In this paper, it is proved that if A is a normal proper contraction on Hilbert space H and F(z) = U(z) + iV(z) is operator-valued analytic on the unit disc Delta and 0 < p < 1, then parallel to F(A)parallel to(...In this paper, it is proved that if A is a normal proper contraction on Hilbert space H and F(z) = U(z) + iV(z) is operator-valued analytic on the unit disc Delta and 0 < p < 1, then parallel to F(A)parallel to(p) less than or equal to parallel to F(0)parallel to(p) + C-p (1 - parallel to A parallel to)(-2) [GRAPHICS]展开更多
This paper consists of dissipative properties and results of dissipation on infinitesimal generator of a C0-semigroup of ω-order preserving partial contraction mapping (ω-OCPn) in semigroup of linear operator. The p...This paper consists of dissipative properties and results of dissipation on infinitesimal generator of a C0-semigroup of ω-order preserving partial contraction mapping (ω-OCPn) in semigroup of linear operator. The purpose of this paper is to establish some dissipative properties on ω-OCPn which have been obtained in the various theorems (research results) and were proved.展开更多
I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is the...I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.展开更多
In this paper, we prove that every operator in a class of contraction operators on a Banach space whose spectrum contains the unit circle has a nontrivial hyperinvariant subspace.
This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed ...This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed point theory is a beautiful mixture of Mathematical analysis to explain some conditions in which maps give excellent solutions. Here later many mathematicians used this fixed point theory to establish their results, see for instance, Picard-Lindel of Theorem, The Picard theorem, Implicit function theorem etc. Also, we developed ideas that many of known fixed point theorems can easily be derived from the Banach theorem. It extends some recent works on the extension of Banach contraction principle to metric space with norm spaces.展开更多
In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm i...In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm in a Banach space is also considered. The results extend some very recent theorems of W. Takahashi.展开更多
1 Introduction and main resultsARVESON in ref. [1] generalized the classical Hahn-Banach Extension Theorem for linear func-tionals to the self-adjoint linear closed subspace of C~* -algebras. From then on numerous au-...1 Introduction and main resultsARVESON in ref. [1] generalized the classical Hahn-Banach Extension Theorem for linear func-tionals to the self-adjoint linear closed subspace of C~* -algebras. From then on numerous au-thors have given various generalizations of the non-commutative Hahn-Banach-Arveson Theo-rem of ref. [1]. The following extension theorem is due to G. Wittstock.展开更多
Forward modeling is the basis of inversion imaging and quantitative interpretation for DC resistivity exploration.Currently,a numerical model of the DC resistivity method must be finely divided to obtain a highly accu...Forward modeling is the basis of inversion imaging and quantitative interpretation for DC resistivity exploration.Currently,a numerical model of the DC resistivity method must be finely divided to obtain a highly accurate solution under complex conditions,resulting in a long calculation time and large storage.Therefore,we propose a 3D numerical simulation method in a mixed space-wavenumber domain to overcome this challenge.The partial differential equation about abnormal potential is transformed into many independent ordinary differential equations with different wavenumbers using a 2D Fourier transform along the x axis and y axis direction.In this way,a large-scale 3D numerical simulation problem is decomposed into several 1D numerical simulation problems,which significantly reduces the computational and storage requirements.In addition,these ordinary 1D differential equations with different wavenumbers are independent of each other and high parallelelism of the algorithm.They are solved using a finite-element algorithm combined with a chasing method,and the obtained solution is modified using a contraction operator.In this method,the vertical direction is reserved as the spatial domain,then grid size can be determined flexibly based on the underground current density distribution,which considers the solution accuracy and calculation efficiency.In addition,for the first time,we use the contraction operator in the integral equation method to iterate the algorithm.The algorithm takes advantage of the high efficiency of the standard Fourier transform and chasing method,as well as the fast convergence of the contraction operator.We verified the accuracy of the algorithm and the convergence of the contraction operator.Compared with a volume integral method and goal-oriented adaptive finite-element method,the proposed algorithm has lower memory requirements and high computational efficiency,making it suitable for calculating a model with large-scale nodes.Moreover,different examples are used to verify the high adaptab展开更多
文摘In this paper, it is proved that if A is a normal proper contraction on Hilbert space H and F(z) = U(z) + iV(z) is operator-valued analytic on the unit disc Delta and 0 < p < 1, then parallel to F(A)parallel to(p) less than or equal to parallel to F(0)parallel to(p) + C-p (1 - parallel to A parallel to)(-2) [GRAPHICS]
文摘This paper consists of dissipative properties and results of dissipation on infinitesimal generator of a C0-semigroup of ω-order preserving partial contraction mapping (ω-OCPn) in semigroup of linear operator. The purpose of this paper is to establish some dissipative properties on ω-OCPn which have been obtained in the various theorems (research results) and were proved.
基金Project supported by the National Natural Science Foundation of China the Doctoral Progamme Foundation of China and the Foundation of Wuhan University.
文摘I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.
基金the Natural Science Foundation of P.R.China (No.10771039)
文摘In this paper, we prove that every operator in a class of contraction operators on a Banach space whose spectrum contains the unit circle has a nontrivial hyperinvariant subspace.
文摘This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed point theory is a beautiful mixture of Mathematical analysis to explain some conditions in which maps give excellent solutions. Here later many mathematicians used this fixed point theory to establish their results, see for instance, Picard-Lindel of Theorem, The Picard theorem, Implicit function theorem etc. Also, we developed ideas that many of known fixed point theorems can easily be derived from the Banach theorem. It extends some recent works on the extension of Banach contraction principle to metric space with norm spaces.
文摘In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm in a Banach space is also considered. The results extend some very recent theorems of W. Takahashi.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19671042).
文摘1 Introduction and main resultsARVESON in ref. [1] generalized the classical Hahn-Banach Extension Theorem for linear func-tionals to the self-adjoint linear closed subspace of C~* -algebras. From then on numerous au-thors have given various generalizations of the non-commutative Hahn-Banach-Arveson Theo-rem of ref. [1]. The following extension theorem is due to G. Wittstock.
文摘Forward modeling is the basis of inversion imaging and quantitative interpretation for DC resistivity exploration.Currently,a numerical model of the DC resistivity method must be finely divided to obtain a highly accurate solution under complex conditions,resulting in a long calculation time and large storage.Therefore,we propose a 3D numerical simulation method in a mixed space-wavenumber domain to overcome this challenge.The partial differential equation about abnormal potential is transformed into many independent ordinary differential equations with different wavenumbers using a 2D Fourier transform along the x axis and y axis direction.In this way,a large-scale 3D numerical simulation problem is decomposed into several 1D numerical simulation problems,which significantly reduces the computational and storage requirements.In addition,these ordinary 1D differential equations with different wavenumbers are independent of each other and high parallelelism of the algorithm.They are solved using a finite-element algorithm combined with a chasing method,and the obtained solution is modified using a contraction operator.In this method,the vertical direction is reserved as the spatial domain,then grid size can be determined flexibly based on the underground current density distribution,which considers the solution accuracy and calculation efficiency.In addition,for the first time,we use the contraction operator in the integral equation method to iterate the algorithm.The algorithm takes advantage of the high efficiency of the standard Fourier transform and chasing method,as well as the fast convergence of the contraction operator.We verified the accuracy of the algorithm and the convergence of the contraction operator.Compared with a volume integral method and goal-oriented adaptive finite-element method,the proposed algorithm has lower memory requirements and high computational efficiency,making it suitable for calculating a model with large-scale nodes.Moreover,different examples are used to verify the high adaptab
