The Fried Average Entropy and Slow Entropy for Actions of Higher Rank Abelian Groups

We consider two numerical entropy-type invariants for actions of \({\mathbb{Z}^k}\) , invariant under a choice of generators and well-adapted for smooth actions whose individual elements have positive entropy. We concentrate on the maximal rank case, i.e. \({\mathbb{Z}^k,\,k \geq 2}\) actions on k + 1-dimensional manifolds. In this case we show that for a fixed dimension (or, equivalently, rank) each of the invariants determines the other and their values are closely related to regulators in algebraic number fields. In particular, in contrast with the classical case of \({{\mathbb Z}}\) actions the entropies of ergodic maximal rank actions take only countably many values. Our main result is the dichotomy that is best expressed under the assumption of weak mixing or, equivalently, no periodic factors: either both invariants vanish, or their values are bounded away from zero by universal constants. Furthermore, the lower bounds grow with dimension: for the first invariant (the Fried average entropy) exponentially, and for the second (the slow entropy) linearly.     

Generalization bounds for function approximation from scattered noisy data

We consider the problem of approximating functions from scattered data using linear superpositions of non-linearly parameterized functions. We show how the total error (generalization error) can be decomposed into two parts: an approximation part that is due to the finite number of parameters of the approximation scheme used; and an estimation part that is due to the finite number of data available. We bound each of these two parts under certain assumptions and prove a general bound for a class of approximation schemes that include radial basis functions and multilayer perceptrons. This revised version was published online in June 2006 with corrections to the Cover Date.     

Testing optimality for quadratic 0-1 problems

Received June 4, 1996 / Revised version received November 19, 1997 Published online November 24, 1998     

Electric Field Enhanced Ammoxidation of Aldehydes Using Supported Fe Clusters Under Ambient Oxygen Pressure

Heterogeneous catalytic ammoxidation provides an eco-friendly route for the cyanide-free synthesis of nitrile compounds, which are important precursors for synthetic chemistry and pharmaceutical applications. However, in general such a process requires high pressures of molecular oxygen at elevated temperatures to accelerate the oxygen reduction and imine dehydrogenation steps, which is highly risky in practical applications. Here, we report an electric field enhanced ammoxidation system using a supported Fe clusters catalyst (Fe/NC), which enables efficient synthesis of nitriles from the corresponding aldehydes under ambient air pressure at room temperature (RT). A synergistic effect between the external electric field and the Fe/NC catalyst promotes the ammonia activation and the dehydrogenation of the generated imine intermediates and avoids the unwanted backwards reaction to aldehydes. This electric field enhanced ammoxidation system presents high efficiency and selectivity for the conversion of a series of aldehydes under mild conditions with high durability, rendering it an attractive process for the green synthesis of nitriles with fragile functional groups.     

Synthesis of rGO–Nps hybrids with electrocatalytic activity for hydrogen evolution reaction

Journal of Solid State Electrochemistry - A hybrid nanomaterial with palladium nanoparticles (PdNps) supported on reduced graphene oxide (rGO) flakes, dispersed in an aqueous solution was...     

A novel deacylation during the amination of trifluoromethyl β-dicarbonyl compounds

Starting from trifluoromethyl β-dicarbonyl compounds, a rare loss of CF₃CO was observed in the amination reactions performed under heterogeneous conditions using NsONHCO₂Et as the aminating agent and CaO or NaH as the base, while corresponding nonfluorinated β-dicarbonyl compounds under analogous conditions give non deacylated aminated compounds. This reaction can facilitate a direct synthesis of N-substituted α-amino esters or α-amino ketones.     

Micro-Mesoporous Carbons from Cyclodextrin Nanosponges Enabling High-Capacity Silicon Anodes and Sulfur Cathodes for Lithiated Si-S Batteries

Manufactured globally on industrial scale, cyclodextrins (CD) are cyclic oligosaccharides produced by enzymatic conversion of starch. Their typical structure of truncated cone can host a wide variety of guest molecules to create inclusion complexes; indeed, we daily use CD as unseen components of food, cosmetics, textiles and pharmaceutical excipients. The synthesis of active material composites from CD resources can enable or enlarge the effective utilization of these products in the battery industry with some economical as well as environmental benefits. New and simple strategies are here presented for the synthesis of nanostructured silicon and sulfur composite materials with carbonized hyper cross-linked CD (nanosponges) that show satisfactory performance as high-capacity electrodes. For the sulfur cathode, the mesoporous carbon host limits polysulfide dissolution and shuttle effects and guarantees stable cycling performance. The embedding of silicon nanoparticles into the carbonized nanosponge allows to achieve high capacity and excellent cycling performance. Moreover, due to the high surface area of the silicon composite, the characteristics at the electrode/electrolyte interface dominate the overall electrochemical reversibility, opening a detailed analysis on the behavior of the material in different electrolytes. We show that the use of commercial LP30 electrolyte causes a larger capacity fade, and this is associated with different solid electrolyte interface layer formation and it is also demonstrated that fluoroethylene carbonate addition can significantly increase the capacity retention and the overall performance of our nanostructured Si/C composite in both ether-based and LP30 electrolytes. As a result, an integration of the Si/C and S/C composites is proposed to achieve a complete lithiated Si−S cell.