Multiplicative Operator Splittings in Nonlinear Diffusion: From Spatial Splitting to Multiple Timesteps

Operator splitting is a powerful concept used in many diversed fields of applied mathematics for the design of effective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an efficient nonlinear diffusion filtering on digital images, we analyze the possibility of using multiplicative operator splittings to process images from different perspectives.We start by examining the potential of using fractional step methods to design a multiplicative operator splitting as an alternative to AOS schemes. By means of a Strang splitting, we attempt to use numerical schemes that are known to be more accurate in linear diffusion processes and apply them on images. Initially we implement the Crank-Nicolson and DuFort-Frankel schemes to diffuse noisy signals in one dimension and devise a simple extrapolation that enables the Crank-Nicolson to be used with high accuracy on these signals. We then combine the Crank-Nicolson in 1D with various multiplicative operator splittings to process images. Based on these ideas we obtain some interesting results. However, from the practical standpoint, due to the computational expenses associated with these schemes and the questionable benefits in applying them to perform nonlinear diffusion filtering when using long timesteps, we conclude that AOS schemes are simple and efficient compared to these alternatives.We then examine the potential utility of using multiple timestep methods combined with AOS schemes, as means to expedite the diffusion process. These methods were developed for molecular dynamics applications and are used efficiently in biomolecular simulations. The idea is to split the forces exerted on atoms into different classes according to their behavior in time, and assign longer timesteps to nonlocal, slowly-varying forces such as the Coulomb and van der Waals interactions, whereas the local forces like bond and angle are treated with smaller timesteps. Multiple timestep integrators can be derived from the Trotter factorization, a decomposition that bears a strong resemblance to a Strang splitting. Both formulations decompose the time propagator into trilateral products to construct multiplicative operator splittings which are second order in time, with the possibility of extending the factorization to higher order expansions. While a Strang splitting is a decomposition across spatial dimensions, where each dimension is subsequently treated with a fractional step, the multiple timestep method is a decomposition across scales. Thus, multiple timestep methods are a realization of the multiplicative operator splitting idea. For certain nonlinear diffusion coefficients with favorable properties, we show that a simple multiple timestep method can improve the diffusion process.     

Effect of plate aspect ratio on the recovery of deuterium from water-isotope mixture in flat-plate thermal diffusion columns with transverse sampling streams

The optimal plate aspect ratios for the best recovery of deuterium from water-isotope mixture in flat-plate thermal diffusion columns with transverse sampling streams have been determined. The maximum recovery and maximum production rate are achieved without changing the total expenditure, while the design with minimum plate surface area results in minimizing the total expense.     

Flammability ranking of foliage species by factor analysis of physical and chemical pyric properties

In this paper, factor analysis is introduced to evaluate the flammability of 55 foliage species that may be used in China for construction of the fuel break network of forest strips with lower flammability. Six pyric parameters, i.e. air dry moisture content, absolute dry moisture content, ignition point, ash content, caloric value and extractive content, are measured and used as variables for factor analysis. The covariance analysis shows that four principal factors can be extracted to reflect the flammability in different physical and chemical senses. In terms of the contributions of the four factors to the variances and the physical significance of the relevant parameters, the four factors are, respectively, termed as ‘flaming factor,’ ‘air dry factor,’ ‘ash factor’ and ‘absolute dry factor.’ The stability of the factor analysis method is examined by a different number of samples considered, and the variation degrees of the orderings indicate that the method has high reliability to measure the total flammability of foliage species. The results of the flammability evaluation are verified by comparison with the recommended tree species in the Chinese technology standard. Copyright © 2008 John Wiley & Sons, Ltd.     

1270轧机弹性曲线的回归及参数估计

首先介绍了轧机弹性曲线的基础知识及 1 2 70轧机AGC系统的基本结构 ,然后论述了数据采集的方法 ,最后根据最小二乘法得到轧机弹性曲线的回归模型及刚度系数的实验结果。     

Assessing Consequences of Substance Use: Psychometric Properties of the Inventory of Drug Use Consequences.

Negative consequences are an important component of the substance use change process, yet no standardized measure exists to assess consequences of use. This study evaluated the psychometric properties of the Inventory of Drug Use Consequences, a self-report measure assessing drinking and drug use consequences. Participants (N=252) were assessed at entry into outpatient substance abuse treatment. Items loaded strongly on 1 factor, and internal consistency of the total scale was high. Fifteen items with the highest correlations with the total scale were chosen to represent the construct. The shortened measure exhibited good internal consistency, convergent and discriminant validity, and detected change over time and may be the measure of substance use consequences that is lacking in the field. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Some better practices for measuring racial and ethnic identity constructs.

Racial and ethnic identity (REI) measures are in danger of becoming conceptually meaningless because of evaluators' insistence that they conform to measurement models intended to assess unidimensional constructs, rather than the multidimensional constructs necessary to capture the complexity of internalized racial or cultural socialization. Some aspects of the intersection of REI theoretical constructs with research design and psychometric practices are discussed, and recommendations for more informed use of each are provided. A table that summarizes some psychometric techniques for analyzing multidimensional measures is provided. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

硬质合金与铁基复合材料热等静压扩散连接

以烧结结态硬质合金和粉末态铁基复合材料为连接对象，研究了两种材料的热等静压扩攻连接工艺，获得了直接连接接头和加镍作中间过渡层的间接连接接头，考察了接头的结合界面形貌，界面的元素扩散和界面结合强度。     

Structural modelling of coprecipitated VTiO catalysts

A statistical study of the particle shape and size of pure V₂O₅ and TiO₂, and samples of coprecipitated V₂O₅---TiO₂ catalysts with different V/Ti ratios, has been performed. They were also characterized by XRD, EDAX, SEM and XPS. The results showed that pure vanadium pentoxide is compose by large square or needle-shaped particles, while pure titanium dioxide has small and rounded ones. VTiO samples presented an area and shape, depending on the V/Ti ratio.

These results and the spectroscopical characterization conducted to a particle model of the catalysts. Those VOTi samples with high V/Ti ratio would have large V₂O₅ crystals acting as support of a V/TiO₂ solid solution. In contrast, those samples with a low V/Ti ratio, would have the solid solution supporting vanadium pentoxide crystals.     

06NiCuCrMoNb钢高温加热时表层铜的行为

将06NiCuCrMoNb钢试样在不同的加热温度保温不同时间后，观察并分析试样表层的形貌和成分。结果表明，在一定条件下铜会扩散进入表层奥氏体晶界，得到沿奥氏体晶界分布的富铜相，并在热变形加工时导致热脆。试验得到了沿奥氏体晶界分布的富铜相与加热温度和保温时间的关系。     

A new approach to the decomposition of Boolean functions by the method of <Emphasis Type="Italic">q</Emphasis>-partitions. III. Joint decomposition of a function system

The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean functions of variables specified in different representation forms. The approach is based on the method of q-partitions of conjuncterms and concept of decomposition clones. Theorems on joint decomposition of a system of full and partial functions are formulated. The approach is illustrated by examples. Parts I and II of this article are published in No. 5 (2001) and No. 1 (2002). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 39–58, March–April 2007.