Facile preparation of nitrogen-doped graphene scrolls via acoustic cavitation as electrocatalyst for glucose biosensing

Nitrogen doping is considered as a promising strategy to tailor and develop the intrinsic properties of graphene. In this work, we report a facile method for preparation of nitrogen-doped graphene scrolls (N-GSS) through acoustic cavitation, which can not only realize graphene nitrogen doping but also simultaneously result in its scrolled topological structure and improvement of reduction degree. As a metal-free electrocatalyst, the prepared N-GSS showed good electrocatalytic activity towards oxidation of hydrogen peroxide with the sensitivity of 87.8 μA mM^?1 cm^?2. Then N-GSS was employed as a matrix for glucose oxidase (GOD) loading, and the fabricated biosensor also exhibited excellent analytical characteristics, such as a high sensitivity (55.2 μA mM^?1 cm^?2), wide linear range (2 μM to 3.56 mM, R = 0.999) and low detection limit (1 μM).     

A Note on the Rate of Convergence of the Euler–Maruyama Method for Stochastic Differential Equations

Stochastic processes are approximated by wavelet operators. For the stochastic process and the scale function satisfying some conditions, a new method is given to estimate the degree of approximation.     

On Gorenstein coalgebras

We investigate the comodule representation category over the Morita-Takeuchi context coalgebra Γ and study the Gorensteinness of Γ. Moreover, we determine explicitly all Gorenstein injective comodules over the Morita-Takeuchi context coalgebra Γ and discuss the localization in Gorenstein coalgebras. In particular, we describe its Gabriel quiver and carry out some examples when the Morita-Takeuchi context coalgebra is basic.     

Lag synchronization of multiple identical Hindmarsh–Rose neuron models coupled in a ring structure

Lag synchronization of multiple identical Hindmarsh–Rose neuron systems coupled in a ring structure is investigated. In the coupled systems, each neuron receives signals only via synaptic strength from the nearest neighbors. Based on the Lyapunov stability theory, the sufficient conditions for synchronization of the multiple systems with chaotic bursting behavior can be obtained. The synchronization condition about the control parameter g is also obtained by numerical method. Finally, numerical simulations are provided to show the effectiveness of the developed methods.     

混合物物态方程的计算

 在采用体积相加原理计算混合物物态方程的基础上,建立了一种物理模型确定混合物温度。根据混合物中各组分温度和压强平衡条件,采用压强-密度迭代方法计算给出混合物物态方程,编制了两种组分的混合物物态方程计算程序。为检验建立的温度模型的合理性及程序的有效性,分析了不同密度、温度状态的氢（H2）和钨（W）组成的混合物状态参量,计算了以下情形及其组合情形的混合物物态方程：H₂和W以不同质量比混合;质量比固定,单组分状态不同;温度区间和密度区间不同。研究表明:实际应用中在建立的混合物温度模型基础上确定的混合物物态方程是合理的。     

求解方程u‘=f（t,u）的最高阶k步精确计算公式

本文建立了求解方程ｕ＇＝ｆ（ｔ，ｕ）的最高阶ｋ步精确计算公式．从而得知４阶Ｓｉｍｐｏｎ型公式，Ｍｉｍｅ公式及Ａｄａｍｓ－Ｍｏｕｌｔｏｎ公式（见［１，２］）将是直接而简单的推论．     

绿色食品生产和消费的数量经济分析

本文从消费者效用出发 ,导出了绿色食品及同类一般食品的需求函数 ;从企业具有追求利润最大化的动机入手 ,分析了绿色食品价格对其生产的影响 ,得出了绿色食品生存必须具有的最低价格 ;给出了使绿色食品及同类一般食品产销尽可能均衡的线性规划模型 ;提出了发展绿色食品的若干建议措施