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1.
In this paper, the properties B^n p,q, and B^n 1,q are introduced.A lot of results on the reflexivity of operator operator subspaces which generalize the results in [1] are obtained.  相似文献   

2.
This paper deals with rational interpolation. From algebraic viewpoint, we present an algebraic formulation of rational interpolation and discuss the existence of the interpolation function. Finally an algorithm for univariate case and an example are presented.  相似文献   

3.
A simple method is developed to identify the rationality of offsets to algebraic curves and surfaces which are given either implicitly or parametrically and to parametrize the offsets if they are rational. In particular, we show that offsets to ellipses and hyperbolas are of nonzero genus except for the circles, and somewhat surprisingly, that offsets to paraboioids and hyperboioids with one sheet can all be rationally parametrtised.  相似文献   

4.
Using value distribution theory and techniques,the problem of the algebroid solutions of second order algebraic differential equation is investigated. Examples show that the results are sharp.  相似文献   

5.
It is proved that the spaces of derivations on some operator algebras are topologically reflexive in the weak operator topology.  相似文献   

6.
Linear Maps Preserving Invertibility or Related Spectral Properties   总被引:2,自引:0,他引:2  
We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrumpreserving elementary operators. Several open problems are also mentioned.  相似文献   

7.
韩德广 《数学杂志》1991,11(1):119-119
本文总假定 H 是可分的 Hilbert 空间;L(H)表示 H 上有界线性算子全体;而 L(?)(H)表示 L(H)上σ-ω算子拓扑连续的线性泛函全体.设(?)L(H)为σ-ω算子拓扑闭的子代数,(?)称为自反的是指(?)=Alg Lat(?)={T∈L(H):TE(?)E (?)E∈Lat(?)},其中 Lat(?)是(?)的不变子空间格.(?)称为超自反的是指存在常数 K>0,使对任意的 T∈L(H)有 d(T,(?))≤K sup{‖P_M~(?)TP_M‖∶M∈Lat(?)}.其中 P_M 是指到 M 上的自伴投影。有关算子代数的超自反性已有一些结果,例如见  相似文献   

8.
This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.  相似文献   

9.
二元插值的一般框架的注记   总被引:2,自引:0,他引:2       下载免费PDF全文
Newton interpolation and Thiele-type continued fractions interpolation may be the favoured linear interpolation and nonlinear interpolation, but these two interpolations could not solve all the interpolant problems. In this paper, several general frames are established by introducing multiple parameters and they are extensions and improvements of those for the general frames studied by Tan and Fang. Numerical examples are given to show the effectiveness of the results in this paper.  相似文献   

10.
In this paper, we introduced the hyperreflexivity of operator algebra A on'Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the invariance of hyperreflexivety under the similarity transformation.  相似文献   

11.
We prove some new results on Hadwin's general version of reflexivity that reduce the study of E-reflexivity (or E-hyperreflexivity) of a linear subspace to a smaller linear subspace. By applying our abstract results, we present a simple proof of D. Hadwin's theorem, which states that every C-algebra is approximately hyperreflexive. We also prove that the image of any C-algebra under any bounded unital homomorphism into the operators on a Banach space is approximately reflexive. We introduce a new version of reflexivity, called approximate algebraic reflexivity, and study its properties.  相似文献   

12.
In this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued Lipschitz functions. We also derive a representation for the generalized bi-circular projections on these spaces.  相似文献   

13.
Nöther-type theorem of piecewise algebraic curves on triangulation   总被引:1,自引:1,他引:0  
The piecewise algebraic curve is a kind generalization of the classical algebraic curve. Nöther-type theorem of piecewise algebraic curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space. In this paper, using the properties of bivariate splines, the Nöther-type theorem of piecewise algebraic curves on the arbitrary triangulation is presented.  相似文献   

14.
We give an elementary proof of the principle of local reflexivity.

  相似文献   


15.
In this paper we propose a construction method of the planar cubic algebraic spline curve with endpoint interpolation conditions and a specific analysis of its properties. The piecewise cubic algebraic curve has G 2 continuous contact with the control polygon at two endpoints and is G 2 continuous between each segments of itself. The process of this method is simple and clear, and provides a new way of thinking to design implicit curves.  相似文献   

16.
Nöther’s theorem of algebraic curves plays an important role in classical algebraic geometry. As the zero set of a bivariate spline, the piecewise algebraic curve is a generalization of the classical algebraic curve. Nöther-type theorem of piecewise algebraic curves is very important to construct the Lagrange interpolation sets for bivariate spline spaces. In this paper, using the characteristics of quasi-cross-cut partition, properties of bivariate splines and results in algebraic geometry, the Nöther-type theorem of piecewise algebraic curves on the quasi-cross-cut is presented.  相似文献   

17.
The piecewise algebraic curve is a kind generalization of the classical algebraic curve.N(o)ther-type theorem of piecewise algebraic curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space. In this paper, using the properties of bivariate splines, the N(o)ther-type theorem of piecewise algebraic curves on the arbitrary triangulation is presented.  相似文献   

18.
19.
A typical approach to decrease computational costs and memory requirements of classical algebraic multigrid methods is to replace a conservative coarsening algorithm and short‐distance interpolation on a fixed number of fine levels by an aggressive coarsening with a long‐distance interpolation. Although the quality of the resulting algebraic multigrid grid preconditioner often deteriorates in terms of convergence rates and iteration counts of the preconditioned iterative solver, the overall performance can improve substantially. We investigate here, as an alternative, a possibility to replace the classical aggressive coarsening by aggregation, which is motivated by the fact that the convergence of aggregation methods can be independent of the problem size provided that the number of levels is fixed. The relative simplicity of aggregation can lead to improved solution and setup costs. The numerical experiments show the relevance of the proposed combination on both academic and benchmark problems in reservoir simulation from oil industry. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

20.
Consider the continuous-time algebraic Riccati equation (CARE) and the discrete-time algebraic Riccati equation (DARE) which arise in linear control and system theory. It is known that appropriate assumptions on the coefficient matrices guarantee the existence and uniqueness of Hermitian positive semidefinite stabilizing solutions. In this note, we apply the theory of condition developed by Rice to define condition numbers of the CARE and DARE in the Frobenius norm, and derive explicit expressions of the condition numbers in a uniform manner. Both the complex case and real case are considered, and connections to certain existing condition numbers of the CARE and DARE are discussed.  相似文献   

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