Mesoporous α-Fe(2)O(3) thin films synthesized via the sol-gel process for light-driven water oxidation

This work reports a facile and cost-effective method for synthesizing photoactive α-Fe(2)O(3) films as well as their performances when used as photoanodes for water oxidation. Transparent α-Fe(2)O(3) mesoporous films were fabricated by template-directed sol-gel chemistry coupled with the dip-coating approach, followed by annealing at various temperatures from 350 °C to 750 °C in air. α-Fe(2)O(3) films were characterized by X-ray diffraction, XPS, FE-SEM and electrochemical measurements. The photoelectrochemical performance of α-Fe(2)O(3) photoanodes was characterized and optimized through the deposition of Co-based co-catalysts via different methods (impregnation, electro-deposition and photo-electro-deposition). Interestingly, the resulting hematite films heat-treated at relatively low temperature (500 °C), and therefore devoid of any extrinsic dopant, achieve light-driven water oxidation under near-to-neutral (pH = 8) aqueous conditions after decoration with a Co catalyst. The onset potential is 0.75 V vs. the reversible hydrogen electrode (RHE), thus corresponding to 450 mV light-induced underpotential, although modest photocurrent density values (40 μA cm(-2)) are obtained below 1.23 V vs. RHE. These new materials with a very large interfacial area in contact with the electrolyte and allowing for a high loading of water oxidation catalysts open new avenues for the optimization of photo-electrochemical water splitting.     

Weak KAM Theory on the Wasserstein Torus with Multidimensional Underlying Space

The study of asymptotic behavior of minimizing trajectories on the Wasserstein space ��(��^d) has so far been limited to the case d = 1 as all prior studies heavily relied on the isometric identification of ��(��) with a subset of the Hilbert space L²(0,1). There is no known analogue isometric identification when d > 1. In this article we propose a new approach, intrinsic to the Wasserstein space, which allows us to prove a weak KAM theorem on ��(��^d), the space of probability measures on the torus, for any d ≥ 1. This space is analyzed in detail, facilitating the study of the asymptotic behavior/invariant measures associated with minimizing trajectories of a class of Lagrangians of practical importance. © 2014 Wiley Periodicals, Inc.     

An elementary proof of the polar factorization of vector-valued functions

We present an elementary proof of an important result of Y. Brenier [Br1, Br2], namely, that vector fields in ^d satisfying a nondegeneracy condition admit the polar factorization (*) u(x)=(s(x)), where is a convex function and s is a measure-preserving mapping. Brenier solves a minimization problem using Monge-Kantorovich theory; whereas we turn our attention to a dual problem, whose Euler-Lagrange equation turns out to be (*).     

New Fibonacci and Lucas primes

Extending previous searches for prime Fibonacci and Lucas numbers, all probable prime Fibonacci numbers have been determined for and all probable prime Lucas numbers have been determined for . A rigorous proof of primality is given for and for numbers with , , , , , , , , the prime having 3020 digits. Primitive parts and of composite numbers and have also been tested for probable primality. Actual primality has been established for many of them, including 22 with more than 1000 digits. In a Supplement to the paper, factorizations of numbers and are given for as far as they have been completed, adding information to existing factor tables covering .

     

Surfactant‐Free Spinning of Composite Carbon Nanotube Fibers

Summary: Fibers and yarns are promising forms to use and control the spatial orientation of carbon nanotubes in macroscopic materials. Various approaches have been proposed in the last few years to achieve fibers with a fraction of carbon nanotubes. Among them, coagulation spinning in aqueous media has proven to be a simple and capable method of leading to super‐tough materials. However, all water‐based processes described so far have made use of surfactant‐stabilized carbon nanotubes. In the present work, a method is shown to spin fibers from surfactant‐free nanotube solutions while preserving an all water‐based process. The resultant fibers exhibit mechanical and electrical properties that compare well with those of previously reported fibers spun with surfactants. The fibers exhibit a significant toughness and a high electrical conductivity.

Scanning electron micrograph of the fiber, showing the surface texture.     

Algebraic switching time identification for a class of linear hybrid systems

In this paper, a method for the finite time estimation of the switching times in linear switched systems is proposed. The approach is based on algebraic tools and distribution theory. Switching time estimates are given by explicit algebraic formulae that can be implemented in a straightforward manner using standard tools from computational mathematics. Simulations illustrate the proposed techniques.