Dynamic Sampling Applied to Problems in Optimal Control

Dynamic sampling utilizes the option of varying the sampling rates according to the situation of the systems, thus obtaining procedures with improved efficiencies. In this paper, the technique is applied to a typical problem in optimal control theory, that of tracking and controlling the position of an object. It is shown that the dynamic sampling results in a significantly improved procedure for this case, even when applying a suboptimal policy which can be analyzed in closed form.     

Universal spaces for homotopy limits of modules over coaugmented functors (I)

For a coaugmented functor J on spaces, we consider J-modules and finite J-limits. The former are spaces X which are retracts of JX via the natural map. The latter are homotopy limits of J-modules arranged in diagrams whose shape is finite dimensional. Familiar examples are generalised Eilenberg MacLane spaces, which are the SP^∞-modules. Finite SP^∞-limits are nilpotent spaces with a very strong finiteness property. We show that the cofacial Bousfield-Kan construction of the functors J_n is universal for finite J-limits in the sense that every map X→Y where Y is a finite J-limit, factors through such natural map X→J_nX, for some n<∞.     

Engineering the interface energetics of solar cells by grafting molecular properties onto semiconductors

The electronic properties of semiconductor surfaces can be controlled by binding tailor-made ligands to them. Here we demonstrate that deposition of a conducting phase on the treated surface enables control of the performance of the resulting device. We describe the characteristics of the free surface of single crystals and of polycrystalline thin films of semiconductors that serve as absorbers in thin film polycrystalline, heterojunction solar cells, and report first data for actual cell structures obtained by chemical bath deposition of CdS as the window semiconductor. The trend of the characteristics observed by systematically varying the ligands suggests changes in work function rather than in band bending at the free surface, and implies that changes in band line-up, which appear to cause changes in band bending, rather than direct, ligand-induced band bending changes, dominate.     

La2−xCexCu1−yZnyO4 perovskites for high temperature water-gas shift reaction

The performance of La_2−xCe_xCu_1−yZn_yO₄ perovskites as catalysts for the high temperature water-gas shift reaction (HT-WGSR) was investigated. The catalysts were characterized by EDS, XRD, BET surface area, TPR, and XANES. The results showed that all the perovskites exhibited the La₂CuO₄ orthorhombic structure, so the Pechini method is suitable for the preparation of pure perovskite. However, the La_1.90Ce_0.10CuO₄ perovskite alone, when calcined at 350/700 °C, also showed a (La_0.935Ce_0.065)₂CuO₄ perovskite with tetragonal structure, which produced a surface area higher than the other perovskites. The perovskites that exhibited the best catalytic performance were those calcined at 350/700 °C and, among these, La_1.90Ce_0.10CuO₄ was outstanding, probably because of the high surface area associated with the presence of the (La_0.935Ce_0.065)₂CuO₄ perovskite with tetragonal structure and orthorhombic La₂CuO₄ phase.     

High throughput production of single core double emulsions in a parallelized microfluidic device

Double emulsions are useful templates for microcapsules and complex particles, but no method yet exists for making double emulsions with both high uniformity and high throughput. We present a parallel numbering-up design for microfluidic double emulsion devices, which combines the excellent control of microfluidics with throughput suitable for mass production. We demonstrate the design with devices incorporating up to 15 dropmaker units in a two-dimensional or three-dimensional array, producing single-core double emulsion drops at rates over 1 kg day(-1) and with diameter variation less than 6%. This design provides a route to integrating hundreds of dropmakers or more in a single chip, facilitating industrial-scale production rates of many tons per year.     

Antichains in partially ordered sets of singular cofinality

In their paper from 1981, Milner and Sauer conjectured that for any poset , if , then P must contain an antichain of size κ. We prove that for λ > cf(λ) = κ, if there exists a cardinal μ < λ such that cov(λ, μ, κ, 2) = λ, then any poset of cofinality λ contains λ ^κ antichains of size κ. The hypothesis of our theorem is very weak and is a consequence of many well-known axioms such as GCH, SSH and PFA. The consistency of the negation of this hypothesis is unknown.      

Trees and Markov Convexity

We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly bounded distortion. We also introduce a new metric invariant called Markov convexity, and show how it can be used to compute the Euclidean distortion of any metric tree up to universal factors. The research of the first author was conducted while he was at U. C. Berkeley and the Institute for Advanced Study.     

Some applications of Ball's extension theorem

We present two applications of Ball's extension theorem. First we observe that Ball's extension theorem, together with the recent solution of Ball's Markov type problem due to Naor, Peres, Schramm and Sheffield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Second, we prove that the distortion required to embed the integer lattice , equipped with the metric, in any -uniformly convex Banach space is of order .