On almost sure max-limit theorems of complete and incomplete samples from stationary sequences

Let M _n denote the partial maximum of a strictly stationary sequence (X _n ). Suppose that some of the random variables of (X _n ) can be observed and let [(M)\tilde]_n\tilde M_n stand for the maximum of observed random variables from the set {X ₁, ..., X _n }. In this paper, the almost sure limit theorems related to random vector ([(M)\tilde]_n\tilde M_n , M _n ) are considered in terms of i.i.d. case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.     

Statistical method for resolving the photon–photoelectron-counting inversion problem

A statistical inversion method is proposed for the photon–photoelectron-counting statistics in quantum key distribution experiment. With the statistical viewpoint, this problem is equivalent to the parameter estimation for an infinite binomial mixture model. The coarse-graining idea and Bayesian methods are applied to deal with this ill-posed problem, which is a good simple example to show the successful application of the statistical methods to the inverse problem. Numerical results show the applicability of the proposed strategy. The coarse-graining idea for the infinite mixture models should be general to be used in the future.     

IN MEMORIAM PROFESSOR DONGGAO DENG

Donggao Deng, professor of mathematics, the associate Editor of ATA,was born in June 8, 1935 in Rongqi Town, Shunde City, GuangdongProvince, China. He passed away by illness in Guangzhou on October21, 2007.     

Bio-inspired and Eco-friendly Synthesis of 3D Spongy Meso-Microporous Carbons from CO2 for Supercapacitors

Inspired by the spongy bone structures, three-dimensional (3D) sponge-like carbons with meso-microporous structures are synthesized through one-step electro-reduction of CO₂ in molten carbonate Li₂CO₃−Na₂CO₃−K₂CO₃ at 580 °C. SPC4-0.5 (spongy porous carbon obtained by electrolysis of CO₂ at 4 A for 0.5 h) is synthesized with the current efficiency of 96.9 %. SPC4-0.5 possesses large electrolyte ion accessible surface area, excellent wettability and electronical conductivity, ensuring the fast and effective mass and charge transfer, which make it an advcanced supercapacitor electrode material. SPC4-0.5 exhibits a specific capacitance as high as 373.7 F g⁻¹ at 0.5 A g⁻¹, excellent cycling stability (retaining 95.9 % of the initial capacitance after 10000 cycles at 10 A g⁻¹), as well as high energy density. The applications of SPC4-0.5 in quasi-solid-state symmetric supercapacitor and all-solid-state flexible devices for energy storage and wearable piezoelectric sensor are investigated. Both devices show considerable capacitive performances. This work not only presents a controllable and facile synthetic route for the porous carbons but also provides a promising way for effective carbon reduction and green energy production.     

Tracking the Electrocatalytic Activity of a Single Palladium Nanoparticle for the Hydrogen Evolution Reaction

The nanoparticle-based electrocatalysts’ performance is directly related to their working conditions. In general, a number of nanoparticles are uncontrollably fixed on a millimetre-sized electrode for electrochemical measurements. However, it is hard to reveal the maximum electrocatalytic activity owing to the aggregation and detachment of nanoparticles on the electrode surface. To solve this problem, here, we take the hydrogen evolution reaction (HER) catalyzed by palladium nanoparticles (Pd NPs) as a model system to track the electrocatalytic activity of single Pd NPs by stochastic collision electrochemistry and ensemble electrochemistry, respectively. Compared with the nanoparticle fixed working condition, Pd NPs in the nanoparticle diffused working condition results in a 2–5 orders magnitude enhancement of electrocatalytic activity for HER at various bias potential. Stochastic collision electrochemistry with high temporal resolution gives further insights into the accurate study of NPs’ electrocatalytic performance, enabling to dramatically enhance electrocatalytic efficiency.