An optimal localization of the canonical molecular orbitals of molecules CH4, C2H6, C2H4, C,H, was successfully performed by means of projection operator method, so for as the restriction of orthogonality is given up.
This paper proves that the linear operator A (1,4) A formed by (1,4)-inverse A (1,4) of Matrix A is the orthogonal projection operator. Its application in the maximum quadratic of linear equations can obtain the geometrical principle of the maximum quadratic orthogonal projection.
For nonlinear two point boundary value problems we show an asymptotic error expansion where u_b is p_1 type finite element solution, Iu is p_1 type interpolant of the solution u, p_h is Ritz projection operator, e is a sufficiently smooth function, ||r||, ∞≤C·h~4.
Neuman discussed the projective operator class {L_n~2} in [1] and asserted that there exists minimal projection in {L_n~2}, But we got the negtive result.
In this paper, via a special corepresentation V0 of A, we construct a pair of sets, and using the theory of Hilbert C*-module, we prove that they are exactly A and A respectively, where A corresponds to Baaj and Skandalis-construction. We also prove that for any a ? G there exists a projective operator pa in A such that dim(α) = dim(pα).
This paper gives some applications of the extreme principal angles between subspaces in Cn. Such applications include matrix approximation, perturbation analysis of projective operator, condition number estimation, perturbation analysis of group inverse, Drazin inverse and Bott-Duffin systems.
A basic conception of a so-called failure self-diagnosis system is presented in this paper, i.e. based on a priori information and measurements of some states and parameters of a system, the residual and failure signature matrix are computed by a computer so as to form the distinguishable projection operators (DPO).
The rorthogonal projective operators on a normed spaces are defined and its operational properties are discussed by using sullivan′s thoughts on rorthogonality.
The problems for searching zeros of projective operators about compact convex subset have many applications in science and engineering. In this paper, we consider Hopfield method for projective operators. We establish Hopfield model and prove the model抯 convergence and stability.
It is proved that the metric projection operator onto a finite-dimensional Chebyshev subspaceM ?C [a, b] locally uniformly satisfies the Lipschitz condition on the SetC[a,b]M.
Using the nearest-neighbor approximation the Hamiltonian is factorized according to different values of the projection operator of the total spin momentum on the direction of the external magnetic field.
In this paper theq-normal-ordered product is realized in theq-analogue bosonic oscillator, the expression of the vacuum projective operator in the form ofq-operators is obtained, some initial applications are also given.
The aim of this article is to characterize compactly supported refinable distributions in Triebel-Lizorkin spaces and Besov spaces by projection operators on certain wavelet space and by some operators on a finitely dimensional space.
We study the similarity of perturbed compact operators to operators of block-diagonal structure with respect to some family of orthogonal projection operators, which allows us to refine and essentially strengthen results due to R.
The proposed procedure has allowed us to find linear combinations of operators which can be considered as the projective operators responsible for each spectral component of spin 1/2, scalar coupled to a quadrupole nucleus (S = 5/2).
投影算子
projection operator
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