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Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

Given a principal bundle pi:A->M, with fiber a Lie group G and base manifold M, and a group representation of G, say phi:G×V->V, then the associated vector bundle is ...

The finite group C_2×C_2 is one of the two distinct groups of group order 4. The name of this group derives from the fact that it is a group direct product of two C_2 ...

Just as many interesting integer sequences can be defined and their properties studied, it is often of interest to additionally determine which of their elements are prime. ...

The dihedral group D_3 is a particular instance of one of the two distinct abstract groups of group order 6. Unlike the cyclic group C_6 (which is Abelian), D_3 is ...

Let Gamma be a representation for a group of group order h, then sum_(R)Gamma_i(R)_(mn)Gamma_j(R)_(m^'n^')^*=h/(sqrt(l_il_j))delta_(ij)delta_(mm^')delta_(nn^'). The proof is ...

A basis for the real numbers R, considered as a vector space over the rationals Q, i.e., a set of real numbers {U_alpha} such that every real number beta has a unique ...

The dimension d of any irreducible representation of a group G must be a divisor of the index of each maximal normal Abelian subgroup of G. Note that while Itô's theorem was ...

A wavelet used in multiresolution representation to analyze the information content of images. The wavelet is defined by ...

A continuous homomorphism of a group into the nonzero complex numbers. A multiplicative character omega gives a group representation on the one-dimensional space C of complex ...