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The total graph T(G) of a graph G has a vertex for each edge and vertex of G and an edge in T(G) for every edge-edge, vertex-edge, and vertex-vertex adjacency in G ...

A matrix for a round-robin tournament involving n players competing in n(n-1)/2 matches (no ties allowed) having entries a_(ij)={1 if player i defeats player j; -1 if player ...

Let H be a Hilbert space and (e_i)_(i in I) an orthonormal basis for H. The set of all products of two Hilbert-Schmidt operators is denoted N(H), and its elements are called ...

Let f:R×R->R be a one-parameter family of C^2 maps satisfying f(0,mu)=0 (1) [(partialf)/(partialx)]_(mu=0,x=0)=0 (2) [(partial^2f)/(partialxpartialmu)]_(0,0)>0 (3) ...

The transitive closure of a binary relation R on a set X is the minimal transitive relation R^' on X that contains R. Thus aR^'b for any elements a and b of X provided that ...

A transformation consisting of a constant offset with no rotation or distortion. In n-dimensional Euclidean space, a translation may be specified simply as a vector giving ...

Two submanifolds X and Y in an ambient space M intersect transversally if, for all p in X intersection Y, TX_p+TY_p={v+w:v in TX_p,w in TY_p}=TM_p, where the addition is in ...

A foliation F of dimension p on a manifold M is transversely orientable if it is integral to a p-plane distribution D on M whose normal bundle Q is orientable. A p-plane ...

The 2-point Newton-Cotes formula int_(x_1)^(x_2)f(x)dx=1/2h(f_1+f_2)-1/(12)h^3f^('')(xi), where f_i=f(x_i), h is the separation between the points, and xi is a point ...

A tree decomposition is a mapping of a graph into a related tree with desirable properties that allow it to be used to efficiently compute certain properties (e.g., ...