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Let G be an algebraic group. G together with the discrete topology is a locally compact group and one may consider the counting measure as a left invariant Haar measure on G. ...

A number of attractive 2-compounds of the regular dodecahedron can be constructed. The first (left figures) has the symmetry of the cube and arises by combining two regular ...

An elliptic curve is the set of solutions to an equation of the form y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6. (1) By changing variables, y->2y+a_1x+a_3, assuming the field ...

The finite volume method is a numerical method for solving partial differential equations that calculates the values of the conserved variables averaged across the volume. ...

Any one of the eight Apollonius circles of three given circles is tangent to a circle H known as a Hart circle, as are the other three Apollonius circles having (1) like ...

Let (q_1,...,q_n,p_1,...,p_n) be any functions of two variables (u,v). Then the expression ...

A quantity used to test nested hypotheses. Let H^' be a nested hypothesis with n^' degrees of freedom within H (which has n degrees of freedom), then calculate the maximum ...

A linear algebraic group is a matrix group that is also an affine variety. In particular, its elements satisfy polynomial equations. The group operations are required to be ...

The n functions f_1(x), f_2(x), ..., f_n(x) are linearly dependent if, for some c_1, c_2, ..., c_n in R not all zero, sum_(i=1)^nc_if_i(x)=0 (1) for all x in some interval I. ...

A maximal ideal of a ring R is an ideal I, not equal to R, such that there are no ideals "in between" I and R. In other words, if J is an ideal which contains I as a subset, ...