Ecologists have recently used integral projection models (IPMs) to study fish and other animals which continue grow throughout their lives. Such cannot shrink, since they bony skeletons; a mathematical consequence of this is that the kernel operator T unbounded, not compact. To our knowledge, all theoretical work done on IPMs has assumed compact, in particular bounded kernel. A priori, it uncle...

We present a multigrid solution of the three dimensional Poisson equation with a fourth order 19-point compact nite diierence scheme. Using a red-black ordering of the grid points and some geometric considerations, we derive an optimal scaled injection operator for the multigrid algorithm. Numerical computations show that this operator yields not only the smallest overall CPU time, but also the...

Approved for public release; distribution is unlimited. ACKNOWLEDGMENTS The author is grateful to have contributed to workload analysis and numerous other aspects of the Multi-Modal Watchstation demonstration project. Specific thanks to Christopher Griffith for software development that allowed capture of workload-related indices, and to Kimberly Heinlein for assistance in obtaining workload da...

A Banach space X has the approximation property if and only if every compact set in X is in the range of a one-to-one bounded linear operator from a space that has a Schauder basis. Characterizations are given for Lp spaces and quotients of Lp spaces in terms of covering compact sets in X by operator ranges from Lp spaces. A Banach space X is a L1 space if and only if every compact set in X is ...

Let K be an absolutely convex infinite-dimensional compact in a Banach space X . The set of all bounded linear operators T on X satisfying TK ⊃ K is denoted by G(K). Our starting point is the study of the closure WG(K) of G(K) in the weak operator topology. We prove that WG(K) contains the algebra of all operators leaving lin(K) invariant. More precise results are obtained in terms of the Kolmo...

We consider (3+1)-dimensional SU(N)/ZN Yang-Mills theory on a space-time with a compact spatial direction, and prove the following result: Under a continuous increase of the theta angle θ → θ+2π, a ’t Hooft operator T (γ) associated with a closed spatial curve γ that winds around the compact direction undergoes a monodromy T (γ) → T (γ). The new ’t Hooft operator T (γ) transforms under large ga...

While it is well-known that the standard integral operator K of (stationary) diffuse-gray radiation, as it occurs in the radiosity equation, is compact if the domain of radiative interaction is sufficiently regular, we show noncompactness of the operator if the domain is polyhedral. We also show that a stationary operator is never compact when reinterpreted in a transient setting. Moreover, we ...