Well-posedness of an evolution problem with nonlocal diffusion

We prove the well-posedness of a general evolution reaction–nonlocal diffusion problem under two sets of assumptions. In the first set, the main hypothesis is the Lipschitz continuity of the range kernel and the bounded variation of the spatial kernel and the initial datum. In the second set of assumptions, we relax the Lipschitz continuity of the range kernel to Hölder continuity, and assume monotonic behavior. In this case, the spatial kernel and the initial data can be just integrable functions. The main applications of this model are related to the fields of Image Processing and Population Dynamics.     

Book review of spectral theory of linear operators and spectral systems in banach algebras,operator theory: advances and applications,Vladimir Müller,Birkhäuser Verlag,Basel-Boston-Berlin, 2003, Volume 139, 381 pages. ISBN 3-7643-6912-4

We explore how randomization can help asymptotic convergence properties of simple directional search-based optimization methods. Specifically, we develop a cheap, iterative randomized Hessian estimation scheme. We then apply this technique and analyse how it enhances a random directional search method. Then, we proceed to develop a conjugate-directional search method that incorporates estimated Hessian information without requiring the direct use of gradients.     

A tunable dual-narrowband band-pass filter using plasma quantum well structure

A tunable dual-narrowband pass-band filter is designed. A one-dimensional photonic crystal(1D PC) is comprised of alternate dielectric layer and vacuum layer. Two quantum wells(QWs) as defects can be constructed by sandwiching two plasma slabs symmetrically in the 1D PC, and a dual-narrowband pass-band filter is formed. The conventional finitedifference time-domain(FDTD) method and piecewise linear current density recursive convolution(PLCDRC)–FDTD method are applied to the dielectric and plasma, respectively. The simulation results illustrate that the dual-narrowband frequencies can be tuned by changing the plasma frequency. The pass band interval and the half-power bandwidths(-3-dB band widths) are related to the space interval between two QWs.     

UV filter 2‐ethylhexyl 4‐methoxycinnamate: a structure,energetic and UV–vis spectral analysis based on density functional theory

2‐Ethylhexyl 4‐methoxycinnamate (EHMC) is a very commonly used UVB filter that is known to isomerize from the (E) to the (Z) isomer in the presence of light. In this study, we have performed high level quantum chemical calculations using density functional theory (DFT) with the B3LYP density functional and extended basis sets to study the gas‐phase molecular structure of EHMC and its energetic stability. Calculations were also performed for related smaller molecules cinnamic acid and 4‐methoxycinnamic acid. Charge delocalization has been analyzed using natural charges and Wiberg bond indexes within the natural bond orbital analysis and using nucleus independent chemical shifts. Density functional theory calculations reveal that the (E) isomer of EHMC is more stable than the (Z) by about 20 kJ mol^?1 in both the gas and aqueous phases. The enthalpy of formation in the gas phase of (E)‐EHMC was derived from an isodesmic bond separation reaction. Long‐range corrected DFT calculations in implicit water were made in order to understand the excited state properties of the (E) and (Z) isomers of EHMC. Copyright © 2013 John Wiley & Sons, Ltd.     

Orthonormal bases generated by Cuntz algebras

We show how some orthonormal bases can be generated by representations of the Cuntz algebra; these include Fourier bases on fractal measures, generalized Walsh bases on the unit interval and piecewise exponential bases on the middle third Cantor set.     

地球静止轨道远程交会过程导航性能评估

远程交会是静止轨道共位卫星自主定点置入的关键途径。针对远程交会过程中大距离跨度下相对运动模型的误差信号特性,理论推导了误差的传递机理,给出了相对导航EKF算法期望及噪声特性的定量分析模型。研究表明,确定距离区间存在最优过程噪声量级及其对应的最优滤波性能,且滤波误差与交会距离正相关,可作为全局最优滤波器的定量设计依据,解决了静止轨道远程交会过程EKF导航算法性能的量化评估问题。仿真表明,分析结论正确,相对速度滤波误差全程优于0.005 m/s(1σ),满足交会任务需求。     

