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Let W(u) be a Wiener process. Then where V_t=f(W(t),tau) for 0<=tau=T-t<=T, and f in C^(2,1)((0,infty)×[0,T]). Note that while Ito's lemma was proved by Kiyoshi Ito (also ...

The Kampyle of Eudoxus is a curve studied by Eudoxus in relation to the classical problem of cube duplication. It is given by the polar equation r=asec^2theta, (1) and the ...

Let D be a domain in R^n for n>=3. Then the transformation v(x_1^',...,x_n^')=(a/(r^'))^(n-2)u((a^2x_1^')/(r^('2)),...,(a^2x_n^')/(r^('2))) onto a domain D^', where ...

Let J_nu(z) be a Bessel function of the first kind, N_nu(z) a Bessel function of the second kind, and j_(nu,n)(z) the zeros of z^(-nu)J_nu(z) in order of ascending real part. ...

An algebraically soluble equation of odd prime degree which is irreducible in the natural field possesses either 1. Only a single real root, or 2. All real roots.

The Kuhn-Tucker theorem is a theorem in nonlinear programming which states that if a regularity condition holds and f and the functions h_j are convex, then a solution ...

A self-adjoint elliptic differential operator defined somewhat technically as Delta=ddelta+deltad, where d is the exterior derivative and d and delta are adjoint to each ...

Let alpha(x) be a monotone increasing function and define an interval I=(x_1,x_2). Then define the nonnegative function U(I)=alpha(x_2)-alpha(x_1). The Lebesgue integral with ...

A likelihood function L(a) is the probability or probability density for the occurrence of a sample configuration x_1, ..., x_n given that the probability density f(x;a) with ...

The line bisecting a given line segment P_1P_2 can be constructed geometrically, as illustrated above.