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For example, two identical transparent gratings of 50% duty cycle and the same orientation will appear fully opaque only if the relative phase is π (180 degrees). Gratings with sine wave profiles are used extensively in optics to determine the transfer functions of lenses. A lens will form an image of a sine wave grating that is still ...
A strong orientation is an orientation that results in a strongly connected graph. The closely related totally cyclic orientations are orientations in which every edge belongs to at least one simple cycle. An orientation of an undirected graph G is totally cyclic if and only if it is a strong orientation of every connected component of G.
The chart is smooth except for a polar coordinate style singularity along β = 0. See charts on SO(3) for a more complete treatment. The space of rotations is called in general "The Hypersphere of rotations ", though this is a misnomer: the group Spin(3) is isometric to the hypersphere S 3 , but the rotation space SO(3) is instead isometric to ...
Grate firing is a type of industrial combustion system used for solid fuels. It now is used mainly for burning waste and biomass, but also for smaller coal furnaces. Capacities 0.3 to 175 MWth in industry and CHP; Fuel fired per grate area 1-2 MW/m 2, maximum grate area 100 m 2
A blazed diffraction grating reflecting only the green portion of the spectrum from a room's fluorescent lighting. For a diffraction grating, the relationship between the grating spacing (i.e., the distance between adjacent grating grooves or slits), the angle of the wave (light) incidence to the grating, and the diffracted wave from the grating is known as the grating equation.
Coordinate charts are mathematical objects of topological manifolds, and they have multiple applications in theoretical and applied mathematics. When a differentiable structure and a metric are defined, greater structure exists, and this allows the definition of constructs such as integration and geodesics .
By definition, a rotation about the origin is a transformation that preserves the origin, Euclidean distance (so it is an isometry), and orientation (i.e., handedness of space). Composing two rotations results in another rotation, every rotation has a unique inverse rotation, and the identity map satisfies the definition of a rotation.