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The word weight has many uses in mathematics. It can refer to a function w(x) (also called a weighting function or weighting function) used to normalize orthogonal functions. ...

A bundle map is a map between bundles along with a compatible map between the base manifolds. Suppose p:X->M and q:Y->N are two bundles, then F:X->Y is a bundle map if there ...

A coequalizer of a pair of maps f,g:X->Y in a category is a map c:Y->C such that 1. c degreesf=c degreesg, where degrees denotes composition. 2. For any other map c^':Y->C^' ...

A group generated by the elements P_i for i=1, ..., n subject to (P_iP_j)^(M_(ij))=1, where M_(ij) are the elements of a Coxeter matrix. Coxeter used the notation [3^(p,q,r)] ...

An equalizer of a pair of maps f,g:X->Y in a category is a map e:E->X such that 1. f degreese=g degreese, where degrees denotes composition. 2. For any other map e^':E^'->X ...

Let F and G be fibered categories over a topological space X. A morphism phi:F->G of fibered categories consists of: 1. a functor phi(U):F->G(U) for each open subset U ...

The theorem in set theory and logic that for all sets A and B, B=(A intersection B^_) union (B intersection A^_)<=>A=emptyset, (1) where A^_ denotes complement set of A and ...

The minimum leaf number ml(G) of a connected graph G is the smallest number of tree leaves in any of its spanning trees. (The corresponding largest number of leaves is known ...

A tree is planted at each lattice point in a circular orchard which has center at the origin and radius r. If the radius of trees exceeds 1/r units, one is unable to see out ...

An alkane graph is a tree in which vertices correspond to atoms and edges to carbon-carbon or hydrogen-carbon bonds in a chemical alkane. In chemistry, an alkane is an ...