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 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 finite topological space, including the empty set, is compact.

# Any collection of closed subsets of X with the finite intersection property has nonempty intersection.

Any rational number with a denominator whose only prime factors are 2 and / or 5 may be precisely expressed as a decimal fraction and has a finite decimal expansion.

# Any finite straight line can be extended in a straight line.

* Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

* Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

Any meaningful theory of quantum gravity that makes sense and is predictive at all energy scales must have some deep principle that reduces the infinitely many unknown parameters to a finite number that can then be measured.

Any topological space which is itself finite or countably infinite is separable, for the whole space is a countable dense subset of itself.

Any symmetry group whose elements have a common fixed point, which is true for all finite symmetry groups and also for the symmetry groups of bounded figures, can be represented as a subgroup of orthogonal group O ( n ) by choosing the origin to be a fixed point.

Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.

Any digital modulation scheme uses a finite number of distinct signals to represent digital data.

Any finite product in a preadditive category must also be a coproduct, and conversely.

Any finite subcover of this cover must be bounded, because all balls in the subcover are contained in the largest open ball within that subcover.

According to the historian of science Norwood Russell Hanson: There is no bilaterally-symmetrical, nor excentrically-periodic curve used in any branch of astrophysics or observational astronomy which could not be smoothly plotted as the resultant motion of a point turning within a constellation of epicycles, finite in number, revolving around a fixed deferent. Any path — periodic or not, closed or open — can be represented with an infinite number of epicycles.

Any rational function of a real variable can be written as the sum of a polynomial function and a finite number of algebraic fractions.

* Any finite contiguous subsequence of a word

Any finite extension of a finite field is a cyclic extension.

Any structure implicit in the finite entropy against a quantum description could then be totally washed out by the huge injection of uncertainty this projection represents.

Any Calabi – Yau manifold has a finite cover that is the product of a torus and a simply-connected Calabi – Yau manifold.

Any finite simplicial complex in the sense talked about here can be embedded as a polytope in that sense, in some large number of dimensions.

Any Fredholm operator has an index, defined as the difference between the ( finite ) dimension of the kernel of D ( solutions of Df = 0 ), and the ( finite ) dimension of the cokernel of D ( the constraints on the right-hand-side of an inhomogeneous equation like Df

* Any category with finite products is monoidal with the product as the monoidal product and the terminal object as the unit.