chi-square distribution vâbâžeš-e Xi-do Fr.: loi du chi-deux A probability density function, denoted χ^{2}, that gives the distribution of the sum of squares of k independent random variables, each being drawn from the normal distribution with zero mean and unit variance. The integer k is the number of degrees of freedom. The distribution has a positive skew; the skew is less with more degrees of freedom. As degrees of freedom increase, the chi-square distribution approaches a normal distribution. The most common application is chi-square tests for goodness of fit of an observed distribution to a theoretical one. If χ^{2} = 0 the agreement is perfect. Chi Gk. letter of alphabet; → square; → distribution. Vâbâžeš, → distribution; do, → two. |
inverse square law qânun-e tavân-e do-ye vârun, qânun-e câruš-e vârun Fr.: loi en carré inverse A force law that applies to the → gravitational and → electromagnetic forces in which the magnitude of the force decreases in proportion to the inverse of the square of the → distance. |
least squares kucaktarin cârušhâ Fr.: moindres carrés Any statistical procedure that involves minimizing the sum of squared differences. |
least-squares deconvolution (LSD) vâhamâgiš-e kucaktarin cârušhâ Fr.: déconvolution des moindres carrés A → cross correlation technique for computing average profiles from thousands of → spectral lines simultaneously. The technique, first introduced by Donati et al. (1997, MNRAS 291,658), is based on several assumptions: additive → line profiles, wavelength independent → limb darkening, self-similar local profile shape, and weak → magnetic fields. Thus, unpolarized/polarized stellar spectra can indeed be seen as a line pattern → convolved with an average line profile. In this context, extracting this average line profile amounts to a linear → deconvolution problem. The method treats it as a matrix problem and look for the → least squares solution. In practice, LSD is very similar to most other cross-correlation techniques, though slightly more sophisticated in the sense that it cleans the cross-correlation profile from the autocorrelation profile of the line pattern. The technique is used to investigate the physical processes that take place in stellar atmospheres and that affect all spectral line profiles in a similar way. This includes the study of line profile variations (LPV) caused by orbital motion of the star and/or stellar surface inhomogeneities, for example. However, its widest application nowadays is the detection of weak magnetic fields in stars over the entire → H-R diagram based on → Stokes parameter V (→ circular polarization) observations (see also Tkachenko et al., 2013, A&A 560, A37 and references therein). → least; → square; → deconvolution. |
least-squares fit saz-e kucaktarin cârušhâ Fr.: ajustement moindres carrées A fit through data points using least squares. → least squares; → fit. |
magic square câruš-e jâdu Fr.: carré magique An n × n matrix in which every row, column, and diagonal add up to the same number. |
method of least squares raveš-e kamtarin cârušhâ Fr.: méthode des moindres carrés A method of fitting a curve to data points so as to minimize the sum of the squares of the distances of the points from the curve. → method; → least squares. |
perfect square câruš-e farsâxt Fr.: carré parfait An → integer of the form n^{2}, where n is a → positive number. In other words, a → perfect power when k = 2. |
root mean square (rms) riše-ye câruši-ye miyângin, ~ dovom-e ~ Fr.: valeur quadratique moyenne The square root of the arithmetic mean of the squares of the numbers in a given set. |
root-mean-square error irang-e riše-ye câruši-ye miyângin, ~ ~ dovom-e ~ Fr.: The square root of the second moment corresponding to the frequency function of a random variable. |
root-mean-square value arzeš-e riše-ye câruši-ye miyângin Fr.: écart quadratique moyen, écart type Statistics: The square root of the arithmetic mean of the squares of the deviation of observed values from their arithmetic mean. |
square câruš, cahârguš Fr.: carré 1) A rectangle having all four sides of equal length. M.E., from O.Fr. esquire "a square, squareness," from V.L. *exquadra, from *exquadrare "to square," from L. → ex- "out" + quadrare "make square," from quadrus "a square," from quattuor→ four. Câruš, from Av. caθruša- "four sides (of a four-sided figure)", from caθru- "four," Mod.Pers. cahâr, câr "four" + uša- "angle," Mod.Pers. guš, gušé. |
square degree daraje-ye câruš Fr.: degré carré A solid angle whose cone is a tetrahedral pyramid with an angle between its edges equal to 1°. 1 square degree = 3.046 x 10^{-4} sr = 2.424 x 10^{-5} solid angle of a complete sphere. |
Square Kilometer Array (SKA) SKA Fr.: SKA An international project to construct a highly sensitive radio interferometer array operating between 0.15 and 20 GHz with an effective collecting area of one square kilometer. The number of individual telescopes will be 2000 to 3000. SKA will have a sensitivity 100 times higher than that of today's best radio telescopes and an angular resolution < 0.1 arcsec at 1.4 GHz. The site will be selected in 2012 and early science with Phase 1 is scheduled for from 2016 on. See also the SKA homepage. |
square matrix matris-e câruš Fr.: matrice carée A → matrix with equal numbers of → rows and → columns (i.e., an n × n matrix). |
Square of Pegasus Chahârguš-e Pegasus Fr.: Carrée de Pégase A large → asterism of four stars, approximately square in shape, in the northern sky. Three of the stars, → → Markab, → Scheat, and → Algenib, belong to the constellation → Pegasus. The fourth, → Alpheratz, was lost to Pegasus when the constellation boundaries were formalised, and now lies just within the borders of → Andromeda. |
square root riše-ye câruš Fr.: racine carée Quantity which when multiplied by itself produces another quantity. |
square wave mowj-e câruš Fr.: onde carrée An oscillation which alternatively assumes, for equal lengths of time, one or two fixed values. |
squaring the square cârušeš-e câruš Fr.: quadrature du carré The mathematical problem of subdividing a square into a number of smaller squares, all of different sizes. |