Half Space

half space

[′haf ‚spās]
(building construction)
A broad step between two half flights of a stair.
(mathematics)
A space bounded only by an infinite plane.

Half Space

 

in mathematics, the set of points in space that lie on one side of some plane. The coordinates x, y, and z of the points of a half space satisfy the inequality Ax + By + Cz + D > 0, where A, B, C, and D are constants such that A, B, and C are not simultaneously equal to zero. The plane Ax + By + Cz + D = 0 is called the boundary of the half space. If the boundary is included in the half space, the half space is said to be closed.

References in periodicals archive ?
The elastic field in half space due to ellipsoidal inclusions with uniform dilatational eigenstrains, ASME Journal of Applied Mechanics 46(3): 568-572.
In which [R.sub.TE] and [R.sub.TM] are reflection coefficients for TE and TM polarizations in the left most half space, respectively.
It is confirmed that the RHCP and LHCP radiation patterns are excited in the upper and lower half space, respectively.
In [5], two-layer reflection and transmission coefficients are obtained in terms of half space coefficients using matrix method.
The influence of piezoelectricity on the reflection-transmission phenomena in fluid-loaded piezoelectric half space and fluid-loaded piezoelectric plate was studied by Nayfeh and Chien [6,7].
The upper half space is the set H = {(x', [x.sub.n]) [member of] [R.sup.n]: [x.sub.n] > 0}, whose boundary is [partial derivative]H.
time is now remaining, Woodilee Located Woodilee boosting with Half space children's new Open Te stylish apartments buyers to be part of running out for discerning home but also Stunning from to Prices start the Colville Wynd success story.
We consider a thermo-elastic half space with diffusion with free surface along x-axis and negative z-axis is taken downward into the half-space as shown in Fig 1.
Thus, assuming a point source as the loading source to analytically predict the surface displacement of an infinite half space appears debatable.
Among the topics are a boundary element solution of thermal creeping flow in a nanometer single mixer, evaluating interface cracks, rotational symmetry applied to boundary element computation for nuclear fusion plasma, fundamental solutions for inverse obstacle acoustic scattering, the volume integral equation method for analyzing scattered waves in an elastic half space, and analyzing layered soil problems with an alternative multi-region boundary element method technique and a new infinite boundary element formulation.
The cases where [OMEGA] is the positive half space [R.sup.2.sub.+] and [R.sup.3.sub.+], respectively, are presented in details under hypotheses different from the ones considered by other authors (subsection 3.1 and subsection 3.2).