On polynomial approximation in the mean

1999 ◽  
pp. 23-26 ◽  
Author(s):  
John Akeroyd ◽  
Elias G. Saleeby
Keyword(s):  
Polynomial Approximation ◽  
The Mean

Biometrische Beitrage Zur Anwendung Von Multiplen Co Varianzanalysen Bei Quantitativen Humangenetischen Fragestellungen

1977 ◽  
Vol 26 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Udo Rempe ◽  
Detlev Hosenfeld
Keyword(s):  
Polynomial Approximation ◽  
Enzyme Activities ◽  
Quantitative Inheritance ◽  
Two Dimensional ◽  
Mothers And Fathers ◽  
Quantitative Variable ◽  
Age Dependent ◽  
The Mean ◽  
Specific Pair ◽  
Using Data

The analysis of quantitative inheritance is complicated by age dependent changes. It is possible to describe them by two separate 5-degree polynomials for boys and girls of one family. Supposing a parallel shifting of these pairs of curves for different families, it is possible to calculate the mean course of such a family specific pair even if only a few children were examined at a few termins. By use of these fitted functions it is possible to estimate the value of the quantitative variable for the examined children at a constant age and to eliminate the influence of sex. Similarly, it is possible to eliminate age-caused differences of the parents. Using the age-corrected values of children, mothers and fathers, it is possible to investigate the relations between the values of parents {not midparents !) and children by means of a two-dimensional polynomial approximation. The resulting complicated formulas can be visualized by plotting lines of equal character values of the children in a diagram with the character values of the fathers on the ordinate and those of the mothers on the abscissa. Effects of dominance and of epistasis can be demonstrated by this method. Some results using data of enzyme activities as an example are discussed.

scholarly journals Mathematical model of a fluxgate magnetometer

2018 ◽  
Vol 158 ◽  
pp. 01006 ◽  
Author(s):  
Pavel F. Baranov ◽  
Vitalia E. Baranova ◽  
Tamara G. Nesterenko
Keyword(s):  
Mathematical Model ◽  
Polynomial Approximation ◽  
Magnetization Curve ◽  
Electromotive Force ◽  
Signal Frequency ◽  
Fluxgate Magnetometer ◽  
Frequency Content ◽  
The Core ◽  
Measuring Coil ◽  
The Mean

In paper analytical equations for calculate the electromotive force in the measuring coil of the fluxgate magnetometer independent of the drive signal frequency content are presented. Also, the equations for es-timation of the fluxgate sensitivity at any harmonic and for study fluxgates operation with a glance to the waveform and the polynomial approximation of the mean magnetization curve of the core are provided.

Photo-electric Hβ and uvby photometry

1966 ◽  
Vol 24 ◽  
pp. 170-180
Author(s):  
D. L. Crawford
Keyword(s):  
Narrow Band ◽  
Line Strength ◽  
Interference Filter ◽  
B Stars ◽  
Relative Line ◽  
The Mean ◽  
F Stars ◽  
Two Parameters ◽  
Filter Photometry ◽  
The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

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