In mathematics, the half-period ratio τ of an elliptic function j is the ratio
of the two half-periods ω1 and ω2 of j, where j is defined in such a way that
is in the upper half-plane.
Quite often in the literature, ω1 and ω2 are defined to be the periods of an elliptic function rather than its half-periods. Regardless of the choice of notation, the ratio ω2/ω1 of periods is identical to the ratio (ω2/2)/(ω1/2) of half-periods. Hence the period ratio is the same as the "half-period ratio".
Note that the half-period ratio can be thought of as a simple number, namely, one of the parameters to elliptic functions, or it can be thought of as a function itself, because the half periods can be given in terms of the elliptic modulus or in terms of the nome.
See the pages on quarter period and elliptic integrals for additional definitions and relations on the arguments and parameters to elliptic functions.
Period may refer to:
In punctuation, the full stop (Commonwealth English) or period (American English) is a punctuation mark placed at the end of a sentence. The full stop glyph is sometimes called a baseline dot because, typographically, it is a dot on the baseline. This term distinguishes the baseline dot from the interpunct (a raised dot).
The full stop glyph is also used for other purposes. It is often placed after an initial letter used to stand for a name, and sometimes placed after each individual letter in an initialism (for example, "U.S.A."; see Acronym#Punctuation). It also has multiple contexts in mathematics and computing, where it may be called dot or point (short for decimal point).
The full stop symbol derives from the Greek punctuation introduced by Aristophanes of Byzantium in the 3rd century BC. In his system, there were a series of dots whose placement determined their meaning. The full stop at the end of a completed thought or expression was marked by a high dot ⟨˙⟩, called the stigmḕ teleía (στιγμὴ τελεία) or "terminal dot". The "middle dot" ⟨·⟩, the stigmḕ mésē (στιγμὴ μέση), marked a division in a thought occasioning a longer breath (essentially a semicolon) and the low dot ⟨.⟩, called the hypostigmḕ (ὑποστιγμή) or "underdot", marked a division in a thought occasioning a shorter breath (essentially a comma). In practice, scribes mostly employed the full stop; the others fell out of use and were later replaced by other symbols. From the 9th century, the full stop began appearing as a low mark instead of a high one; by the advent of printing in Western Europe, the low mark was regular and then universal.
Period (Another American Lie) is the debut studio album by B.A.L.L., released in 1987 by Shimmy Disc.
All lyrics written by Don Fleming, all music composed by B.A.L.L..
Adapted from the Period (Another American Lie) liner notes.