Permutationally Invariant Polynomial Expansions with Unrestricted Complexity

2021 ◽  
Vol 17 (9) ◽  
pp. 5440-5455 ◽  
Author(s):  
Daniel R. Moberg ◽  
Ahren W. Jasper
Keyword(s):  
Invariant Polynomial ◽  
Polynomial Expansions

An accurate full-dimensional potential energy surface for the reaction OH + SO → H + SO2

2021 ◽  
Vol 23 (1) ◽  
pp. 487-497
Author(s):  
Jie Qin ◽  
Jun Li
Keyword(s):  
Neural Network ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Invariant Polynomial ◽  
Network Approach ◽  
Neural Network Approach ◽  
Polynomial Neural Network

An accurate full-dimensional PES for the OH + SO ↔ H + SO2 reaction is developed by the permutation invariant polynomial-neural network approach.

Microwave On-Line Measurements on Conveyed Products Application to Paper and Wood Industries

1994 ◽  
Vol 347 ◽  
Author(s):  
J.Ch. Bolomey ◽  
G. Cottard ◽  
P. Berthaud ◽  
A. Lemaitre ◽  
J. F. Portala
Keyword(s):  
High Speed ◽  
Transformation Process ◽  
Wood Material ◽  
Quantitative Measurements ◽  
On Line ◽  
Phase Data ◽  
Polynomial Expansions ◽  
Physical Quantities ◽  
Data Calibration

ABSTRACTMicrowave multiport sensors have been shown to provide some unique capabilities to achieve real-time testing of products conveyed at high speed. In many applications, quantitative measurements of physical quantities such as moisture content, density, etc… are required, either to guarantee reliable production or to optimally control a fabrication/transformation process. In this paper, different ways of extracting such physical quantities from microwave measurements performed by multiport sensors are presented. Model approaches are used, based on polynomial expansions of the physical quantities to be measured as a function of the microwave amplitude and phase data. Calibration procedures have been investigated for both paper and wood material samples. Comparisons between in-situ, microwave and conventional, measurements are analysed.

A Novel Sampling Method based on Orthogonal Polynomial Expansions and Applications

2021 ◽  
Author(s):  
Zhenyu Cui ◽  
Justin Kirkby ◽  
Duy Nguyen ◽  
Stephen Michael Taylor
Keyword(s):  
Orthogonal Polynomial ◽  
Sampling Method ◽  
Polynomial Expansions

scholarly journals Low-redshift measurement of the sound horizon through gravitational time-delays

2019 ◽  
Vol 632 ◽  
pp. A91 ◽  
Author(s):  
Nikki Arendse ◽  
Adriano Agnello ◽  
Radosław J. Wojtak
Keyword(s):  
Time Delay ◽  
Standard Model ◽  
Percent Level ◽  
Acoustic Oscillations ◽  
Microwave Background ◽  
Direct Measurements ◽  
The Standard Model ◽  
Model Independent ◽  
Competitive Test ◽  
Polynomial Expansions

Context. The matter sound horizon can be infered from the cosmic microwave background within the Standard Model. Independent direct measurements of the sound horizon are then a probe of possible deviations from the Standard Model. Aims. We aim at measuring the sound horizon rs from low-redshift indicators, which are completely independent of CMB inference. Methods. We used the measured product H(z)rs from baryon acoustic oscillations (BAO) together with supernovae Ia to constrain H(z)/H0 and time-delay lenses analysed by the H0LiCOW collaboration to anchor cosmological distances (∝ H0−1). Additionally, we investigated the influence of adding a sample of quasars with higher redshift with standardisable UV-Xray luminosity distances. We adopted polynomial expansions in H(z) or in comoving distances so that our inference was completely independent of any cosmological model on which the expansion history might be based. Our measurements are independent of Cepheids and systematics from peculiar motions to within percent-level accuracy. Results. The inferred sound horizon rs varies between (133 ± 8) Mpc and (138 ± 5) Mpc across different models. The discrepancy with CMB measurements is robust against model choice. Statistical uncertainties are comparable to systematics. Conclusions. The combination of time-delay lenses, supernovae, and BAO yields a distance ladder that is independent of cosmology (and of Cepheid calibration) and a measurement of rs that is independent of the CMB. These cosmographic measurements are then a competitive test of the Standard Model, regardless of the hypotheses on which the cosmology is based.

scholarly journals The Discretization for a Special Class of Ideal Projectors

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Zhe Li ◽  
Shugong Zhang ◽  
Tian Dong
Keyword(s):  
Special Class ◽  
Invariant Polynomial ◽  
Classical Type ◽  
Matrix Computation ◽  
New Class

We focus on a special class of ideal projectors, subspaces, which possesses two classes of D-invariant polynomial subspaces. The first is a classical type, while the second is a new class. With matrix computation, we discretize this class of ideal projectors into a sequence of Lagrange projectors.

scholarly journals Polynomial expansions in the Borel region

1937 ◽  
Vol 5 (2) ◽  
pp. 82-89
Author(s):  
J. T. Hurt ◽  
L. R. Ford
Keyword(s):  
Analytic Functions ◽  
In Series ◽  
Polynomial Expansions

This paper deals with certain expansions of analytic functions in series of polynomials. Explicit forms for the polynomials are given in terms of the coefficients of the Taylor's expansion and of prescribed positive constants hk. Under suitable conditions, to be presently discussed, the series converge to the function in the Borel region.

Sign in / Sign up

Export Citation Format

Share Document