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 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 directed graph generates a small category: the objects are the vertices of the graph, and the morphisms are the paths in the graph ( augmented with loops as needed ) where composition of morphisms is concatenation of paths.

Any undirected graph may be made into a DAG by choosing a total order for its vertices and orienting every edge from the earlier endpoint in the order to the later endpoint.

Reconstruction Conjecture: Any two hypomorphic graphs on at least three vertices are isomorphic.

Set Reconstruction Conjecture: Any two graphs on at least four vertices with the same sets of vertex-deleted subgraphs are isomorphic.

Any four exterior vertices determine a cyclic quadrilateral, and all cyclic quadrilaterals are convex quadrilaterals, so each set of four exterior vertices have exactly one point of intersection formed by their diagonals ( chords ).

A graph coloring is an assignment of one of k colors to a graph G so that the endpoints of each edge have different colors, for some number k. Any coloring corresponds to a homomorphism from G to a complete graph K < sub > k </ sub >: the vertices of K < sub > k </ sub > correspond to the colors of G, and f maps each vertex of G with color c to the vertex of K < sub > k </ sub > that corresponds to c. This is a valid homomorphism because the endpoints of each edge of G are mapped to distinct vertices of K < sub > k </ sub >, and every two distinct vertices of K < sub > k </ sub > are connected by an edge, so every edge in G is mapped to an adjacent pair of vertices in K < sub > k </ sub >.

Any point located on this triangle may then be written as a weighted sum of these three vertices, i. e.

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 ).

Let now v and w be two vertices in G. Any spanning tree contains precisely one simple path between v and w. Taking this path in the uniform spanning tree gives a random simple path.

Any tournament on a finite number of vertices contains a Hamiltonian path, i. e., directed path on all vertices ( Rédei 1934 ).

Any pair of adjacent vertices can be mapped to another by an Graph automorphism | automorphism, since any five-vertex ring can be mapped to any other.

Any vertices affected by the merge are added or removed from the stacks as appropriate.

Any planar graph with vertices has at most edges, from which it follows by Nash-Williams ' formula that planar graphs have arboricity at most three.

Any spanning tree T of a graph G has at least two leaves, vertices that have only one edge of T incident to them.

Any set of five points in the plane in general position has a subset of four points that form the vertices of a convex quadrilateral.

* Any Lie group G defines an associated real Lie algebra.

Any Lie group G can be decomposed into discrete, simple, and abelian groups in a canonical way as follows.

Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.

Unsigned, Mushroom ( Andy Vowles ), Daddy G ( Grant Marshall ) and 3D ( Robert Del Naja ) put out " Any Love " as a single, co-produced by Bristol double-act Smith & Mighty.

# Any group G may be regarded as an " abstract " category with one object,, and one morphism for each element of the group.

* Any open set is trivially a G < sub > δ </ sub > set

* Any principal bundle with structure group G gives a groupoid, namely over M, where G acts on the pairs componentwise.

* Any Lie group with an infinite group of components G / G < sup > o </ sup > cannot be realized as an algebraic group ( see identity component ).

* Any group G can be considered as a one-object category in which every morphism is invertible.

Any group scheme G of finite type is an extension of the connected component of the identity ( i. e., the maximal connected subgroup scheme ) by a constant group scheme.

Any canonical transformation involving a type-2 generating function G < sub > 2 </ sub >( q, P, t ) leads to the relations

** Any parabolic element of G fixing a boundary point of D is in H.

( 2 ) Any sequence of continuous positive definite functions on G converging to 1 uniformly on compact subsets, converges to 1 uniformly on G.