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The score function u(theta) is the partial derivativeof the log-likelihood function F(theta)=lnL(theta), where L(theta) is the standard likelihood function. Defining the ...

A series is said to be convergent if it approaches some limit (D'Angelo and West 2000, p. 259). Formally, the infinite series sum_(n=1)^(infty)a_n is convergent if the ...

The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...

The components of the gradient of the one-form dA are denoted A_(,k), or sometimes partial_kA, and are given by A_(,k)=(partialA)/(partialx^k) (Misner et al. 1973, p. 62). ...

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

A set A of integers is productive if there exists a partial recursive function f such that, for any x, the following holds: If the domain of phi_x is a subset of A, then f(x) ...

The Reynolds transport theorem, also called simply the Reynolds theorem, is an important result in fluid mechanics that's often considered a three-dimensional analog of the ...

The term "recursive function" is often used informally to describe any function that is defined with recursion. There are several formal counterparts to this informal ...

Given a metric g_(alphabeta), the discriminant is defined by g = det(g_(alphabeta)) (1) = |g_(11) g_(12); g_(21) g_(22)| (2) = g_(11)g_(22)-(g_(12))^2. (3) Let g be the ...

The trace of a second-tensor rank tensor T is a scalar given by the contracted mixed tensor equal to T_i^i. The trace satisfies ...