Mathematical aspects of the LCAO MO first order density function (4): a discussion on the connection of Taylor series expansion of electronic density (TSED) function with the holographic electron density theorem (HEDT) and the Hohenberg-Kohn theorem (HKT)

2010 ◽  
Vol 49 (4) ◽  
pp. 836-842 ◽  
Author(s):  
R. Carbó-Dorca ◽  
E. Besalú
Keyword(s):  
Density Function ◽  
Electron Density ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Density Theorem ◽  
Electronic Density ◽  
First Order ◽  
Holographic Electron Density Theorem ◽  
Lcao Mo

Income and factor substitution: an investigation on the Solow growth model under the constant elasticity of substitution

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sedat Alatas
Keyword(s):  
Developing Countries ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Elasticity Of Substitution ◽  
Data Driven ◽  
Constant Elasticity ◽  
Content Type ◽  
Constant Elasticity Of Substitution ◽  
First Order

PurposeThe purpose of this study is to examine whether the elasticity of substitution (ES) varies between developed and developing countries.Design/methodology/approachThe author derives the growth regressions from the Solow model under the constant elasticity of substitution production function by using the first-order Taylor series expansion and estimate them for each country group classified based on time-varying behavior of income per worker using the data-driven algorithm.FindingsThe ES is not unitary and varies among country groups. Developed countries generally have a higher ES than developing countries.Originality/valueFor the first time, the author uses the first-order Taylor series expansion to linearize the steady-state value of income per worker, as the author considers this approach to be relatively more straight-forward and tractable. Furthermore, the author estimates the equations using both cross-section and panel data techniques and employs the data-driven algorithm proposed by Phillips and Sul (2007) to classify countries.

Full-Scale Bounds Estimation for the Nonlinear Transient Heat Transfer Problems with Interval Uncertainties

2021 ◽  
pp. 2150026
Author(s):  
Ruifei Peng ◽  
Haitian Yang ◽  
Yanni Xue
Keyword(s):  
Heat Transfer ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Transient Heat Transfer ◽  
High Fidelity ◽  
Interval Scale ◽  
Nonlinear Transient ◽  
Transfer Problems ◽  
Derivatives Of

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

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