A class of martingales with non-symmetric limit distributions

Summary A class of non-pathological martingales is exhibited to which current martingale central limit theory does not apply. The problem consists in the convergence of the normalized sums of squares being only in distribution. The class is that of degenerate U-statistics.This work was done while the first two authors were on Sabbatical leave at the Technion.Work supported in part by National Research Council of Canada, Grant No. A-9068Work supported in part by National Research Council of Canada, Grant No. A-9076     

A Versatile Ionomer-Based Soft Actuator with Multi-Stimulus Responses,Self-Sustainable Locomotion,and Photoelectric Conversion

The prospects of endowing artificial robotics or devices with increasingly complex and emergent life-like behaviors have attracted growing interest in the soft functional materials that mimic the versatile motions of living creatures in the iridescent nature. However, despite the flourishing achievements so far, soft actuators capable of sensitive multi-stimulus responses and self-sustainable movements, have been extensively pursued to reduce control complexity yet remains a challenging target. Here, through material-structural synergistic design incorporating stress-mismatching structure, high pseudo-negative coefficient of thermal expansion of perfluoro-sulfonic acid ionomer, comprehensive converting properties of carbon nanotube, and anisotropic large thermal expansion of PE polymer, an ionomer-based bilayer actuator is proposed, presenting high-performance actuation of various forms and nice stability, responsive to light (including sunlight without focusing, LED light), low voltage, mild heating, and humidity/solvent change. With a built-in structural feedback loop, the actuation performances are further explored to realize intelligent systems, including: 1) self-sustainable locomotion under sunlight irradiation with adjustable photophobic and phototropic direction as well as adaption to different topographies and loading conditions, 2) self-sustainable oscillation and solar-electric generating, and 3) bionic floristic reaction according to environmental change. These diversified actuation modes allow promising following-up designs for bio-hybrid soft robotics fueled by and harmonized with natural environments.     

Studies of crystalline native celluloses using potential energy calculations

Energies for various trial packing arrangements of unit cells for the I and I phases of native cellulose discovered by Sugiyamaet al. were evaluated. Both a rigid-ring method, PLMR, and the full-optimization, molecular mechanics program, MM3(90), were used. For both phases the models that had the lowest PLMR energy also had the lowest MM3 energy. Both calculated models have the chains packed up, O6s intg positions, and the same sheets of hydrogen-bonded chains. The I structure model is essentially identical to that proposed previously for ramie cellulose by Woodcock and Sarko. It is also the same as the best parallel model previously proposed that was based on the X-ray data of Mann, Gonzalez and Wellard, once the various unit cell conventions are considered. Also, the energies from both methods for all three celluloses, I, I and II, are in the order that rationalizes their relative stabilites.     

All-Printed Green Micro-Supercapacitors Based on a Natural-derived Ionic Liquid for Flexible Transient Electronics

The fabrication and characterization of green, flexible, and ultra-thin supercapacitors that are able to operate above 1.5 V is reported, using an all-printed fabrication process. The devices are produced by aqueous spray casting of a natural-derived electrolyte ionogel composed by 2-hydroxyethyl cellulose and by the ionic liquid choline lactate, while the electrodes are composed of highly porous nanostructured carbon films deposited by supersonic cluster beam deposition (SCBD). The obtained supercapacitors (device thickness < 10 μm) are stable to bending and they possess power values up to 120 kW kg^–1. The combination of aqueous spray casting and SCBD constitutes a versatile, scalable, and eco-friendly fabrication process able to directly print interconnected elements suitable for transient electronic systems.     

Detecting change points in the stress‐strength reliability P(X < Y)

We address the statistical problem of detecting change points in the stress‐strength reliability R=P(X<Y) in a sequence of paired variables (X,Y). Without specifying their underlying distributions, we embed this nonparametric problem into a parametric framework and apply the maximum likelihood method via a dynamic programming approach to determine the locations of the change points in R. Under some mild conditions, we show the consistency and asymptotic properties of the procedure to locate the change points. Simulation experiments reveal that, in comparison with existing parametric and nonparametric change‐point detection methods, our proposed method performs well in detecting both single and multiple change points in R in terms of the accuracy of the location estimation and the computation time. Applications to real data demonstrate the usefulness of our proposed methodology for detecting the change points in the stress‐strength reliability R. Supplementary materials are available online.     

Optical absorption spectra from rare-earth ions in polymers: the effect of the polymer host

A Molecular Dynamics (MD) based modified Judd/Ofelt approach has been used to simulate UV-VIS absorption spectra for different concentrations of Er(CF₃SO₃)₃ (erbium triflate) in the amorphous polymer host poly(ethylene oxide), PEO. The simulations have been performed for systems containing both single-chain PEO and PEO with an attached side-chain. Effects on the optical properties of the introduction of side-chains are demonstrated. Qualitative inspection of the calculated spectra would suggest that similarities in the crystal field experienced by individual Er ions in qualitatively different local environments will make structural information difficult to access from this procedure.     

Development of a force field for Li(2)SiF(6)

A force field has been developed for Li(2)SiF(6) for subsequent use in Molecular Dynamics (MD) simulations involving Li(+) and SiF(2-) (6) ions in a polymer electrolyte host. Both ab initio calculations and available empirical data have been used. The force field has been verified in simulations of the crystal structure of Li(2)SiF(6) in two different space groups: P321 and P3(-)m1. The use of MD simulation to assess the correct space group for Li(2)SiF(6) shows that it is probably P321.