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 ?
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.
We propose a numerical algorithm for solving inverse problems of spectral analysis for Sturm-Liouville differential operators on the half-line.
v] is a model of half-line composition for this first-draft material, which provides the poet with a number of different possible combinations.
The purpose of this paper is the computation of quadrature formulas based on Laurent polynomials in two particular situations: the Real Half-Line and the Unit Circle.
43-46), with its tight metrical scheme (4+7), where the half-line is often entirely filled with pre-made syntactic units.
Note that distance d and direction I in drawing 1 are represented in drawing 3, respectively, by the length of C'E" and by the direction of the half-line through C' and M.
The `unnecessary entity' here requiring excision is a spurious macaronic half-line (one already ensconced as a `quotation' in Alford's 1992 Guide), and I myself would prefer lefte for north, a word simple, unusual, but contextually apt and firmly part of the poet's lexicon.
Because the sprayed product's half-line on leaves and fruit is only about three days, researchers think much of it may dissipate by the time the food reaches consumers.
Under a moment condition, it is shown that the asymptotics of the sequence of occupancy numbers, and of the small-parts counts (singletons, doubletons, etc) can be read off from a limiting model involving a unit Poisson point process and a self-similar renewal process on the half-line.
be a half-line issuing from a point of the sphere [parallel] x [parallel] = [sigma](t).