The pre-launch distortion definition of SIMBIO-SYS/STC stereo camera by rational function models

2018 ◽  
Author(s):  
Emanuele T. Simioni ◽  
Vania Da Deppo ◽  
Cristina Re ◽  
Alessandra Slemer ◽  
Gabriele Cremonese ◽  
...  
Keyword(s):  
Rational Function ◽  
Stereo Camera ◽  
Definition Of ◽  
Function Models

scholarly journals COVARIANCE FUNCTION MODELLING IN LOCAL GEODETIC APPLICATIONS USING THE SIMPLEX METHOD

2016 ◽  
Vol 22 (2) ◽  
pp. 342-357
Author(s):  
Carlo Iapige De Gaetani ◽  
Noemi Emanuela Cazzaniga ◽  
Riccardo Barzaghi ◽  
Mirko Reguzzoni ◽  
Barbara Betti
Keyword(s):  
Simplex Method ◽  
Covariance Function ◽  
Real Data ◽  
Data Sets ◽  
Covariance Functions ◽  
The Earth ◽  
Function Modelling ◽  
Covariance Models ◽  
Definition Of ◽  
Function Models

Collocation has been widely applied in geodesy for estimating the gravity field of the Earth both locally and globally. Particularly, this is the standard geodetic method used to combine all the available data to get an integrated estimate of any functional of the anomalous potential T. The key point of the method is the definition of proper covariance functions of the data. Covariance function models have been proposed by many authors together with the related software. In this paper a new method for finding suitable covariance models has been devised. The covariance fitting problem is reduced to an optimization problem in Linear Programming and solved by using the Simplex Method. The procedure has been implemented in a FORTRAN95 software and has been tested on simulated and real data sets. These first tests proved that the proposed method is a reliable tool for estimating proper covariance function models to be used in the collocation procedure

scholarly journals On the expression of a symmetric function in terms of the elementary symmetric functions

1888 ◽  
Vol 7 ◽  
pp. 41-42
Author(s):  
R. E. Allardice
Keyword(s):  
Rational Function ◽  
Symmetric Function ◽  
Symmetric Functions ◽  
Elementary Proof ◽  
Elementary Symmetric Functions ◽  
Definition Of

The theorem that any rational symmetric function of n variables x1, x2, … xn is expressible as a rational function of the n elementary symmetric functions, Σx1, Σx1x2, Σx1x2x3, etc., is usually proved by means of the properties of the roots of an equation. It is obvious, however, that the theorem has no necessary connection with the properties of equations; and the object of this paper is to give an elementary proof of the theorem, based solely on the definition of a symmetric function.

scholarly journals Cauchy type functional equations related to some associative rational functions

2019 ◽  
Vol 18 (1) ◽  
pp. 145-156
Author(s):  
Katarzyna Domańska
Keyword(s):  
Rational Function ◽  
Functional Equations ◽  
Rational Functions ◽  
Cauchy Type ◽  
Cauchy Equation ◽  
Local Solutions ◽  
Definition Of

Abstract L. Losonczi [4] determined local solutions of the generalized Cauchy equation f(F (x, y)) = f(x) + f(y) on components of the definition of a given associative rational function F. The class of the associative rational function was described by A. Chéritat [1] and his work was followed by paper [3] of the author. The aim of the present paper is to describe local solutions of the equation considered for some singular associative rational functions.

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