Branching fractionIn particle physics and nuclear physics, the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to either the radioactive decay of atoms or the decay of elementary particles. It is equal to the ratio of the partial decay constant to the overall decay constant. Sometimes a partial half-life is given, but this term is misleading; due to competing modes, it is not true that half of the particles will decay through a particular decay mode after its partial half-life.
SubgiantA subgiant is a star that is brighter than a normal main-sequence star of the same spectral class, but not as bright as giant stars. The term subgiant is applied both to a particular spectral luminosity class and to a stage in the evolution of a star. The term subgiant was first used in 1930 for class G and early K stars with absolute magnitudes between +2.5 and +4. These were noted as being part of a continuum of stars between obvious main-sequence stars such as the Sun and obvious giant stars such as Aldebaran, although less numerous than either the main sequence or the giant stars.
Gauss's continued fractionIn complex analysis, Gauss's continued fraction is a particular class of continued fractions derived from hypergeometric functions. It was one of the first analytic continued fractions known to mathematics, and it can be used to represent several important elementary functions, as well as some of the more complicated transcendental functions. Lambert published several examples of continued fractions in this form in 1768, and both Euler and Lagrange investigated similar constructions, but it was Carl Friedrich Gauss who utilized the algebra described in the next section to deduce the general form of this continued fraction, in 1813.
