As is Wellknown in both elastic mechanics andfluid mechanics, the plane problems are more convenient than space problems. One of the causes is that there has been a complete theory about the complex Junction and the a...As is Wellknown in both elastic mechanics andfluid mechanics, the plane problems are more convenient than space problems. One of the causes is that there has been a complete theory about the complex Junction and the analytic junction, hut in space problems, the case is quite different.We have no effective method to deal with these problems. In this paper, we first introduces general theories of Clifford algebra. Then we emphatically explain Clifford algebra in three dimensions and establish theories of regular Junction in three dimensions analogically to analytic function in plane. Thus we extend some results of plane problem-la three dimensions or high dimensions. Obviously, it is very important for elastic and fluid mechanics. But because Clifford algebra is not a commutative algebra, we can't simply extend the results of two dimensions to high dimensions. The left problems are yet to be found out.展开更多
In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of C^n＋l, so-called complex holomorphic Cli...In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of C^n＋l, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D△^mf= 0, obtain the integral representation formula for the complex holo-morphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of C^n＋1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.展开更多
In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness...In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness, give the definitions of k-poles, isolated and essential singular points and removable singularity, discuss some properties, and further obtain the residue theorems.展开更多
In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl（Vn,n） is studied and Gauss-mean value formula for triharmonic functions with values in a Clif...In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl（Vn,n） is studied and Gauss-mean value formula for triharmonic functions with values in a Clifford algebra Cl（Vn,n） are proved by using Stokes formula and higher order Cauchy-Pompeiu formula. As application some results about growth condition at infinity are obtained.展开更多
The main goal of this article is to present a new result of a possible approach to the geometrical description of the birth and evolution of the universe. The novelty of the article is that it is possible to explain t...The main goal of this article is to present a new result of a possible approach to the geometrical description of the birth and evolution of the universe. The novelty of the article is that it is possible to explain the nature of supersymmetry in terms of the geometric representation of the wave function and to propose a mechanism of spontaneous symmetry breaking of the excitation of the universe with different degrees of freedom. It is under such conditions that the well-known spontaneous symmetry breaking occurs and individual excitation acquires mass. At the same time, a phase transition of the first kind occurs with the formation of a new phase.展开更多
In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to inv...In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.展开更多
A spacial approach to the geometrization the theory of the electron has been proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the ...A spacial approach to the geometrization the theory of the electron has been proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. New experiments concerning the geometric nature wave function of electrons are proposed.展开更多
An approach to the theory of geometrization of the Universe is proposed. The wave function of the Universe is represented by the Clifford number with the transfer rules that have the structure of the Dirac equation fo...An approach to the theory of geometrization of the Universe is proposed. The wave function of the Universe is represented by the Clifford number with the transfer rules that have the structure of the Dirac equation for any manifold. Solutions of this equation may be obtained in terms of the geometric interpretation. A new model is proposed that can explain the manifestation of the dark energy and dark matter in the Universe as a geometrical entity with a mechanism involving the spontaneous symmetry breaking.展开更多
基金This is a comprehensive report at the Second National Symposium on Modern Mathematics and MechanicsProject Supported by the Science Foundation of the Chinese Academy of Sciences
文摘As is Wellknown in both elastic mechanics andfluid mechanics, the plane problems are more convenient than space problems. One of the causes is that there has been a complete theory about the complex Junction and the analytic junction, hut in space problems, the case is quite different.We have no effective method to deal with these problems. In this paper, we first introduces general theories of Clifford algebra. Then we emphatically explain Clifford algebra in three dimensions and establish theories of regular Junction in three dimensions analogically to analytic function in plane. Thus we extend some results of plane problem-la three dimensions or high dimensions. Obviously, it is very important for elastic and fluid mechanics. But because Clifford algebra is not a commutative algebra, we can't simply extend the results of two dimensions to high dimensions. The left problems are yet to be found out.
基金Supported by NNSF of China (6087349, 10871150)863Project of China (2008AA01Z419)+1 种基金RFDP of Higher Education (20060486001)Post-Doctor Foundation ofChina (20090460316)
文摘In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of C^n＋l, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D△^mf= 0, obtain the integral representation formula for the complex holo-morphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of C^n＋1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.
基金Supported by the National Natural Science Foundation of China (10471107)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20060486001)
文摘In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness, give the definitions of k-poles, isolated and essential singular points and removable singularity, discuss some properties, and further obtain the residue theorems.
基金supported by NNSF for Young Scholars of China(11001206)
文摘In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl（Vn,n） is studied and Gauss-mean value formula for triharmonic functions with values in a Clifford algebra Cl（Vn,n） are proved by using Stokes formula and higher order Cauchy-Pompeiu formula. As application some results about growth condition at infinity are obtained.
文摘The main goal of this article is to present a new result of a possible approach to the geometrical description of the birth and evolution of the universe. The novelty of the article is that it is possible to explain the nature of supersymmetry in terms of the geometric representation of the wave function and to propose a mechanism of spontaneous symmetry breaking of the excitation of the universe with different degrees of freedom. It is under such conditions that the well-known spontaneous symmetry breaking occurs and individual excitation acquires mass. At the same time, a phase transition of the first kind occurs with the formation of a new phase.
基金supported by the Daejin University grants in 2010
文摘In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.
文摘A spacial approach to the geometrization the theory of the electron has been proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. New experiments concerning the geometric nature wave function of electrons are proposed.
文摘An approach to the theory of geometrization of the Universe is proposed. The wave function of the Universe is represented by the Clifford number with the transfer rules that have the structure of the Dirac equation for any manifold. Solutions of this equation may be obtained in terms of the geometric interpretation. A new model is proposed that can explain the manifestation of the dark energy and dark matter in the Universe as a geometrical entity with a mechanism involving the spontaneous symmetry breaking.