Gaussian pre-filtering for uncertainty minimization in digital image correlation using numerically-designed speckle patterns

This paper discusses the effect of pre-processing image blurring on the uncertainty of two-dimensional digital image correlation (DIC) measurements for the specific case of numerically-designed speckle patterns having particles with well-defined and consistent shape, size and spacing. Such patterns are more suitable for large measurement surfaces on large-scale specimens than traditional spray-painted random patterns without well-defined particles. The methodology consists of numerical simulations where Gaussian digital filters with varying standard deviation are applied to a reference speckle pattern. To simplify the pattern application process for large areas and increase contrast to reduce measurement uncertainty, the speckle shape, mean size and on-center spacing were selected to be representative of numerically-designed patterns that can be applied on large surfaces through different techniques (e.g., spray-painting through stencils). Such “designer patterns” are characterized by well-defined regions of non-zero frequency content and non-zero peaks, and are fundamentally different from typical spray-painted patterns whose frequency content exhibits near-zero peaks. The effect of blurring filters is examined for constant, linear, quadratic and cubic displacement fields. Maximum strains between ±250 and ±20,000 µε are simulated, thus covering a relevant range for structural materials subjected to service and ultimate stresses. The robustness of the simulation procedure is verified experimentally using a physical speckle pattern subjected to constant displacements. The stability of the relation between standard deviation of the Gaussian filter and measurement uncertainty is assessed for linear displacement fields at varying image noise levels, subset size, and frequency content of the speckle pattern. It is shown that bias error as well as measurement uncertainty are minimized through Gaussian pre-filtering. This finding does not apply to typical spray-painted patterns without well-defined particles, for which image blurring is only beneficial in reducing bias errors.     

Handling uncertainties in toxicity modelling using a fuzzy filter

A fundamental concern in the Quantitative Structure-Activity Relationship approach to toxicity evaluation is the generalization of the model over a wide range of compounds. The data driven modelling of toxicity, due to the complex and ill-defined nature of eco-toxicological systems, is an uncertain process. The development of a toxicity predicting model without considering uncertainties may produce a model with a low generalization performance. This study presents a novel approach to toxicity modelling that handles the involved uncertainties using a fuzzy filter, and thus improves the generalization capability of the model. The method is illustrated by considering a data set dealing with the fathead minnow (Pimephales promelas) toxicity of 568 organic compounds.     

Quadrupole mass filter operation under the influence of magnetic field

This work demonstrates resolution enhancement of a quadrupole mass filter (QMF) under the influence of a static magnetic field. Generally, QMF resolution can be improved by increasing the number of rf cycles an ion experiences when passing through the mass filter. In order to improve the resolution, the dimensions of the QMF or the operating parameters need to be changed. However, geometric modifications to improve performance increase the manufacturing cost and usually the size of the instrument. By applying a magnetic field, a low‐cost, small footprint instrument with reduced power requirements can be realized. Significant improvement in QMF resolution was observed experimentally for certain magnetic field conditions, and these have been explained in terms of our theoretical model developed at the University of Liverpool. This model is capable of accurate simulation of spectra allowing the user to specify different values of mass spectrometer dimensions and applied input signals. The model predicts enhanced instrument resolution R>26 000 for a CO₂ and N₂ mixture with a 200‐mm long mass filter operating in stability zone 3 via application of an axial magnetic field. Copyright © 2013 John Wiley & Sons, Ltd.     

Calorimetric Estimation Employing the Unscented Kalman Filter for a Batch Emulsion Polymerization Reactor

Reaction calorimetry is a very useful tool to monitor exothermic polymerization reactions as it is based on the estimation of the heat generated by the reaction. The objective of this work is to analyze the performance of an unscented Kalman filter (UKF) for online monitoring of batch vinyl acetate emulsion polymerization reactions. Reactions are performed in isoperibolic and isothermal conditions. The UKF is compared to an extended Kalman filter that has a very poor performance. The results show that the UKF is able to provide good estimates for the conversion, for the reactor and jacket temperatures, for the overall heat transfer coefficient between the reaction medium and the jacket, and for the heat loss from the jacket to the surroundings.