Charles Vernon Coffman

Existence and uniqueness results for semi-linear Dirichlet problems in annuli

A foot clamping device for ski boots comprises, inside the boot body a presser member at the foot heel region and a threaded peg extending from the presser member and rotatably engaged in a threaded bush associated with a boss on the outside of the boot body. When the boss is rotated by a strap rigid therewith and constituting a closure element for the boot, the presser member is caused to traverse.

On the growth of populations with narrow spread in reproductive age

SummaryThe general theory discussed by Colement in the first paper, I, of this series is here specialized to the case in which the rate, ρ=ρ(x(a,t), a) at which a population loses, through death and dispersal, individuals of agea is convex in the numberx(a, t) of individuals which have agea at timet, while the fecundity functionF in the formula,x(0,t)=F(x(af, t)), is concave inx(af, t); hereaf is the reproductive age. Such an assumption of convexity for ρ(·,a) and −F(·) renders mathematical the idea that when one considers the immediate contribution which an additional individual, of given age, makes to those processes which tend to increase the population, one should find that such an incremental contribution declines as the number of present individuals at the given age increases. It is shown that convexity of ρ(·,a) and −F(·) implies that a given population belongs to one of three classes, regardless of initial conditions: (i) the class of ‘endangered populations’ for whichx(a, t)→0 ast→∞, (ii) the class of populations with a stable, non-zero, stationary age distribution, or (iii) the class of populations which exhibit unbounded growth. The properties of ρ andF which determine the class to which a population belongs are found and discussed in detail. For example, when ρ(0,a)∈0 andF is monotone increasing withF(0)=0, the parameter,

Lyusternik-Schnirelman theory and eigenvalue problems for monotone potential operators

T = \ln \frac{d}{{dx}}F(0) - \int_0^{a_f } {\frac{\partial }{{\partial x}}} \rho (0,a)da,

Are adobe walls optimal phase-shift filters?

, introduced in I, plays a central role: whenT is negative the population is of class (i); whenT is positive the population is of either class (ii) or class (iii), and it is then of class (ii) if and only if the parameter,

The structure of translation-invariant memories

U = \mathop {\lim }\limits_{x \to \infty } \left[ {\ln \frac{d}{{dx}}F(x)} \right] - \int_0^{a_f } {\mathop {\lim }\limits_{x \to \infty } } \frac{\partial }{{\partial x}}\rho (x,a)da,

Classification of balanced sets and critical points of even functions on spheres

obeys the condition −∞≤U<0.