A highly sensitive mean-reverting process in finance and the Euler-Maruyama approximations

Empirical studies show that the most successful continuous-time models of the short-term rate in capturing the dynamics are those that allow the volatility of interest changes to be highly sensitive to the level of the rate. However, from the mathematics, the high sensitivity to the level implies that the coefficients do not satisfy the linear growth condition, so we can not examine its properties by traditional techniques. This paper overcomes the mathematical difficulties due to the nonlinear growth and examines its analytical properties and the convergence of numerical solutions in probability. The convergence result can be used to justify the method within Monte Carlo simulations that compute the expected payoff of financial products. For illustration, we apply our results compute the value of a bond with interest rate given by the highly sensitive mean-reverting process as well as the value of a single barrier call option with the asset price governed by this process.     

一类矩阵的特征值分布域

本文研究了块乘积型对角占优矩阵的特征值分布域,改进了[2～5]中相应结论的条件。     

Parameter estimation for the stochastic SIS epidemic model

In this paper we estimate the parameters in the stochastic SIS epidemic model by using pseudo-maximum likelihood estimation (pseudo-MLE) and least squares estimation. We obtain the point estimators and $100 (1-\alpha )\%$ confidence intervals as well as $100 (1-\alpha )\%$ joint confidence regions by applying least squares techniques. The pseudo-MLEs have almost the same form as the least squares case. We also obtain the exact as well as the asymptotic $100 (1-\alpha )\%$ joint confidence regions for the pseudo-MLEs. Computer simulations are performed to illustrate our theory.     

Preparation of cellulose nanocrystals and carboxylated cellulose nanocrystals from borer powder of bamboo

Carboxylated cellulose nanocrystals (CCN) and cellulose nanocrystals (CNC) were prepared from borer powder of bamboo by two different kinds of procedures: one-step approach with ammonium persulfate for CCN and two-step approach with sulfuric acid for CNC. The obtained samples were characterizated by transmission electron microscopy, Fourier transform infrared spectroscopy, X-ray diffraction and thermogravimetric analysis. The results show that the particles of CCN and CNC present spherical shape with diameters of 20–50 and 20–70 nm, respectively. The crystallinity of CCN and CNC is significantly improved after a series of chemical treatment, which is up to 62.75 and 69.84 %, respectively. The research indicates that the borer powder from bamboo could be an excellent raw material for manufacturing CNC in a low-cost and environmental-friendly way. Rational and sustainable utilization of the bamboo borer powder to develop new bioproducts holds great potential value for industry and offers many benefits and opportunities.     

Designing Breathing Air-electrode and Enhancing the Oxygen Electrocatalysis by Thermoelectric Effect for Efficient Zn-air Batteries

The sluggish kinetics and mutual interference of oxygen evolution and reduction reactions in the air electrode resulted in large charge/discharge overpotential and low energy efficiency of Zn-air batteries. In this work, we designed a breathing air-electrode configuration in the battery using P-type Ca₃Co₄O₉ and N-type CaMnO₃ as charge and discharge thermoelectrocatalysts, respectively. The Seebeck voltages generated from thermoelectric effect of Ca₃Co₄O₉ and CaMnO₃ synergistically compensated the charge and discharge overpotentials. The carrier migration and accumulation on the cold surface of Ca₃Co₄O₉ and CaMnO₃ optimized the electronic structure of metallic sites and thus enhanced their intrinsic catalytic activity. The oxygen evolution and reduction overpotentials were enhanced by 101 and 90 mV, respectively, at temperature gradient of 200 °C. The breathing Zn-air battery displayed a remarkable energy efficiency of 68.1 %. This work provides an efficient avenue towards utilizing waste heat for improving the energy efficiency of Zn-air battery.     

Tracking the state of the delay hyperchaotic Lü system using the coullet chaotic system via a single controller

In this article, a partial synchronization scheme is proposed based on Lyapunov stability theory to track the signal of the delay hyperchaotic Lü system using the Coullet system based on only one single controller. The proposed tracking control design has two advantages: only one controller is adopted in our approach and it can allow us to drive the hyperchaotic system to a simple chaotic system even with uncertain parameters. Numerical simulation results are given to demonstrate the effectiveness and robustness of the proposed partial synchronization scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 125–130, 2016     

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).     

Numerical solutions of stochastic differential delay equations under the generalized Khasminskii-type conditions

The classical existence-and-uniqueness theorem of the solution to a stochastic differential delay equation (SDDE) requires the local Lipschitz condition and the linear growth condition (see e.g. [11], [12] and [20]). The numerical solutions under these conditions have also been discussed intensively (see e.g. [4], [10], [13], [16], [17], [18], [21], [22] and [24]). Recently, Mao and Rassias [14] and [15] established the generalized Khasminskii-type existence-and-uniqueness theorems for SDDEs, where the linear growth condition is no longer imposed. These generalized Khasminskii-type theorems cover a wide class of highly nonlinear SDDEs but these nonlinear SDDEs do not have explicit solutions, whence numerical solutions are required in practice. However, there is so far little numerical theory on SDDEs under these generalized Khasminskii-type conditions. The key aim of this paper is to close this gap.     

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。