矩阵方程AX=B的中心对称定秩解及其最佳逼近

本文研究了矩阵方程AX=B的中心对称解.利用矩阵对的广义奇异值分解和广义逆矩阵,获得了该方程有中心对称解的充要条件以及有解时,最大秩解、最小秩解的一般表达式,并讨论了中心对称最小秩解集合中与给定矩阵的最佳逼近解.     

A defect correction approach to turbulence modeling

A method for resolving turbulent flow problems is presented, aiming at competing with the existing mathematical tractable Approximate Deconvolution Models in terms of accuracy, and outperforming these models in terms of the computational time needed. Full numerical analysis is performed, and the method is shown to be stable, easy to implement and parallelize, and computationally fast. The proposed method employs the defect correction approach to solve spatially filtered Navier–Stokes equations. A simple numerical test is provided that compares the method against the approximate deconvolution turbulence model (ADM). When resolving a fluid flow at high Reynolds number, the numerical example verifies the key feature of the method: while having the accuracy comparable to that of the ADM, the method computes in less than 80% of the time needed for the turbulence model—even before the parallelization.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 268–288, 2015     

Explicit Solutions of Quadratic FBSDEs Arising From Quadratic Term Structure Models

We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to similar results on affine term structure models of Hyndman (Math. Financ. Econ. 2(2):107–128, 2009) due to the relationship between quadratic functionals of Gaussian processes and linear functionals of affine processes. Similar to the affine case a sufficient condition for the explicit solutions to hold is the solvability in a fixed interval of Riccati-type ordinary differential equations. However, in contrast to the affine case, these Riccati equations are easily associated with those occurring in linear-quadratic control problems. We also consider quadratic models for a risky asset price and characterize the futures price and forward price of the asset in terms of similar FBSDEs. An example is considered, using an approach based on stochastic flows that is related to the FBSDE approach, to further emphasize the parallels between the affine and quadratic models. An appendix discusses solvability and explicit solutions of the Riccati equations.     

Marginal filtering in large state spaces

Recognising everyday activities including information about the context requires to handle large state spaces. The usage of wearable sensors like six degree of freedom accelerometers increases complexity even more. Common approaches are unable to maintain an accurate belief state within such complex domains. We show how marginal filtering can overcome limitations of standard particle filtering and efficiently infer the context of actions. Symbolic models of human behaviour are used to recognise activities in two different settings with different state space sizes. Based on these scenarios we compare the marginal filter to the standard particle filter. An evaluation shows that the marginal filter performs comparably in small state spaces but outperforms the particle filter in large state spaces.     

基于残差加权经验过程方法的自回归模型分布变点监测

Change monitoring of distribution in time series models is an important issue.This paper proposes a procedure for monitoring changes in the error distribution of autoregressive time series,which is based on a weighed empirical process of residuals with weights equal to the regressors.The asymptotic properties of our monitoring statistic are derived under the null hypothesis of no change in distribution.The finite sample properties are investigated by a simulation.As it turns out,the procedure is not only able to detect distributional changes but also changes in the regression coefficient and mean.Finally,we apply the statistic to a groups of financial data.     

The importance of OH radical–neutral low temperature tunnelling reactions in interstellar clouds using a new model

Recent laboratory experiments using a pulsed Laval nozzle apparatus have shown that reactions between a neutral molecule and the radical OH can occur efficiently at low temperatures despite activation energy barriers if there is a hydrogen-bonded complex in the entrance channel which allows the system to tunnel efficiently under the barrier. Since OH is a major radical in the interstellar medium, this class of reactions may well be important in the chemistry that occurs in the gas phase of interstellar clouds. Using a new gas-grain chemical network with both gas-phase reactions and reactions on the surfaces of dust particles, we studied the role of OH–neutral reactions in dense interstellar clouds at 10, 50, and 100 K. We determined that at least one of these reactions can be significant, especially at the lowest temperatures studied, where the rate constants are large. It was found in particular that the reaction between CH₃OH and OH provides an effective and unambiguous gas-phase route to the production of the gaseous methoxy radical (CH₃O), which has been recently detected in cold, dense interstsellar clouds. The role of other reactions in this class is explored.     

基于选择性填充的超高非线性纳米纤芯光纤特性

为了改善纳米纤芯光纤的非线性与色散特性,提出利用气孔填充非线性液体的新型纳米纤芯光纤结构来增强现有纳米纤芯光纤的非线性系数,利用选择性填充方法来改进现有纳米纤芯光纤的特性调控能力,实现改善光纤非线性和色散特性目的.分析结果表明采用选择性气孔填充方式和适当的光纤参量有助于实现光纤单模单偏振工作,可以大幅度地提升纳米纤芯光纤的非线性系数和改善光纤色散特性.     

力学问题加权残值法的双侧优化逼近

本文给出的力学问题加权残值法的数值解法,可直观地表示出解的最小上边界和最大下边界。     

结构综合的曲线寻优近似解析方法

本文首次在结构优化领域应用曲线寻优近似解析方法，数值实验表明本文方法的效率较高     

Mathematical Models in Polymer Processing

This paper is a concise overview of some problems in polymer science that are particularly stimulating from the point of view of modeling. Far from being exhaustive, it deals with two main subjects: phase change and polymerization.