semigroups. Moreover,the semigroup differences between positive BCK algebras and implicative BCK algebras are discussed,and some semigroup characterizations of implicative BCK algebras are given.展开更多
Lattice implication algebras is an algebraic structure which is established by combining lattice and implication algebras. In this paper,the relationship between lattice implication algebras and MV algebra was discuss...Lattice implication algebras is an algebraic structure which is established by combining lattice and implication algebras. In this paper,the relationship between lattice implication algebras and MV algebra was discussed,and then proved that both of the categorys of the two algebras are categorical equivalence. Finally,the infinitely distributivity in lattice implication algebras were proved.展开更多
In this paper,we combine L-fuzzy syntopogenous structure on X with algebraic structure on X.First,the *-increasing and *-decreasing spaces have been studied.Second,we define a-order-convexity on syntopogenous structur...In this paper,we combine L-fuzzy syntopogenous structure on X with algebraic structure on X.First,the *-increasing and *-decreasing spaces have been studied.Second,we define a-order-convexity on syntopogenous structures(X,S,≤).some important properties of a-order-convexity have been obtained.展开更多
In this paper, we denote by A a commutative and unitary algebra over a commutative field K of characteristic 0 and r an integer ≥1. We define the notion of r-Jacobi algebra A and we construct the canonical form assoc...In this paper, we denote by A a commutative and unitary algebra over a commutative field K of characteristic 0 and r an integer ≥1. We define the notion of r-Jacobi algebra A and we construct the canonical form associated with the r-Jacobi algebra A.展开更多
Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract ...Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.展开更多
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
基金Supported by the Natural Science Foundation of Guangdong Province（04010474） Supported by the Foundation of the Education Department of Anhui Province for Outstanding Young Teachers in University（2011SQRL172）
文摘This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
文摘In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the BSE property then A has so.We also establish the converse of this result,whenever X is discrete and A has the BSE-norm property.Furthermore,we prove the same result for the BSE property of type I.Finally,we prove that C0(X,A)has the BSE-norm property if and only if A has so.
基金supported by the Natural Science Foundationof China (10471065)the Natural Science Foundation of Guangdong Province (N04010474)
文摘We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.
基金Science & Technology Depart ment of Sichuan Province,China(No.03226125)the Education Foundation of Sichuan Province,China(No.2006A084)
文摘Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implication algebra is discussed. Also, the concept of filter is proposed with some basic properties being studied.
基金This work is supported in part by the Natural ScienceFoundation of Hainan
文摘This paper investigates the high order differential neighbourhoods of holomorphic mappings from S-1 x S-1 to a vector space and gives a new extension of the high-order Virasoro algebra.
文摘The following problem in an OBA （ordered Banach algebra） has been studied by various authors： If a and b are positiveelements in an OBA such that 0 ≤ α ≤ b and ifb has a certain property, under what conditions does a inherit that property？ This will be referred to as the domination problem. In this paper we will introduce absolute value ｜.｜ in an OBA and obtain results for the domination problem under the more general inequality ｜α｜ ≤｜b｜. We will show that these results are applicable to positive operators on a Banach lattice. Furthermore, it will be demonstrated that some known results for the domination problem in OBAs continue to hold true if 0 ≤ α≤ b is replaced by ｜a｜≤｜b｜.
文摘In this paper, we study the relation of the algebraic properties of the higher-order Courant bracket and Dorfman bracket on the direct sum bundle TM⊕∧<sup>p</sup>T*M for an m-dimensional smooth manifold M, and a Lie 2-algebra which is a “categorified” version of a Lie algebra. We prove that the higher-order Courant algebroids give rise to a semistrict Lie 2-algebra, and we prove that the higher-order Dorfman algebroids give rise to a hemistrict Lie 2-algebra. Consequently, there is an isomorphism from the higher-order Courant algebroids to the higher-order Dorfman algebroids as Lie 2-algebras homomorphism.
基金The National Natural Science Founda-tion of China (No.60474022)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20060613007)
文摘Some new properties of lattice filters are presented based on the order-preserving mapping and lattice homomorphism, and two necessary and sufficient conditions for lattice filters under the chain type are given. Then, the relations between lattice filter and lattice implication algebras （LIAs）, i. e., the relations between lattice filter and LIA-filters, and the related properties are investigated. In addition, three necessary and sufficient conditions for LIA-filters are discussed. The obtained results may serve as some theoretical supports to lattice-valued logical system.
基金supported by the National Natural Science Foundation of China (6057408860274014)
文摘This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays.
文摘Orders of magnitude reasoning in artificial intelligence (AI) and qualitative algebra are discussed and applied in selecting shield in this paper. It includes basic quantitative calculation, qualitative constraint and principle of orders of magitude reasoning. The method has potential prospects in dealing with the engineering problems.
文摘Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the adjoint semigroups. Moreover,the semigroup differences between positive BCK algebras and implicative BCK algebras are discussed,and some semigroup characterizations of implicative BCK algebras are given.
文摘Lattice implication algebras is an algebraic structure which is established by combining lattice and implication algebras. In this paper,the relationship between lattice implication algebras and MV algebra was discussed,and then proved that both of the categorys of the two algebras are categorical equivalence. Finally,the infinitely distributivity in lattice implication algebras were proved.
文摘In this paper,we combine L-fuzzy syntopogenous structure on X with algebraic structure on X.First,the *-increasing and *-decreasing spaces have been studied.Second,we define a-order-convexity on syntopogenous structures(X,S,≤).some important properties of a-order-convexity have been obtained.
文摘In this paper, we denote by A a commutative and unitary algebra over a commutative field K of characteristic 0 and r an integer ≥1. We define the notion of r-Jacobi algebra A and we construct the canonical form associated with the r-Jacobi algebra A.
基金supported by the National Key Basic Research Project of China (973 Program)(No. 2004CB318000)
文摘Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.
