In this paper we prove Garvan's conjectured formula for the square of the modular discriminant Delta as a 3-by-3 hankel determinant of classical Eisenstein series E_2n. We ...

A recursion operator is an integro-differential operator which maps a generalized symmetry of a nonlinear partial differential equation (PDE) to a new symmetry. Therefore, ...

In calculus, students are introduced to the partial fraction decomposition of a rational function of the form F(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials with real ...

In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent ...

A remote tutoring system of algebra, especially for the factorization of polynomials, is described. The system is aimed at improving the calculating ability of students aged ...

The results of filter design obtained by solving non-linear coefficient derived polynomial equations is reported. Taking Butterworth filters as an example, and working with ...

The multistage shuffle-exchange network is generalized, by replacing the perfect shuffle with an arbitrary permutation pi, in order to pass all permutations using a minimal ...

A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. The algorithm is implemented in ...

We present a Mathematica package that performs the symbolic calculation of integrals of the form ∞  0 e−x/uxn jν (x) jμ(x)dx (1) where jν (x) and ...

Most algebraic calculations which one sees in linear systems theory, for example in IEEE TAC, involve block matrices and so are highly non-commutative. Thus conventional ...