Improved Potentiometric and Optic Sensitivity of Polyaniline Film to Dissolved Oxygen by Incorporating Iron‐Porphyrin

Polyaniline (PAn) films can be used in an electrochemical and optical combination system to amplify the optical signal for dissolved oxygen (DO) detection. To further improve the sensitivity of PAn film to DO, an oxygen‐sensitive molecule, Fe(III) meso‐tetera (4‐sulfonatophenyl) porphyrin (FeTSPP) is incorporated into PAn during the film generation. Results show that, after incorporating FeTSPP into the PAn matrix, both optical and potentiometric responses to DO are improved. The optimal optical signal is obtained under the application of ?2.5 μA to the modified electrode. Under this applied current, both optical and potentiometric signals show linear relations with the DO concentration within the range of 0.00–4.63 mg L^?1, and the sensitivities for optical and potentiometric signals are 4.18 grayscale units mg^?1 L and 13.39 mV mg^?1 L, respectively.     

单种群离散模型的全局稳定性

本文证明了■全局稳定的充要条件是方程无二点环.可以证明本文的结论与“C—R 定理是等价的.利用本文的结果不仅可以简化“C—R 定理”的证明,而且为推广到多个极值点的情形提供了方便的工具.     

基于协整理论的DFT-GARCH模型的统计套利研究

现有的统计套利策略大多建立在协整理论和GARCH模型的基础上.离散Fourier变换(DFT)的思想可以挖掘价差序列周期性、非线性的特征,保证其在拟合和预测中的精确度.利用沪铜期货合约的收盘价数据进行实证分析,研究结果表明:在高频数据下,新模型对数据的拟合和预测效果要明显优于传统的套利模型,在相同的交易规则下,新模型的套利成功率和收益率都高于传统的统计套利模型.     

Effect of discreteness on heterogeneous flames: Propagation limits in regular and random particle arrays

In a system with discrete heat sources distributed in an inert, heat conducting medium, there exists two asymptotic regimes of flame propagation. When the flame thickness is much greater than the inter-particle spacing, the system approximates a homogeneous medium and the flame can be modeled as a continuum. In the other extreme, when the flame is very thin due to rapid reaction of particles, the heterogeneous flame can no longer be treated as a continuum since discrete effects become dominant. The effects of discreteness are characterized by a strong dependence on the spatial distribution of the sources. The present work investigates the effects of discreteness on flame propagation and demonstrates that these effects result in a propagation limit in the absence of losses. For a system of regularly spaced particles, this limit can be found analytically for one-, two-, and three-dimensional systems, although the flame exhibits a complex dynamic of bifurcations as it approaches this limit. Propagation of a flame beyond this limit is only possible through concentration fluctuations in a system with randomly distributed particles. Two-dimensional numerical simulations with randomly distributed particles show a strong dependence of the propagation limit on the size of the computational domain. A consequence of the random particle distribution is that the flammability limit can only be defined as a probabilistic outcome of the flame propagation simulations.     

HYPERGEOMETRIC SOLUTIONS TO AN ULTRADISCRETE PAINLEVÉ EQUATION

We show that an ultradiscrete analogue of the third Painlevé equation admits discrete Riccati type solutions. We derive these solutions by considering a framework in which the ultradiscretization process arises as a restriction of a non-archimedean valuation over a field. Using this framework we may relax the conditions one requires to apply the ultradiscretization process. We derive a family of transcendental solutions that appear as the non-archimedean field valuation of hypergeometric functions.     

Interrelations of discrete Painlevé equations through limiting procedures

We study the discrete Painlevé equations associated to the affine Weyl group which can be obtained by the implementation of a special limits of -associated equations. This study is motivated by the existence of two -associated discrete both having a double ternary dependence in their coefficients and which have not been related before. We show here that two equations correspond to two different limits of a -associated discrete Painlevé equation. Applying the same limiting procedures to other -associated equations we obtained several -related equations most of which have not been previously derived.     

The Virasoro action on the tau function for the constrained discrete KP hierarchy

With the help of the squared eigenfunction potential, the action of the Virasoro symmetry on the tau function of the constrained discrete KP hierarchy is derived.     

On the Recurrence Coefficients for Generalized q-Laguerre Polynomials

In this paper we consider a semi-classical variation of the weight related to the q-Laguerre polynomials and study their recurrence coefficients. In particular, we obtain a second degree second order discrete equation which in particular cases can be reduced to either the qPV or the qPIII equation.     

Combinatorics of Matrix Factorizations and Integrable Systems

We study relations between the eigenvectors of rational matrix functions on the Riemann sphere. Our main result is that for a subclass of functions that are products of two elementary blocks it is possible to represent these relations in a combinatorial–geometric way using a diagram of a cube. In this representation, vertices of the cube represent eigenvectors, edges are labeled by differences of locations of zeroes and poles of the determinant of our matrix function, and each face corresponds to a particular choice of a coordinate system on the space of such functions. Moreover, for each face this labeling encodes, in a neat and efficient way, a generating function for the expressions of the remaining four eigenvectors that label the opposing face of the cube in terms of the coordinates represented by the chosen face. The main motivation behind this work is that when our matrix is a Lax matrix of a discrete integrable system, such generating functions can be interpreted as Lagrangians of the system, and a choice of a particular face corresponds to a choice of the direction of the motion.     

A symmetry-preserving discretisation and regularisation model for compressible flow with application to turbulent channel flow

Most simulation methods for compressible flow attain numerical stability at the cost of swamping the fine turbulent flow structures by artificial dissipation. This article demonstrates that numerical stability can also be attained by preserving conservation laws at the discrete level. A new mathematical explanation of conservation in compressible flow reveals that many conservation properties of convection are due to the skew-symmetry of the convection operator. By preserving this skew-symmetry at the discrete level, a fourth-order accurate collocated symmetry-preserving discretisation with excellent conservation properties is obtained. Also a new symmetry-preserving regularisation subgrid-scale model is proposed. The proposed techniques are assessed in simulations of compressible turbulent channel flow. The symmetry-preserving discretisation for compressible flow has good stability without artificial dissipation and yields acceptable results already on coarse grids. Regularisation does not consistently improve upon no-model results, but often compares favourably with eddy-viscosity models.