Search Results for ""

Let psi_1(x) and psi_2(x) be any two real integrable functions in [a,b], then Schwarz's inequality is given by |<psi_1|psi_2>|^2<=<psi_1|psi_1><psi_2|psi_2>. (1) Written out ...

In the above illustration, black dots appear to form and vanish at the intersections of the gray horizontal and vertical lines. When focusing attention on a single white dot, ...

A secant line, also simply called a secant, is a line passing through two points of a curve. As the two points are brought together (or, more precisely, as one is brought ...

The second Brocard point is the interior point Omega^' (also denoted tau_2 or Z_2) of a triangle DeltaABC with points labeled in counterclockwise order for which the angles ...

Let c_1, c_2, and c_3 be the circles through the vertices A_2 and A_3, A_1 and A_3, and A_1 and A_2, respectively, which intersect in the first Brocard point Omega. ...

In the most commonly used convention (e.g., Apostol 1967, pp. 205-207), the second fundamental theorem of calculus, also termed "the fundamental theorem, part II" (e.g., ...

Every smooth nonzero vector field on the 3-sphere has at least one closed orbit. The conjecture was proposed in 1950 and proved true for Hopf maps. The conjecture was ...

Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress. The formula for the volume of a cylinder leads to the ...

A sequential substitution system is a substitution system in which a string is scanned from left to right for the first occurrence of the first rule pattern. If the pattern ...

Series reversion is the computation of the coefficients of the inverse function given those of the forward function. For a function expressed in a series with no constant ...