A New Version of Orthonormal Polynomial Expansion Method

2007 ◽  
Author(s):  
Nina Bogdanova Bogdanova
Keyword(s):  
Expansion Method ◽  
Polynomial Expansion ◽  
Orthonormal Polynomial ◽  
Polynomial Expansion Method

scholarly journals Fitting by Orthonormal Polynomials of Silver Nanoparticles Spectroscopic Data

2018 ◽  
Vol 173 ◽  
pp. 04003
Author(s):  
Nina Bogdanova ◽  
Mihaela Koleva
Keyword(s):  
Silver Nanoparticles ◽  
Spectroscopic Data ◽  
Expansion Method ◽  
Polynomial Expansion ◽  
Orthonormal Polynomial ◽  
Optimal Behavior ◽  
Dimensional Version ◽  
Experimental Errors ◽  
Polynomial Expansion Method ◽  
First Time

Our original Orthonormal Polynomial Expansion Method (OPEM) in one-dimensional version is applied for first time to describe the silver nanoparticles (NPs) spectroscopic data. The weights for approximation include experimental errors in variables. In this way we construct orthonormal polynomial expansion for approximating the curve on a non equidistant point grid. The corridors of given data and criteria define the optimal behavior of searched curve. The most important subinterval of spectra data is investigated, where the minimum (surface plasmon resonance absorption) is looking for. This study describes the Ag nanoparticles produced by laser approach in a ZnO medium forming a AgNPs/ZnO nanocomposite heterostructure.

scholarly journals Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 27
Author(s):  
Hari Mohan Srivastava ◽  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Expansion Method ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
The Subject ◽  
Polynomial Expansion Method

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

scholarly journals Double Exchange Model in Triangular Lattice Studied by Truncated Polynomial Expansion Method

2011 ◽  
Vol 10 (2) ◽  
pp. 422-432 ◽  
Author(s):  
Gui-Ping Zhang
Keyword(s):  
Triangular Lattice ◽  
Finite Size ◽  
Double Exchange ◽  
Expansion Method ◽  
Exchange Model ◽  
Polynomial Expansion ◽  
Finite Size Effect ◽  
Spin Configuration ◽  
Half Filling ◽  
Polynomial Expansion Method

AbstractThe low temperature properties of double exchange model in triangular lattice are investigated via truncated polynomial expansion method (TPEM), which reduces the computational complexity and enables parallel computation. We found that for the half-filling case a stable 120° spin configuration phase occurs owing to the frustration of triangular lattice and is further stabilized by antiferromagnetic (AF) su-perexchange interaction, while a transition between a stable ferromagnetic (FM) phase and a unique flux phase with small finite-size effect is induced by AF superexchange interaction for the quarter-filling case.

Generalized Polynomial Expansion Method for the Dynamic Analysis of Rotor-Bearing Systems

1991 ◽  
Author(s):  
Ting Nung Shiau ◽  
Jon Li Hwang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Expansion Method ◽  
Polynomial Expansion ◽  
The Finite Element Method ◽  
Rotor Systems ◽  
Generalized Polynomial ◽  
Rotor Bearing ◽  
Polynomial Expansion Method ◽  
Element Method

The determination of critical speeds and modes and the unbalance response of rotor-bearing systems is investigated with the application of a technique called the generalized polynomial expansion method (GPEM). This method can be applied to both linear and nonlinear rotor systems, however, only linear systems are addressed in this paper. Three examples including single spool and dual rotor systems are used to demonstrate the efficiency and the accuracy of this method. The results indicate a very good agreement between the present method and the finite element method (FEM). In addition, computing time will be saved using this method in comparison with the finite element method.

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