There is a simple type of electric network termed a series-parallel connection which occurs frequently in both theoretical and applied electrical engineering. One reason for the importance ofâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

1972

If H denotes the classical Hilbert transform and Hu(x) = v(x), then the functions u(x) and v(x) are the values on the real axis of a pair of conjugate functions, harmonic in the upper half-plane.â€¦ (More)

The object of this paper is to show that a certain system of nonlinear differential equations has one and only one periodic solution. These equations are of interest in that they describe theâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

1985

The kth Markoff-Duffin-Schaeffer inequality provides a bound for the maximum, over the interval -1 </= x </= 1, of the kth derivative of a normalized polynomial of degree n. The bound is theâ€¦ (More)

The theme of this paper is the application of linear analysis to simplify and extend convex analysis. The central problem treated is the standard convex program -minimize a convex function subject toâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

1978

Given a linear minimization program, then there is an associated linear maximization program termed the dual. F. E. Clark proved the following theorem. "If the set of feasible points of one programâ€¦ (More)

Paley and Wiener have formulated a criterion for a set of functions {gn} to be "near" a given orthonormal set {/w}. The interest of this criterion is that it guarantees the set {gn} to have expansionâ€¦ (More)

Of concern are solutions of the classical wave equation in three-dimensions. It is shown that if a solution has compact support then after a finite time the kinetic energy of the wave is constant andâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

1981

Fourth-order differential equations such as 16y'(m)y'(2) - 32y(m)y(n)y' + 17y(0(3) ) = 0 are developed. It is shown that the equation is "universal" in the sense that any continuous function can beâ€¦ (More)