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Any transformation of the plane leaving this pattern invariant can be decomposed into a translation, ( x, y ) → ( n + x, y ), optionally followed by a reflection in either the horizontal axis, ( x, y ) → ( x ,− y ), or the vertical axis, ( x, y ) → (− x, y ), provided that this axis is chosen through or midway between two dots, or a rotation by 180 °, ( x, y ) → (− x ,− y ) ( ditto ).
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Any and transformation
Any conformal map on a portion of Euclidean space of dimension greater than 2 can be composed from three types of transformation: a homothetic transformation, an isometry, and a special conformal transformation.
: Any linear transformation f: V → A from V to an algebra A over K can be uniquely extended to an algebra homomorphism from T ( V ) to A as indicated by the following commutative diagram:
Any waveform can be disassembled into its spectral components by Fourier analysis or Fourier transformation.
Any segments of the enterprise that are not service-oriented can also be documented in order to consider transformation requirements if a service needs to communicate with the business processes automated by such segments.
Any canonical transformation involving a type-2 generating function G < sub > 2 </ sub >( q, P, t ) leads to the relations
Any two triplets obeying these relationships must be related by a linear transformation ; they represent utility indices differing only by scale and origin.
Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space.
Any and plane
Any direction can potentially serve as the plane of reference, as long as it is clearly defined for everyone using that system.
Any non-singular curve on a smooth surface will have its tangent vector T lying in the tangent plane of the surface orthogonal
Any real analytic function on some open set on the real line can be extended to a complex analytic function on some open set of the complex plane.
Any transversal section of a plane perpendicular to this axis has to behave as a two dimensional rotation.
Any precise description of a brain section plane therefore has to make reference to the anteroposterior part of the brain to which the description refers ( e. g., transverse to the midbrain, or horizontal to the diencephalon ).
Any stereographic projection of a sphere onto a plane will produce one " point at infinity ", and it will map the lines of latitude and longitude on the sphere into circles and straight lines, respectively, in the plane.
Any plane can be defined by two non-collinear vectors lying in that plane ; taking their cross product and normalizing yields the normal unit vector to the plane.
Any number of vanishing points are possible in a drawing, one for each set of parallel lines that are at an angle relative to the plane of the drawing.
Any plane that attempted to break off contact by going into a dive would soon be overcome by the remarkable speed of the P-47.
Any closed curve within the plane bounds a disk below the plane that does not pass through any other graph feature, and any closed curve through the apex bounds a disk above the plane that does not pass through any other graph feature.
# Any three points A, B, C of a plane α, which do not lie in the same straight line, completely determine that plane.
Any finite set of lines in the Euclidean plane has a combinatorially equivalent arrangement in the hyperbolic plane ( e. g. by enclosing the vertices of the arrangement by a large circle and interpreting the interior of the circle as a Klein model of the hyperbolic plane ).
Any unprotected living creature exposed to the Negative Energy plane has its life force rapidly drained and will die when they run out.
Any plants or animals swallowed by the bag in this way are transported to the creature's stomach, digested, and lost forever, while inedible items are swallowed and spat into another plane.
Any and leaving
Any player entering or leaving the play must cross the substitution line which is part of the side line and extends 4. 5 meters from the middle line to the team's side.
Any and all plans for the character were ultimately shelved, and Victoria Winters was unceremoniously written out with an off-screen death, leaving her as much of a mystery as when she first arrived.
Any attempt to pan up or down would cause it to flop down, leaving it pointing uselessly at the ground and requiring an astronaut to repoint it.
Any and pattern
" Any sequence of numbers that may be modeled by a mathematical function can be considered a pattern.
Any value that matches the pattern in the second clause will also match the pattern in the first clause, so the second clause is unreachable.
The angles in this pattern are not intrinsic properties of water ; Any isentropic and incompressible liquid with low viscosity will exhibit the same phenomenon.
Plus, under " Other Varieties ", a fifth group, the BRC allows " Any Other Color ... so long as it conforms to the normal pattern of accepted colours of other breeds.
The February 2002 ICG report says that this attack was made by pursuing ‘ a strategy of infiltration of south-western Liberia through the thick bush of Southern Lofa, looping around government strongholds and disrupting supply lines ... while LURD claims between 300 and 500 men were assigned to that mission ,... the number that actually attacked was likely closer to twenty .’ Any image of a large force gradually pushing toward Monrovia is mistaken ; ‘ hit and run ’ raids, rather than a continuous advance, seem to have been the pattern.
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