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The discriminant Δ of the cubic is the square of = () (), where a is the leading coefficient of the cubic, and r 1, r 2 and r 3 are the three roots of the cubic. As Δ {\displaystyle {\sqrt {\Delta }}} changes of sign if two roots are exchanged, Δ {\displaystyle {\sqrt {\Delta }}} is fixed by the Galois group only if the Galois group is A 3 .
cubic centimetre of atmosphere; standard cubic centimetre: cc atm; scc ≡ 1 atm × 1 cm 3 = 0.101 325 J: cubic foot of atmosphere; standard cubic foot: cu ft atm; scf ≡ 1 atm × 1 ft 3 = 2.869 204 480 9344 × 10 3 J: cubic foot of natural gas: ≡ 1000 BTU IT = 1.055 055 852 62 × 10 6 J: cubic yard of atmosphere; standard cubic yard: cu yd ...
Vieta's formulas are frequently used with polynomials with coefficients in any integral domain R.Then, the quotients / belong to the field of fractions of R (and possibly are in R itself if happens to be invertible in R) and the roots are taken in an algebraically closed extension.
In condensed matter physics and crystallography, the static structure factor (or structure factor for short) is a mathematical description of how a material scatters incident radiation. The structure factor is a critical tool in the interpretation of scattering patterns ( interference patterns ) obtained in X-ray , electron and neutron ...
Just as in 1D, the FWHM varies as the inverse of the characteristic size. For example, for a spherical crystallite with a cubic lattice, [2] the factor of 5.56 simply becomes 6.96, when the size is the diameter D, i.e., the diameter of a spherical nanocrystal is related to the peak FWHM by
The graph of any cubic function is similar to such a curve. The graph of a cubic function is a cubic curve, though many cubic curves are not graphs of functions. Although cubic functions depend on four parameters, their graph can have only very few shapes. In fact, the graph of a cubic function is always similar to the graph of a function of ...
Daily rates only, for packages equal to or less than one cubic foot / 1,728 cubic inches.) Canada Domestic: 139 cubic inches per pound (5,000 cm 3 /kg) or 1 ⁄ 5 kg/dm 3 (12 lb/cu ft) (All except UPS Standard within Canada.) Canada Domestic: 166 cubic inches per pound (6,000 cm 3 /kg) or 1 ⁄ 6 kg/dm 3 (10 lb/cu ft) (UPS Standard within Canada.)
Conversion of units is the conversion of the unit of measurement in which a quantity is expressed, typically through a multiplicative conversion factor that changes the unit without changing the quantity. This is also often loosely taken to include replacement of a quantity with a corresponding quantity that describes the same physical property.