Knot points of typical continuous functions

It is well known that most continuous functions are nowhere differentiable. Furthermore, in terms of Dini derivatives, most continuous functions are nondifferentiable in the strongest possible sense except in a small set of points. In this paper, we completely characterise families S of sets of points for which most continuous functions have the property that such small set of points belongs to S. The proof uses a topological zero-one law and the Banach-Mazur game.Comment: 24 page

Differentiability of Lipschitz Functions in Lebesgue Null Sets

We show that if n>1 then there exists a Lebesgue null set in R^n containing a point of differentiability of each Lipschitz function mapping from R^n to R^(n-1); in combination with the work of others, this completes the investigation of when the classical Rademacher theorem admits a converse. Avoidance of sigma-porous sets, arising as irregular points of Lipschitz functions, plays a key role in the proof.Comment: 33 pages. Corrected minor misprints and added more detail to the proofs of Lemma 3.2 and Lemma 8.

Diabetic microvascular complications as simple indicators of risk for cardiovascular outcomes and heart failure

No abstract available

Mean field dynamics of superfluid-insulator phase transition in a gas of ultra cold atoms

A large scale dynamical simulation of the superfluid to Mott insulator transition in the gas of ultra cold atoms placed in an optical lattice is performed using the time dependent Gutzwiller mean field approach. This approximate treatment allows us to take into account most of the details of the recent experiment [Nature 415, 39 (2002)] where by changing the depth of the lattice potential an adiabatic transition from a superfluid to a Mott insulator state has been reported. Our simulations reveal a significant excitation of the system with a transition to insulator in restricted regions of the trap.Comment: final version, correct Fig.7 (the published version contains wrong fig.7 by mistake

Development of a figure-of-merit for space missions

The concept of a quantitative figure-of-merit (FOM) to evaluate different and competing options for space missions is further developed. Over six hundred individual factors are considered. These range from mission orbital mechanics to in-situ resource utilization (ISRU/ISMU) plants. The program utilizes a commercial software package for synthesis and visual display; the details are completely developed in-house. Historical FOM's are derived for successful space missions such as the Surveyor, Voyager, Apollo, etc. A cost FOM is also mentioned. The bulk of this work is devoted to one specific example of Mars Sample Return (MSR). The program is flexible enough to accommodate a variety of evolving technologies. Initial results show that the FOM for sample return is a function of the mass returned to LEO, and that missions utilizing ISRU/ISMU are far more cost effective than those that rely on all earth-transported resources