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 complete subtree of the tree is a constituent.

Any set of sequences can be represented as paths in a tree, by forming a tree node for every prefix of a sequence and making the parent of one of these nodes represent the sequence with one fewer element ; the tree formed in this way for a set of strings is called a trie.

Any suitable tree or large bush may be used for nesting, though an evergreen is preferred.

* Any member of the genus Pseudohaje, the tree cobras, a group of venomous elapids found in Africa

Any subtree that can be used to solve the game is known as a decision tree, and the sizes of decision trees of various shapes are used as measures of game complexity.

Any rain that falls is channeled down the phyllodes and branches to be collected in the soil immediately next to the trunk, providing the tree with a more than threefold increase in effective rainfall.

Any pa ( or sentential logic ) formula B can be viewed as an ordered tree with branches.

* Any of several species of tree of genus Shorea

Any binary tree can be viewed as defining a prefix code for the leaves of the tree.

* Widowmaker: Any branch or treetop that is poorly or no longer attached to a tree, but still tangled overhead ; does not discriminate among potential victims by gender or marital status.

* Any of a number of tree species in the genera Gleditsia or Robinia

Any other Amber ( such as Baltic Amber ) will not display this phenomenon, because its original resin is not from the Hymenaea protera tree.

:“ Any linear map from V to an algebra A can be uniquely extended to an algebra homomorphism from T ( V ) to A .”

Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and / or its surrounding.

Any such value of q is called a Lipschitz constant for T, and the smallest one is sometimes called " the best Lipschitz constant " of T.

Any actions taken today, at time T, will affect who exists after only a few generations.

Any non-singular curve on a smooth surface will have its tangent vector T lying in the tangent plane of the surface orthogonal

Any advantage of the I. T. A.

: 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 function T of the form

Any Hausdorff ( T < sub > 2 </ sub >) space is sober ( the only irreducible subsets being points ), and all

Any self-adjoint operator T has a unique Borel functional calculus.

Any theory T categorical in some infinite cardinal κ is very close to being complete.

Any non-singular matrix S of the same size is said to transform A into another symmetric matrix B = SAS < sup > T </ sup >, also of order n, where S < sup > T </ sup > is the transpose of S. If A is the coefficient matrix of some quadratic form of R < sup > n </ sup >, then B is the matrix for the same form after the change of coordinates defined by S.

Any symmetric real matrix A has an eigendecomposition of the form QEQ < sup > T </ sup > where E is a diagonal matrix containing the eigenvalues of A, and Q is an orthonormal square matrix containing the eigenvectors.

Any temperature below T < sub > base </ sub > is set to T < sub > base </ sub > before calculating the average.

Any of these compounds supplies the body with its iodine required for the biosynthesis of thyroxine ( T < sub > 4 </ sub >) and triiodothyronine ( T < sub > 3 </ sub >) hormones by the thyroid gland.

* Any countable discrete group with property ( T ) is finitely generated.

However, it was the ability of japan black to dry quickly that made it a favorite of early mass produced automobiles such as Henry Ford's Model T. The Ford company's reliance on japan black led Henry Ford to quip " Any customer can have a car painted any colour that he wants so long as it is black ".

Any NatureServe rank may be used alone, or G -, T -, N -, and S-ranks may be combined in that sequence, such as a G5N3S1 rank for a particular species ( or ecological community ) within a particular subnational unit of a particular nation.

Any nonuniformity, such as caused by a wave front in the air at T, causes a scattered light beam to evade the screen, K2 ( path a ), and reach the film.

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.

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 nonplanar graph has as minors either the complete graph, or the complete bipartite graph, but the Petersen graph has both as minors.

Any ten-vertex Hamiltonian 3-regular graph consists of a ten-vertex cycle C plus five chords.

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.

Any directed graph may be made into a DAG by removing a feedback vertex set or a feedback arc set.

Any square matrix can be viewed as the adjacency matrix of a weighted directed graph, with representing the weight of the arc from vertex i to vertex j.

Any of these equations can be plotted on a graph.

Any linear code can be represented as a graph, where there are two sets of nodes-a set representing the transmitted bits and another set representing the constraints that the transmitted bits have to satisfy.

Any graph is homomorphically equivalent to a unique core.

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 induced subgraph of a comparability graph is itself a comparability graph, formed from the restriction of the partial order to a subset of its elements.

Any finite graph has a finite ( though perhaps exponential ) number of distinct simple cycles, and if the graph is embedded into three-dimensional space then each of these cycles forms a simple closed curve.

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 Bayesian network or Markov random field can be represented as a factor graph.