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The set of n quantities v_j are components of an n-dimensional vector v iff, under rotation, v_i^'=a_(ij)v_j (1) for i=1, 2, ..., n. The direction cosines between x_i^' and ...

A compact set W_infty with area mu(W_infty)=8/9(24)/(25)(48)/(49)...=pi/4 created by punching a square hole of length 1/3 in the center of a square. In each of the eight ...

The singleton set {0}, with respect to the trivial group structure defined by the addition 0+0=0. The element 0 is the additive identity element of the group, and also the ...

The constant polynomial P(x)=0 whose coefficients are all equal to 0. The corresponding polynomial function is the constant function with value 0, also called the zero map. ...

A group is called k-transitive group if there exists a set of elements on which the group acts faithfully and k-transitively. It should be noted that transitivity computed ...

The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain ...

The n-crown graph for an integer n>=3 is the graph with vertex set {x_0,x_1,...,x_(n-1),y_0,y_1,...,y_(n-1)} (1) and edge set {(x_i,y_j):0<=i,j<=n-1,i!=j}. (2) It is ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...

An affine variety V is an algebraic variety contained in affine space. For example, {(x,y,z):x^2+y^2-z^2=0} (1) is the cone, and {(x,y,z):x^2+y^2-z^2=0,ax+by+cz=0} (2) is a ...