It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces ...It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces can not be preserved by equivalent norms.展开更多
We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M a...We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M and the quotient space W/M.展开更多
In this paper, first, we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Cheb...In this paper, first, we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Chebyshev. Examples of those algebras are given including the algebras of continuous functions on compact sets. We also see some results in C＊-algebras and Hilbert C＊-modules. Next, by considering some conditions, we study Chebyshev of subalgebras in C＊-algebras.展开更多
Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. ...Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional Advection-dispersion equation (ADE) is considered. The fractional derivative is described in the Caputo sense. The method is based on Chebyshev approximations. The properties of Chebyshev polynomials are used to reduce ADE to a system of ordinary differential equations, which are solved using the finite difference method (FDM). Moreover, the convergence analysis and an upper bound of the error for the derived formula are given. Numerical solutions of ADE are presented and the results are compared with the exact solution.展开更多
We will define and characterize ε-pseudo Chebyshev and ε-quasi Chebyshev subspaces of Banach spaces. We will prove that a closed subspace W is ε-pseudo Chebyshev if and only if W is ε-quasi Chebyshev.
In this paper, we consider solving the Helmholtz equation in the Cartesian domain , subject to homogeneous Dirichlet boundary condition, discretized with the Chebyshev pseudo-spectral method. The main purpose of this ...In this paper, we consider solving the Helmholtz equation in the Cartesian domain , subject to homogeneous Dirichlet boundary condition, discretized with the Chebyshev pseudo-spectral method. The main purpose of this paper is to present the formulation of a two-level decomposition scheme for decoupling the linear system obtained from the discretization into independent subsystems. This scheme takes advantage of the homogeneity property of the physical problem along one direction to reduce a 2D problem to several 1D problems via a block diagonalization approach and the reflexivity property along the second direction to decompose each of the 1D problems to two independent subproblems using a reflexive decomposition, effectively doubling the number of subproblems. Based on the special structure of the coefficient matrix of the linear system derived from the discretization and a reflexivity property of the second-order Chebyshev differentiation matrix, we show that the decomposed submatrices exhibits a similar property, enabling the system to be decomposed using reflexive decompositions. Explicit forms of the decomposed submatrices are derived. The decomposition not only yields more efficient algorithm but introduces coarse-grain parallelism. Furthermore, it preserves all eigenvalues of the original matrix.展开更多
文摘It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces can not be preserved by equivalent norms.
文摘We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M and the quotient space W/M.
基金The National Natural Science Foundation of China(11301446)the Postdoctoral Science Foundation of China(2013M531789)+1 种基金the Scientific Research Fund of Hunan Provincial Science and Technology Department(2013RS4057)the Research Foundation of Hunan Provincial Education Department(13B116)
文摘In this paper, first, we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Chebyshev. Examples of those algebras are given including the algebras of continuous functions on compact sets. We also see some results in C＊-algebras and Hilbert C＊-modules. Next, by considering some conditions, we study Chebyshev of subalgebras in C＊-algebras.
文摘Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional Advection-dispersion equation (ADE) is considered. The fractional derivative is described in the Caputo sense. The method is based on Chebyshev approximations. The properties of Chebyshev polynomials are used to reduce ADE to a system of ordinary differential equations, which are solved using the finite difference method (FDM). Moreover, the convergence analysis and an upper bound of the error for the derived formula are given. Numerical solutions of ADE are presented and the results are compared with the exact solution.
文摘We will define and characterize ε-pseudo Chebyshev and ε-quasi Chebyshev subspaces of Banach spaces. We will prove that a closed subspace W is ε-pseudo Chebyshev if and only if W is ε-quasi Chebyshev.
文摘In this paper, we consider solving the Helmholtz equation in the Cartesian domain , subject to homogeneous Dirichlet boundary condition, discretized with the Chebyshev pseudo-spectral method. The main purpose of this paper is to present the formulation of a two-level decomposition scheme for decoupling the linear system obtained from the discretization into independent subsystems. This scheme takes advantage of the homogeneity property of the physical problem along one direction to reduce a 2D problem to several 1D problems via a block diagonalization approach and the reflexivity property along the second direction to decompose each of the 1D problems to two independent subproblems using a reflexive decomposition, effectively doubling the number of subproblems. Based on the special structure of the coefficient matrix of the linear system derived from the discretization and a reflexivity property of the second-order Chebyshev differentiation matrix, we show that the decomposed submatrices exhibits a similar property, enabling the system to be decomposed using reflexive decompositions. Explicit forms of the decomposed submatrices are derived. The decomposition not only yields more efficient algorithm but introduces coarse-grain parallelism. Furthermore, it preserves all eigenvalues of the original matrix.
