Statistics: The correlation coefficient of two random variables X and Y is in general defined as the ratio of the Cov(X,Y) to the two standard deviations of X and Y. It varies between 1 and -1 corresponding to complete correlation or anticorrelation.
1) In radio astronomy, a process performed by an → autocorrelator.
Autocorrelation, from → auto- "self" + → correlation.
Xod-hambâzâneš, from xod- "self" + hambâzâneš, → correlation.
Fr.: fonction d'autocorrélation
A mathematical function that describes the correlation between two values of the same variable at different points in time.
Fr.: relation de Boltzmann
A relation between the → entropy of a given → state of a → thermodynamic system and the → probability of the state: S = k . ln Ω where S is the entropy of the system, k is → Boltzmann's constant, and Ω the thermodynamic probability of the state. Boltzmann's relation connects → statistical mechanics and → thermodynamics. Ω is the number of possible → microstates of the system, and it represents the → randomness of the system. The relation also describes the statistical meaning of the → second law of thermodynamics. This expression has been carved above Boltzmann's name on his tombstone in Zentralfreihof in Vienna. Same as → Boltzmann's entropy formula.
Fr.: correlation canonique
The highest correlation between linear functions of two data sets when specific restrictions are imposed upon them.
The degree to which two or more attributes or measurements on the
same group of elements show a tendency to vary together;
the state or relation of being correlated.
From M.Fr. corrélation, from cor- "together," → com- + → relation.
Fr.: coefficient de corrélation
A number between -1 and 1 which measures the degree to which two variables are linearly related.
hamvbâzâneš-e calipâyi, ~ xâji
Fr.: corrélation croisée
In radio astronomy, the process performed by a → cross correlator or the result of the process.
Fr.: corrélation directe
A correlation between two variables such that as one variable becomes large, the other also becomes large, and vice versa. The correlation coefficient is between 0 and +1. Also called positive correlation.
Fr.: relation de dispersion
An equation that describes how the → angular frequency, ω, of a wave depends on its → wave number, k. For the simplest of waves, where the speed of propagation, c, is a constant, ω(k) = ck. If the → phase velocity depends on k, that is for a dispersive medium, the function ω(k) is nonlinear.
Fr.: relation Faber-Jackson
An empirical power-law correlation between the luminosity (L) and the velocity dispersion of stars (σ) in the center of a elliptical galaxies. The original relation can be expressed mathematically as: L ∝ σγ, where the index γ is observed to be approximately equal to 4, but depends on the range of galaxy luminosities that is fitted. → Tully-Fisher relation.
After the astronomers Sandra M. Faber and Robert Earl Jackson, who first noted this relation in 1976 (ApJ 204, 668); → relation.
Fr.: relation de Larson
An → empirical relationship between the internal → velocity dispersion of → molecular clouds and their size. The velocity dispersions are derived from molecular → linewidths, in particular those of → carbon monoxide. It was first established on star forming regions and found to be: σ (km s-1) = 1.10 L (pc)0.38, where σ is the velocity dispersion and L the size. The relation holds for 0.1 ≤ L ≤ 100 pc. More recent set of cloud data yield: σ (km s-1) = L (pc)0.5. This relation indicates that larger molecular clouds have larger internal velocity dispersions. It is usually interpreted as evidence for → turbulence in molecular clouds. Possible sources of interstellar turbulence include the following processes operating at various scales: galactic-scale (→ differential rotation, → infall of extragalactic gas on the galaxy), intermediate-scale (expansion of → supernova remnants, → shocks, → stellar winds from → massive stars), and smaller-scale processes (→ outflows from → young stellar objects).
First derived by Richard B. Larson, American astrophysicist working at Yale University (Larson, 1981, MNRAS 194, 809). See Falgarone et al. (2009, A&A 507, 355) for a recent study; → relation.
Fr.: corrélation linéaire
A measure of how well data points fit a straight line. When all the points fall on the line it is called a perfect correlation. When the points are scattered all over the graph there is no correlation.
Fr.: relation masse-énergie
The famous equation proposed by Einstein as a consequence of his special theory of relativity describing the equivalence of mass and energy: E = mc2, where E is energy, m is the equivalent amount of mass, and c is the velocity of light.
Fr.: relation masse-luminosité
A relationship between luminosity and mass for stars that are on the main sequence, specifying how bright a star of a given mass will be. Averaged over the whole main sequence, it has been found that L = M3.5, where both L and M are in solar units. This means, for example, that if the mass is doubled, the luminosity increases more than 10-fold.
Fr.: relation morphologie-densité
An observationally determined relationship between the → morphological classification of galaxies and the → environments in which they are located. Specifically, the morphology-density relation indicates that early-type galaxies (→ ETG) are preferentially located in high density environments, whereas late-type galaxies (→ LTG) are preferentially found in low density environments. Hence, spiral galaxies are rare in the high densities of clusters and are common in the lower density group environments. Early-type galaxies, on the other hand, are common in clusters and are rarely found in isolation.
Fr.: corrélation négative
A correlation between two variables such that as one variable's values tend to increase, the other variable's values tend to decrease.
Orion correlation theory
negare-ye hambâzâneš-e Oryon
Fr.: théorie de la corrélation d'Orion
A controversial proposition according to which a coincidence would exist between the mutual positions of the three stars of → Orion's Belt and those of the main Giza pyramids. More specifically, Khufu, Khafre, and Menkaure would be the monumental representation of → Alnitak, → Alnilam, and → Mintaka, respectively.
Fr.: relation période-luminosité
A correlation between the periods and luminosities of → Cepheid variable stars. Once the period of a Cepheid variable is determined from observations, the period-luminosity relation can be used to derive its luminosity. Since luminosity is a function of distance, the distance can then be calculated with the luminosity. The period-luminosity relation is an invaluable tool for the measurements of distances out to the nearest galaxies and thus for studying the structure of our own Galaxy and of the Universe. The relation was discovered by Henrietta Leavitt in 1912 when studying Cepheids in the → Small Magellanic Cloud.
period-mean density relation
bâzâneš-e dowré-cagâli-ye miyângin
Fr.: relation période-densité moyenne
A relation that gives a rough estimate of the oscillation period of a → pulsating star as a function of its mean density. This relation is obtained by considering how long it would take a sound wave to travel across the diameter of a model star: Π ≅ (3π/2γGρ)1/2, where ρ is the mean density, γ the ratio of → specific heats (Cp/Cv), and G the → gravitational constant. This relation shows that the pulsation period of a star is inversely proportional to the square root of its mean density. And this is the reason why the pulsation periods decrease along the → instability strip from the luminous, very tenuous → supergiants to the faint, very dense → white dwarfs.