Lie Atoms and Their Deformations

A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of a deformation with respect to the first algebra, endowed with a trivialization with respect to the second. Such deformations occur commonly in algebraic geometry, for instance as deformations of subvarieties of a fixed ambient variety. Here we study some basic notions related to Lie atoms, focussing especially on their deformation theory, in particular the universal deformation. We introduce Jacobi–Bernoulli cohomology, which yields the deformation ring, and show that, under suitable hypotheses, infinitesimal deformations are classified by certain Kodaira–Spencer data. Received: May 2006 Revision: January 2007 Accepted: March 2007     

Two remarkable doubly exponential series transformations of Ramanujan

The purpose of this note is to prove two doubly exponential series transformations found in Ramanujan’s second notebook. Dedicated to the memory of Professor K G Ramanathan     

Some results for the q-Bernoulli and q-Euler polynomials

We show some results for the q-Bernoulli and q-Euler polynomials. The formulas in series of the Carlitz's q-Stirling numbers of the second kind are also considered. The q-analogues of well-known formulas are derived from these results.     

Assessing the heterogeneity of a disease spread through a community

A multivariate non-parametric test and a semi-parametric regression model via counting process are proposed for detecting the heterogeneity of a disease spread through a community. The infection rates are allowed to depend on time in an arbitrary manner. Infectious data usually are not completely observed, nevertheless only partial information of the epidemic is needed for the suggested methods. The testing procedures and the associated methods of analysis are illustrated with reference to epidemics of respiratory disease on the Island of Tristan da Cunha in the South Atlantic     

Review of nanofluids for heat transfer applications

Research on nanofluids has progressed rapidly since its enhanced thermal conductivity was first repotted about a decade ago,though much controversy and inconsistency have been reported,and insufficient understanding of the formulation and mechanism of nanofluids further limits their applications.This work presents a critical review of research on heat transfer applications of nanofluids with the aim of identifying the limiting factors so as to push forward their further development.     

Criteria for -continuity

Bernoullicity is the strongest mixing property that a measure-theoretic dynamical system can have. This is known to be intimately connected to the so-called metric on processes, introduced by Ornstein. In this paper, we consider families of measures arising in a number of contexts and give conditions under which the measures depend -continuously on the parameters. At points where there is -continuity, it is often straightforward to establish that the measures have the Bernoulli property.

     

基于AHP-DEMATEL法的权重计算方法研究

权重是重要程度的体现形式,常用于系统评价过程.AHP就是一种将定性问题定量化,既简单又灵活的权重计算方法,但将复杂问题简单化会常常忽略因素之间的相互影响,可能造成结果的偏差.围绕系统评价中权重计算问题,提出了改进的AHP-DEMATEL的方法,通过计算初始权重和影响度、被影响度,并将被影响度融入到影响权重中,从而获得综合权重.方法不仅考虑了各风险因素在风险指标系统中对上层指标的作用,而且考虑了风险因素之间的依存关系避免单个专家意见的局限性,也降低了信息过渡使用所带来的评价误差.将改进后的方法用于物流信息集成风险的因素关系分析的实例,实证表明,改进方法在物流信息集成风险分析中的应用不仅简化了计算过程而且更加逼近现实情况,为决策者提供更为科学、准确的决策依据.     

The effects of ultrasound on micromixing

The Villermaux–Dushman reaction is a widely used technique to study micromixing efficiencies with and without sonication. This paper shows that ultrasound can interfere with this reaction by sonolysis of potassium iodide, which is excessively available in the Villermaux–Dushman solution, into triiodide ions. Some corrective actions, to minimize this interference, are proposed. Furthermore, the effect of ultrasonic frequency, power dissipation, probe tip surface area and stirring speed on micromixing were investigated. The power and frequency seem to have a significant impact on micromixing in contrast to the stirring speed and probe tip surface area. Best micromixing was observed with a 24 kHz probe and high power intensities. Experiments with different frequencies but a constant power intensity, emitter surface, stirring speed, cavitation bubble type and reactor design showed best micromixing for the highest frequency of 1135 kHz. Finally, these results were used to test the power law model of Rahimi et al. This model was not able to predict micromixing accurately and the addition of the frequency, as an additional parameter, was needed to improve the simulations.     

On-line HPLC combined with multivariate statistical process control for the monitoring of reactions

On-line high performance liquid chromatography is used to monitor a steady state reaction over 35.2 h, with 197 chromatograms recorded as the reaction progresses. For each chromatogram, peaks are detected, baseline corrected, aligned and integrated to provide a peak table consisting of the intensities of 19 peaks, two corresponding to the reactants, one to the product and one to the solvent, the remaining being impurities, by-products or intermediates. D-charts and Q-charts from multivariate statistical process control are applied to the data to determine which samples are out of control and also provide diagnostic insight into why these samples are problematic. The D-chart is best at looking at overall performance issues such as problems with mixing or difficulties with instrument operation, whereas the Q-charts are best at detecting impurities during the reaction.     

超Ornstein-Uhlenbeck过程的占位时过程的绝对连续性

证明了分支特征为ψ（z)=z^2,底过程为d≤3的暂留Ornstein-Uhlenbeck（O．U．）过程的超过程Xt的占位时过程Y（t)=∫^t0Xsds关于Lebesgue测度绝对连续,且其密度过程Y（t,x)关于t≥0,x∈R^d联合连续。