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The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...

A Vandermonde matrix is a type of matrix that arises in the polynomial least squares fitting, Lagrange interpolating polynomials (Hoffman and Kunze p. 114), and the ...

Let p be an irregular prime, and let P=rp+1 be a prime with P<p^2-p. Also let t be an integer such that t^3≢1 (mod P). For an irregular pair (p,2k), form the product ...

Let [arg(f(z))] denote the change in the complex argument of a function f(z) around a contour gamma. Also let N denote the number of roots of f(z) in gamma and P denote the ...

Let a vault consist of two equal half-cylinders of radius r which intersect at right angles so that the lines of their intersections (the "groins") terminate in the ...

The vertex figure at a vertex V of a polygon is the line segment joining the midpoints of the two adjacent sides meeting at V. For a regular n-gon with side length a, the ...

Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

If at least one of d, e, or f has the form q^(-N) for some nonnegative integer N (in which case both sums terminate after N+1 terms), then ...

To find the motion of a rectangular membrane with sides of length L_x and L_y (in the absence of gravity), use the two-dimensional wave equation ...

Let all of the functions f_n(z)=sum_(k=0)^inftya_k^((n))(z-z_0)^k (1) with n=0, 1, 2, ..., be regular at least for |z-z_0|<r, and let F(z) = sum_(n=0)^(infty)f_n(z) (2) = (3) ...