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Find necessary and sufficient conditions that determine when the integral curve of two periodic functions kappa(s) and tau(s) with the same period L is a closed curve.

The underlying set of the fundamental group of X is the set of based homotopy classes from the circle to X, denoted [S^1,X]. For general spaces X and Y, there is no natural ...

The converse of Fisher's theorem.

A theorem that guarantees that the trajectory of Langton's ant is unbounded.

Two lines that lie on top of one another are called coincident lines.

An abbreviation for the cokernel.

The logarithm of the reciprocal of a number, equal to the negative of the logarithm of the number itself, cologx=log(1/x)=-logx.

An m×1 matrix [a_(11); a_(21); |; a_(m1)].

Two algebraic objects that are commutative, i.e., A and B such that A*B=B*A for some operation *, are said to commute with each other.

The process of taking the complement of a set or truth function. In the latter case, complementation is equivalent to the NOT operation.