On the uniqueness of Gaussian ansatz parameters equations: generalized projection operator method

2004 ◽  
Vol 332 (3-4) ◽  
pp. 239-243 ◽  
Author(s):  
P.K.A. Wai ◽  
K. Nakkeeran
Keyword(s):  
Projection Operator ◽  
Operator Method ◽  
Generalized Projection ◽  
Generalized Projection Operator ◽  
Projection Operator Method

The generalized -projection operator and set-valued variational inequalities in Banach spaces

2009 ◽  
Vol 71 (7-8) ◽  
pp. 2481-2490 ◽  
Author(s):  
Ke-Qing Wu ◽  
Nan-Jing Huang
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Projection Operator ◽  
Generalized Projection ◽  
Generalized Projection Operator

scholarly journals The generalized projection methods in countably normed spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Tawfeek ◽  
Nashat Faried ◽  
H. A. El-Sharkawy
Keyword(s):  
Banach Spaces ◽  
Projection Operator ◽  
Metric Projection ◽  
Projection Methods ◽  
Generalized Projection ◽  
Uniformly Convex ◽  
Normed Spaces ◽  
Generalized Projection Operator ◽  
Set Valued Mapping ◽  
Uniformly Smooth

AbstractLet E be a Banach space with dual space $E^{*}$ E ∗ , and let K be a nonempty, closed, and convex subset of E. We generalize the concept of generalized projection operator “$\Pi _{K}: E \rightarrow K$ Π K : E → K ” from uniformly convex uniformly smooth Banach spaces to uniformly convex uniformly smooth countably normed spaces and study its properties. We show the relation between J-orthogonality and generalized projection operator $\Pi _{K}$ Π K and give examples to clarify this relation. We introduce a comparison between the metric projection operator $P_{K}$ P K and the generalized projection operator $\Pi _{K}$ Π K in uniformly convex uniformly smooth complete countably normed spaces, and we give an example explaining how to evaluate the metric projection $P_{K}$ P K and the generalized projection $\Pi _{K}$ Π K in some cases of countably normed spaces, and this example illustrates that the generalized projection operator $\Pi _{K}$ Π K in general is a set-valued mapping. Also we generalize the generalized projection operator “$\pi _{K}: E^{*} \rightarrow K$ π K : E ∗ → K ” from reflexive Banach spaces to uniformly convex uniformly smooth countably normed spaces and study its properties in these spaces.

Novel Technique for Quantum-Mechanical Eigenstate and Eigenvalue Calculations based on Seke's Self-Consistent Projection-Operator Method

1997 ◽  
Vol 11 (06) ◽  
pp. 245-258 ◽  
Author(s):  
J. Seke ◽  
A. V. Soldatov ◽  
N. N. Bogolubov
Keyword(s):  
Projection Operator ◽  
Equations Of Motion ◽  
Operator Method ◽  
Approximation Order ◽  
Quantum Mechanical ◽  
Approximation Technique ◽  
Operator Structure ◽  
Projection Operator Method ◽  
Self Consistent ◽  
Effective Hamiltonians

Seke's self-consistent projection-operator method has been developed for deriving non-Markovian equations of motion for probability amplitudes of a relevant set of state vectors. This method, in a Born-like approximation, leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamiltonians. In the present paper, in order to explain the efficiency of Seke's method in particular applications, its algebraic operator structure is analyzed and a new successive approximation technique for the calculation of eigenstates and eigenvalues of an arbitrary quantum-mechanical system is developed. Unlike most perturbative techniques, in the present case each order of the approximation determines its own effective (approximating) Hamiltonian ensuring self-consistency and formal exactness of all results in the corresponding approximation order.

ERRATA: "PHOTOFIELD EMISSION CALCULATIONS BY USING PROJECTION OPERATOR METHOD"

2007 ◽  
Vol 21 (24) ◽  
pp. 1651-1652
Author(s):  
R. K. THAPA ◽  
M. P. GHIMIRE ◽  
GUNAKAR DAS ◽  
S. R. GURUNG ◽  
B. I. SHARMA ◽  
...  
Keyword(s):  
Projection Operator ◽  
Operator Method ◽  
Projection Operator Method
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