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In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees.
2-dimensional section of Reeb foliation 3-dimensional model of Reeb foliation. In mathematics (differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension p, modeled on the decomposition of the real coordinate space R n into the cosets x + R p of the standardly embedded ...
Nonconcatenative morphology is extremely well developed in the Semitic languages in which it forms the basis of virtually all higher-level word formation (as with the example given in the diagram). That is especially pronounced in Arabic , which also uses it to form approximately 41% [ 5 ] of plurals in what is often called the broken plural .
In the iterative generation, it is applied with probability 7% and is intuitively responsible for the generation of the lower-left leaf. f 4 x n + 1 = −0.15 x n + 0.28 y n y n + 1 = 0.26 x n + 0.24 y n + 0.44. Similarly, this transformation encodes the self-similarity of the entire fern with the bottom right leaf.
Diagram of flower parts. In botany, floral morphology is the study of the diversity of forms and structures presented by the flower, which, by definition, is a branch of limited growth that bears the modified leaves responsible for reproduction and protection of the gametes, called floral pieces.
In mathematics, an isomorphism is a structure-preserving mapping (a morphism) between two structures of the same type that can be reversed by an inverse mapping.Two mathematical structures are isomorphic if an isomorphism exists between them.
The commutative diagram used in the proof of the five lemma. In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. [1] It is said that commutative diagrams play the role in category theory that equations play in ...
A parse tree is made up of nodes and branches. [4] In the picture the parse tree is the entire structure, starting from S and ending in each of the leaf nodes (John, ball, the, hit). In a parse tree, each node is either a root node, a branch node, or a leaf node. In the above example, S is a root node, NP and VP are branch nodes, while John ...