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Given a system of ordinary differential equations of the form d/(dt)[x; y; v_x; v_y]=-[0 0 -1 0; 0 0 0 -1; Phi_(xx)(t) Phi_(yx)(t) 0 0; Phi_(xy)(t) Phi_(yy)(t) 0 0][x; y; ...

A bitangent is a line that is tangent to a curve at two distinct points. Aa general plane quartic curve has 28 bitangents in the complex projective plane. However, as shown ...

Given a ring R with identity, the special linear group SL_n(R) is the group of n×n matrices with elements in R and determinant 1. The special linear group SL_n(q), where q is ...

A formal power series, sometimes simply called a "formal series" (Wilf 1994), of a field F is an infinite sequence {a_0,a_1,a_2,...} over F. Equivalently, it is a function ...

There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...

A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

For real, nonnegative terms x_n and real p with 0<p<1, the expression lim_(k->infty)x_0+(x_1+(x_2+(...+(x_k)^p)^p)^p)^p converges iff (x_n)^(p^n) is bounded.

The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers aleph_0 and the "large" ...

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

An approach for the calculation of a Gröbner basis into several smaller computations following a path in the Gröbner fan of the ideal generated by the system of inequalities.