Half Line

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half line

[′haf ¦līn]

Half Line


in mathematics, the set of points on a line that lie on one side of some point of the line. The coordinates x of the points of a half line satisfy one, and only one, of the inequalities x > a and x < a, where a is a constant. The point x = a is called the boundary of the half line. If the boundary is included in the half line, the half line is said to be closed. A closed half line is also called a ray.

References in periodicals archive ?
or -],*], +, *) are convolution algebras over C, called the half-line convolution subalgebras.
The most spectacular shot of the match came off the foot of Iran's Ehsan Haji in the 46th minute as he fired a volley on-the-run from nearly the half-line.
In this paper we study a new type of boundary condition for the half-line problem.
Pakistan already have several experienced players in the half-line that is likely to get a shot in the arm with the return of Waseem Ahmed, a former Pakistan captain and Sohail's close friend.
The functions of one variable are supposed to be C[infinity] with respect to [rho] = [parallel]x[parallel] on the half-line [0, +[infinity][(or, possibly, on the entire real line] - [infinity], +[infinity][), but since the norm [parallel]x[parallel] is not differentiable at the origin with respect to the coordinates [x.
The enjambed half-line "an apparence" is syntactically tied to both the preceding and the subsequent half-line.
Let us start with the line Lab = {x|[xab]}, with a [not equal to] b, the interval ab = {x|(axb)}, and the half-line (ab = {x|(axb) [disjunction] (x = b) [disjunction] (abx)} of the line [L.
Both argue that taceo nouercas would make an unusually effective half-line, though Dr Heyworth prefers to delete all of 558 as an interpolation.
Although the sense of the quoted passage is clear enough, the half-line Grendeles maegum (Beowulf, line 2353b) presents a serious problem for the grammatical analysis: At first sight it would seem plausible to interpret maegum as dative plural of maeg 'kinsman'.
The rhythm is straightforward: it begins with a B-type half-line and follows with three A-type half-lines, which remains the basic rhythm throughout the fiddle, upon which more complex patterns are laid.
Typically and regularly in Homer we find half-line phrases running to the third foot caesura, such as [tau][omicron][nu] [delta] a[pi]a[mu][epsilon][iota][beta][omicron][mu][epsilon][nu][omicron]s.
A line of Old English poetry is divided into two half-lines, and each half-line contains two stressed syllables with a variable number and arrangement of unstressed syllables.