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Page "Involution (mathematics)" ¶ 14
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Any and two
Any example of grand or exquisite diction may have been created by the poet who compiled numerous lays into the two works we possess or may be due to one of his completely unknown fellow-craftsmen.
Any player may declare the game over at any time during his turn if either of two conditions is true: one chain has 41 or more tiles, or there is at least one chain on the board and every chain on the board has 11 or more tiles.
Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to classical ( i. e. non-quantum ) mechanics.
Any solute partitions between two immiscible solvents.
Any two regular curves are locally isometric.
Note: Any nonlinear electronic block driven by two signals with frequencies f < sub > 1 </ sub > and f < sub > 2 </ sub > would generate intermodulation ( mixing ) products.
* Any two finite fields with the same number of elements are isomorphic.
# Any two points can be joined by a straight line.
* Extensibility: Any database system has its own predefined set of data types which we can use to build new types ( see Complex Objects ), but a purely extensible system is designed such that there are no logical differences between built-in ( or ' primitive ') data types and ' custom ' data types, though there may be strong differences in the way the two are implemented.
Any potato variety can also be propagated vegetatively by planting tubers, pieces of tubers, cut to include at least one or two eyes, or also by cuttings, a practice used in greenhouses for the production of healthy seed tubers.
Any sort of wavetable synthesis requires one of the two SH-2 processors to do this in software.
# Any live cell with fewer than two live neighbours dies, as if caused by under-population.
# Any live cell with two or three live neighbours lives on to the next generation.
In July 2006, a book, ' Peace at Any Price: How the World Failed Kosovo ', written by two former senior staffers at UNMIK, exposed a catalogue of errors and incompetence in the institution over its seven year history.
There are two exceptions: 1 ) Any affidavit sworn in the course of the collaboration and vouching documentation attaching to same and 2 ) any interim agreement made and signed off in the course of the collaboration or correspondence relating thereto.
Any induced noise would be present in equal amounts and in identical polarity on each of the balanced signal conductors, so the two signals ’ difference from each other would be unchanged.
Eastwood's only comedies have been Every Which Way but Loose ( 1978 ) and its sequel Any Which Way You Can ( 1980 ), which are his two most commercially successful films after adjustment for inflation.
Any player reduced to two pieces is unable to remove any more opposing pieces and thus loses the game.
* Any two vertices in G can be connected by a unique simple path.
Any two of these bases are conjugate to each other, and so any two can be used in the protocol.
Any discussion of the sources of Titus Andronicus is complicated by the existence of two other versions of the story ; a prose history and a ballad ( both of which are anonymous and undated ).
* Any topological space can be viewed as a category by taking the open sets as objects, and a single morphism between two open sets and if and only if.
Any category with this property is necessarily a thin category: for any two objects there can be at most one morphism from one object to the other.
Any non-zero change of direction is possible: if this distance is zero the velocities are reversed in the collision ; if it is close to the sum of the radii of the spheres the two bodies are only slightly deflected.

Any and points
Any convex polyhedron can be distorted into a canonical form, in which a midsphere ( or intersphere ) exists tangent to every edge, such that the average position of these points is the center of the sphere, and this form is unique up to congruences.
# Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold.
Any overbid or underbid loses the number of points their bid was off ( a player bidding 3 tricks that wins only 2 would lose a point, as would a player bidding 2 and winning 3 ).
Any geostationary object placed between the equilibrium points would ( without any action ) be slowly accelerated towards the stable equilibrium position, causing a periodic longitude variation.
Any hyperplane can be written as the set of points satisfying
Any list of indigetes, however, is conjectural ; Raimo Anttila points out that " we do not know the list of the di indigetes.
Any set or euchre by a single defender going alone is worth 4 points to the defending partnership, or 3 in some regions.
:* Any conic should meet the line at infinity at two points according to the theorem.
Any conic that passes through the four orthocentric points can only be a rectangular hyperbola.
Any rider taking a tactical substitute ride or double points ride is denoted by a black and white helmet colour as rather than one of the four usual coloured helmets.
* Any line has at least 3 points on it.
* Any two distinct points lie on a unique line.
Any dog that has earned the title of Field Champion and has earned 45 additional championship points from the Special or Veterans Stake, shall be awarded the suffix title of Lure Courser Excellent ( LCX ).
* Any unit not reporting within 15 minutes of their set inspection time shall be penalized 2 points ; a unit not reporting within 30 minutes shall be penalized 4 points.
Any point x gives rise to a continuous function p < sub > x </ sub > from the one element topological space 1 ( all subsets of which are open ) to the space X by defining p < sub > x </ sub >( 1 ) = x. Conversely, any function from 1 to X clearly determines one point: the element that it " points " to.
Any perspective representation of a scene that includes parallel lines has one or more vanishing points in a perspective drawing.
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 discrete subset of Euclidean space is countable, since the isolation of each of its points ( together with the fact the rationals are dense in the reals ) means that it may be mapped 1-1 to a set of points with rational co-ordinates, of which there are only countably many.
Any team now going into administration is automatically deducted 10 points, although even with this punishment Leicester would still have been two points clear of United, albeit with a far stronger team as a result of the move into administration.
* Any attempt to manipulate a match in regard to the result ( In a negative way ), net run rate, bonus points or otherwise.

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