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A metric space Z^^ in which the closure of a congruence class B(j,m) is the corresponding congruence class {x in Z^^|x=j (mod m)}.

A pseudo-Riemannian manifold is a manifold which has a metric that is of the signature diag(-,+,...,+), as compared to a Riemannian manifold, which has a signature of all ...

An action which adds a single element to the top of a stack, turning the stack (a_1, a_2, ..., a_n) into (a_0, a_1, a_2, ..., a_n).

Given the binary quadratic form ax^2+2bxy+cy^2 (1) with polynomial discriminant b^2-ac, let x = pX+qY (2) y = rX+sY. (3) Then a(pX+qY)^2+2b(pX+qY)(rX+sY)+c(rX+sY)^2 ...

A commutative unit ring having only finitely many maximal ideals.

When a measure lambda is absolutely continuous with respect to a positive measure mu, then it can be written as lambda(E)=int_Efdmu. By analogy with the first fundamental ...

For a delta function at (x_0,y_0), R(p,tau) = int_(-infty)^inftyint_(-infty)^inftydelta(x-x_0)delta(y-y_0)delta[y-(tau+px)]dydx (1) = ...

int_0^inftycos(2zt)sech(pit)dt=1/2sechz for |I[z]|<pi/2. A related integral is int_0^inftycosh(2zt)sech(pit)dt=1/2secz for |R[z]|<pi/2.

A statistical distribution in which the variates occur with probabilities asymptotically matching their "true" underlying statistical distribution is said to be random.

A real matrix is a matrix whose elements consist entirely of real numbers. The set of m×n real matrices is sometimes denoted R^(m×n) (Zwillinger 1995, p. 116).