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The term "loop" has a number of meanings in mathematics. Most simply, a loop is a closed curve whose initial and final points coincide in a fixed point p known as the ...

Let A and B be two algebras over the same signature Sigma, with carriers A and B, respectively (cf. universal algebra). B is a subalgebra of A if B subset= A and every ...

Qubic is a generalization of tic-tac-toe in which players alternately place pieces to get four in a row (rows, columns, pillars, face diagonals, or space diagonals) on a ...

A topological space fulfilling the T_2-axiom: i.e., any two points have disjoint neighborhoods. In the terminology of Alexandroff and Hopf (1972), a T_2-space is called a ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

A diagram lemma which states that the above commutative diagram of Abelian groups and group homomorphisms with exact rows gives rise to an exact sequence This commutative ...

Let phi_0 be the latitude for the origin of the Cartesian coordinates and lambda_0 its longitude, and let phi_1 and phi_2 be the standard parallels. Then for a unit sphere, ...

Plouffe's constants are numbers arising in summations of series related to r_n=f(2^n) where f is a trigonometric function. Define the Iverson bracket function rho(x)={1 for ...

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 ...

Let phi:M->M be a C^1 diffeomorphism on a compact Riemannian manifold M. Then phi satisfies Axiom A if the nonwandering set Omega(phi) of phi is hyperbolic and the periodic ...