scholarly journals Orthonormal Polynomial Expansions and Lognormal Sum Densities

2019 ◽  
pp. 127-150 ◽  
Author(s):  
Søren Asmussen ◽  
Pierre-Olivier Goffard ◽  
Patrick J. Laub
Keyword(s):  
Orthonormal Polynomial ◽  
Polynomial Expansions

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 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.

Higher-Order Theories for Structural Analysis Using Legendre Polynomial Expansions

1969 ◽  
Vol 36 (4) ◽  
pp. 757-762 ◽  
Author(s):  
A. I. Soler
Keyword(s):  
Structural Analysis ◽  
Legendre Polynomials ◽  
Direct Reduction ◽  
Beam Theory ◽  
Plane Elasticity ◽  
Higher Order ◽  
Governing Equations ◽  
Field Equations ◽  
Displacement Boundary ◽  
Polynomial Expansions

Governing equations of plane elasticity are examined to define suitable approximate theories. Each dependent variable in the problem is considered as a series expansion in Legendre polynomials; attention is focused on establishment of a logical approach to truncation of the series. Important variables for approximate theories of any order are established from energy considerations, and the desired approximate theories are established by direct reduction of the field equations and also from an energy viewpoint. A new “classical” beam theory is developed capable of treating displacement boundary conditions on lateral surfaces. Higher-order approximate theories are studied to make certain comparisons with exact solutions; the results of these comparisons indicate that the new method yields approximate theories which may be more accurate than previous theories with similar levels of approximation.

Buckling and Postbuckling Analyses of a Skew Plate

2008 ◽  
Vol 24 (4) ◽  
pp. 347-355 ◽  
Author(s):  
H. W. Liao ◽  
H. Y. Huang
Keyword(s):  
Composite Laminates ◽  
High Order ◽  
Design Parameters ◽  
Aerospace Structures ◽  
Critical Buckling Load ◽  
Buckling Strength ◽  
Skew Plate ◽  
Post Buckling ◽  
Polynomial Expansions ◽  
Important Design

AbstractThe applications of skew plates in the construction of aerospace structures are well known. The critical buckling load and post-buckling strength are two important design parameters of skew composite laminates. In this study, the refined buckling and nonlinear postbuckling solutions of a homogenous isotropic skew plate based on polynomial expansions of various degrees have been examined. Numerical results based on high-order Rayleigh-Ritz solutions are presented for certain type of oblique plates.

Sign in / Sign up

Export Citation Format

Share Document