A strong form of almost differentiability

We present a uniformization of Reeken's macroscopic differentiability (see [5]), discuss its relations to uniform differentiability (see [6]) and classical continuous differentiability, prove the corresponding chain rule, Taylor's theorem, mean value theorem, and inverse mapping theorem. An attempt to compare it with the observability (see [1, 4]) is made too. © 2009 Springer Science+Business Media, Inc.CEOCFCTFEDER/POCT

Retroreflecting curves in nonstandard analysis

We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C(1), except for a hyper-finite set of values, such that the probability of a particle being reflected from the curve with the velocity opposite to the velocity of incidence, is infinitely close to 1. The constructed curves are of two kinds: a curve infinitely close to a straight line and a curve infinitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: find the curve of maximum resistance infinitely close to a given curve.CEOCFCTFEDER/POCT

On the propagation of semiclassical Wigner functions

We establish the difference between the propagation of semiclassical Wigner functions and classical Liouville propagation. First we re-discuss the semiclassical limit for the propagator of Wigner functions, which on its own leads to their classical propagation. Then, via stationary phase evaluation of the full integral evolution equation, using the semiclassical expressions of Wigner functions, we provide the correct geometrical prescription for their semiclassical propagation. This is determined by the classical trajectories of the tips of the chords defined by the initial semiclassical Wigner function and centered on their arguments, in contrast to the Liouville propagation which is determined by the classical trajectories of the arguments themselves.Comment: 9 pages, 1 figure. To appear in J. Phys. A. This version matches the one set to print and differs from the previous one (07 Nov 2001) by the addition of two references, a few extra words of explanation and an augmented figure captio

Is Cash Negative Debt? A Hedging Perspective on Corporate Financial Policies

We model the interplay between cash and debt policies in the presence of financial constraints. While saving cash allows financially constrained firms to hedge against future income shortfalls, reducing debt - "saving borrowing capacity" - is a more effective way of securing future investment in high cash flow states. This trade-off implies that constrained firms will allocate excess cash flows into cash holdings if their hedging needs are high (i.e., if the correlation between operating cash flows and investment opportunities is low). However, constrained firms will use excess cash flows to reduce current debt if their hedging needs are low. The empirical examination of cash and debt policies of a large sample of constrained and unconstrained firms reveals evidence that is consistent with our theory. In particular, our evidence shows that financially constrained firms with high hedging needs have a strong propensity to save cash out of cash flows, while showing no propensity to reduce outstanding debt. In contrast, constrained firms with low hedging needs systematically channel free cash flows towards debt reduction, as opposed to cash savings. Our analysis points to an important hedging motive behind standard financial policies such as cash and debt management. It suggests that cash should not be viewed as negative debt.