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An algebraic equation in n variables is an polynomial equation of the form f(x_1,x_2,...,x_n)=sum_(e_1,...,e_n)c_(e_1,e_2,...,e_n)x_1^(e_1)x_2^(e_2)...x_n^(e_n)=0, where the ...

An algebraic set is the locus of zeros of a collection of polynomials. For example, the circle is the set of zeros of x^2+y^2-1 and the point at (0,0) is the set of zeros of ...

A Banach algebra A for which H^1(A,X^*)=Z^1(A,X^*)/B^1(A,X^*)=0 for all Banach A-bimodules X is called amenable (or Johnson amenable; Helemskii 1989, 1997). This notion was ...

The Andrews-Schur identity states sum_(k=0)^nq^(k^2+ak)[2n-k+a; k]_q =sum_(k=-infty)^inftyq^(10k^2+(4a-1)k)[2n+2a+2; n-5k]_q([10k+2a+2]_q)/([2n+2a+2]_q) (1) where [n; m]_q is ...

A plane tiling is said to be isohedral if the symmetry group of the tiling acts transitively on the tiles, and n-isohedral if the tiles fall into n orbits under the action of ...

Consider the circle map. If K is nonzero, then the motion is periodic in some finite region surrounding each rational Omega. This execution of periodic motion in response to ...

If, for n>=0, beta_n=sum_(r=0)^n(alpha_r)/((q;q)_(n-r)(aq;q)_(n+r)), (1) then beta_n^'=sum_(r=0)^n(alpha_r^')/((q;q)_(n-r)(aq;q)_(n+r)), (2) where alpha_r^' = ...

The Bickart points are the foci F_1 and F_2 of the Steiner circumellipse. They have trilinear coordinates alpha_1:beta_1:gamma_1 and alpha_2:beta_2:gamma_2, where alpha_i = ...

The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties of function algebras. The theorem says that, given a ...

A map is called bijective if it is both injective and surjective. A bijective map is also called a bijection. A function f admits an inverse f^(-1) (i.e., "f is invertible") ...