Extensions of matrix valued functions with rational polynomial inverses

1979 ◽  
Vol 2 (4) ◽  
pp. 503-528 ◽  
Author(s):  
Harry Dym ◽  
Israel Gohberg
Keyword(s):  
Rational Polynomial

Method for intersecting algebraic surfaces with rational polynomial patches

1990 ◽  
Vol 22 (10) ◽  
pp. 645-654 ◽  
Author(s):  
G.A. Kriezis ◽  
P.V. Prakash ◽  
N.M. Patrikalakis
Keyword(s):  
Algebraic Surfaces ◽  
Rational Polynomial

Rational polynomial approximants and scattering amplitude for long range potentials

1976 ◽  
Vol 277 (1) ◽  
pp. 1-7 ◽  
Author(s):  
O. D. Corbella ◽  
C. R. Garibotti ◽  
F. F. Grinstein
Keyword(s):  
Long Range ◽  
Scattering Amplitude ◽  
Rational Polynomial

Technical Note: Rational Polynomial Functions for Modeling E. coli and Bromide Breakthrough

2012 ◽  
Vol 55 (5) ◽  
pp. 1821-1826 ◽  
Author(s):  
D. W. Meek ◽  
C. K. Hoang ◽  
R. W. Malone ◽  
R. S. Kanwar ◽  
G. A. Fox ◽  
...  
Keyword(s):  
Technical Note ◽  
Polynomial Functions ◽  
E Coli ◽  
Rational Polynomial

Rational Polynomial Transfer Function Approximations for Fluid Transients in Lines

2003 ◽  
Author(s):  
Patompong Wongputorn ◽  
David A. Hullender ◽  
Robert L. Woods
Keyword(s):  
Exact Solution ◽  
Transmission Lines ◽  
Transfer Functions ◽  
Viscous Friction ◽  
Total System ◽  
Nonlinear Frequency ◽  
Maximum Frequency ◽  
Rational Polynomial ◽  
Curve Fit ◽  
Fluid Transients

This paper introduces a simple approach utilizing MATLAB® computational tools for generating rational polynomial transfer functions for fluid transients in both liquid and gas fluid transmission lines. These transfer functions are obtained by curve fitting in the frequency domain the exact solution to the distributed parameter laminar flow “Dissipative Model” for fluid transients that includes nonlinear frequency dependent viscous friction terms as well as heat transfer effects in gas lines. These transfer functions are formulated so they are applicable to arbitrary line terminations and so they can be inserted directly into SIMULINK® models for time domain simulation and analysis of a total system of which the fluid lines are only internal components. The inputs to the algorithm are the internal radius and length of the line; the kinematic viscosity, density, Prandtl number, and speed of sound of the fluid; and the maximum frequency to which an accurate curve fit of the exact solution is desired. This maximum frequency normally is equal to or greater than the bandwidth of the other components in the total system to be analyzed or the maximum frequency associated with the input. The simplicity of use and accuracy in the results of the exact solution representations are demonstrated for examples of a blocked fluid line and of a line terminating into a tank. The computational algorithms are available for download from the Author’s web site. This is the first of two papers pertaining to transfer functions for fluid transients. The second paper pertains to formulating simulation diagrams for total systems containing fluid lines represented by rational polynomial transfer functions.

scholarly journals Geometric Accuracy Assessment of Deimos-2 Panchromatic Stereo Pairs: Sensor Orientation and Digital Surface Model Production

Sensors ◽  
2020 ◽  
Vol 20 (24) ◽  
pp. 7234
Author(s):  
Manuel A. Aguilar ◽  
Rafael Jiménez-Lao ◽  
Abderrahim Nemmaoui ◽  
Fernando J. Aguilar
Keyword(s):  
Urban Areas ◽  
Satellite Images ◽  
Accuracy Assessment ◽  
Bare Soil ◽  
Surface Model ◽  
Stereo Pair ◽  
Rational Polynomial ◽  
Sensor Orientation ◽  
Vertical Accuracy ◽  
Land Covers

Accurate elevation data, which can be extracted from very high-resolution (VHR) satellite images, are vital for many engineering and land planning applications. In this way, the main goal of this work is to evaluate the capabilities of VHR Deimos-2 panchromatic stereo pairs to obtain digital surface models (DSM) over different land covers (bare soil, urban and agricultural greenhouse areas). As a step prior to extracting the DSM, different orientation models based on refined rational polynomial coefficients (RPC) and a variable number of very accurate ground control points (GCPs) were tested. The best sensor orientation model for Deimos-2 L1B satellite images was the RPC model refined by a first-order polynomial adjustment (RPC1) supported on 12 accurate and evenly spatially distributed GCPs. Regarding the Deimos-2 based DSM, its completeness and vertical accuracy were compared with those obtained from a WorldView-2 panchromatic stereo pair by using exactly the same methodology and semiglobal matching (SGM) algorithm. The Deimos-2 showed worse completeness values (about 6% worse) and vertical accuracy results (RMSEZ 42.4% worse) than those computed from WorldView-2 imagery over the three land covers tested, although only urban areas yielded statistically significant differences (p < 0.05).

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