Half Plane

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half plane

[′haf ¦plān]
The portion of a plane lying on one side of some line in the plane; in particular, all points of the complex plane either above or below the real axis.

Half Plane


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

The complex plane z = x + iy contains an upper half plane y = Im z > 0, a lower half plane y = Im z < 0, a left half plane x = Re z < 0, a right half plane x = Re z > 0, and so on. The upper half plane of the complex z-plane is mapped conformally onto the circle ǀwǀ < 1 by the linear fractional function

where θ is an arbitrary real number and Im β > 0.

References in periodicals archive ?
The other issue was the lack of the so-called half-space.
The Institute for Meteorology and Climate Research, Troposphere Research Unit (IMK-TRO) at the Karlsruhe Institute of Technology (KIT) intends to procure 2 pairs of Doppler Lidar wind meters with 2-axis scanners for contactless scanning of the entire half-space above the device.
In the frame of improving the method of electromagnetic diagnosis of the grounding device based on the analytical solution of the problem of the electric field of a point power source located on the surface of the four-layer conducting half-space with plane-parallel boundaries of division, the authors have developed mathematical apparatus [5] for the interpretation of results of sounding and equivalentiation [2] of multilayer structures in the computational models.
In the upper half-space model however, this is, in general, not the case.
With this in mind, the greatest number of solutions is developed for the soil as linearly elastic, homogenous and isotropic half-space [5].
The effect of porosity, initial stress, and gravity has been described by many researchers in several Earth structures as when the porosity of the porous half-space increases, the phase velocity decreases, whereas the sandy parameter has increasing effect in the propagation of Love waves concluded by Pal and Ghorai [5].
Coman likes to hog the touchline, opening room for the attacking full-back or the half-space channels for a midfielder.
In a three-dimensional elastic half-space, elastic equilibrium equations in terms of displacement components [u.
Love waves in a two-layered half-space was studied by Singh [30].
An imperfect interface of a homogeneous, isotropic generalized thermoelastic half-space (medium [M.
Transient loading of elastic half-space by a point force, whose time distribution is given by the Heaviside function