Multiparameter Polynomial Adaptive Stabilizers

In 1983 Morse proved, for unknown scalar one-dimensional linearsystems, the nonexistence of rational or polynomial universalstabilizers (UAS). In 1983, Nussbaum gave an example of an analyticUAS. In our paper, it is shown that there exist time-invariantpolynomial UAS's with multidimensional gain adaptation. Thedesign procedure is developed for linear, minimum-phase systemsof relative degree one. Convergence of the closed-loop systemis proved. Some numerical simulations are provided.     

A new route to spirooxindoles

[reaction: see text]Reaction of indole amides 5 with tributylstannane gave spiroindolenines 9 which are readily converted into spiropyrrolidinyloxindoles. This tricyclic system is found in a number of interesting natural products.     

The concerted addition of HBr to aryl alkynes; orthogonal pi bond selectivity

In a weakly acidic solution, the addition of HBr to 1-phenylprop-1-yne produces predominantly the anti-Markovnikov product. In this paper, we consider five possible explanations for this behavior and conclude that the concerted addition is occurring on the acetylenic pi bond orthogonal to the extended aromatic pi system. The electronic effect of the distal methyl group and the steric hindrance of the coplanar phenyl ring combine to promote bromide attack at the beta carbon. Attack on this pi bond is insensitive to the electronic effect of meta and para substituents on the ring but is very (sterically) sensitive toward all ortho substituents.     

Plasma total homocysteine measurement by ion-paired reversed-phase HPLC with electrochemical detection

Homocysteine is thought to be a risk factor for vascular disease and this has led to an increase in demand for its assay in clinical laboratories. An HPLC method, incorporating electrochemical detection, for measurement of plasma total homocysteine is presented. The method is simple to perform, precise and suitable for clinical applications.     

Development of a systems analysis approach for resolving the structure of biodegrading soil systems

An experimental and mathematical method is developed for the microbial systems analysis of polyaromatic hydrocarbon (PAH)-degrading mixed cultures in PAH-contaminated “town gas” soil systems. Frequency response is the primary experimental and data analysis tool used to probe the structure of these complicated systems. The objective is to provide a fundamental protocol for evaluating the performance of specific mixed microbial cultures on specific soil systems by elucidating the salient system variables and their interactions. Two well-described reactor systems, a constant volume stirred tank reactor (CSTR) and a plug flow differential volume reactor, are used in order to remove performance effects that are related to reactor type as opposed to system structure. These two reactor systems are well-defined systems that can be described mathematically and represent the two extremes of one potentially important system variable, macroscopic mass transfer. The experimental and mathematical structure of the protocol is described, experimental data is presented, and data analysis is demonstrated for the stripping, sorption, and biodegradation of napththalene.     

Some results on sperner families

Let F be a Sperner family of subsets of {1,…,m}. Bollobás showed that if $\text{A ∈ F ?}\text{A}\text{= {1,…,m}βA ∈ F}$, and if the parameters of F are p₀,…,p_m then

$\text{∑}\text{i=0}\text{[}\text{m}\text{2}\text{Pi}\text{m?1}\text{i?1}\text{+}\text{∑}\text{i=[}\text{m}\text{2}\text{]+1}\text{m}\text{Pi}\text{m?1}\text{m?i?1}\text{? 2}$

Here we generalize this result and prove some analogues of it. A corollary of Bollobás' result is that $\text{|F| ? 2(}{}_{\mathrm{<mtext>[</mtext><mtext>m</mtext><mtext>2</mtext><mtext>]?1</mtext>}}{}^{\mathrm{m?1}}\text{)}$. Purdy proved that if $\text{A ∈ F ?}\text{A}\text{? F}$ then $\text{|F| ? (}{}_{\mathrm{<mtext>[</mtext><mtext>m</mtext><mtext>2</mtext><mtext>]+1</mtext>}}{}^{\mathrm{m}}\text{)}$, which implies Bollobás' corollary. We also show that Purdy's result may be deduced from Bollobás' by a short argument. Finally, we give a canonical form for Sperner families which are also pairwise intersecting.     

Dust modelling using a combined CFD and discrete element formulation

The production and dispersal of airborne dust is an important issue in both environmental and industrial contexts. Dust pollution is a major environmental concern, and long exposure in occupational settings has been linked with numerous respiratory health issues. Industrial dust pollution can also present a significant explosion hazard, even in facilities with dust extraction systems. Computational models for dust generation and dispersal have, however, generally been formulated for specific geophysical applications and restricted to static, two‐dimensional, approaches. Here, we present a method for simulating dust production from a dynamic granular bed by using a three‐dimensional coupled discrete element method and Navier–Stokes computational model. Dust production is based on an energy formulation in which micro‐scale dust particles are assumed to overcome cohesion to macro‐scale grains. This model is used over the entire range of energies present within the system, from macro‐scale collisions to aerodynamic entrainment and bombardment of micro‐scale particles. The dust concentration is modelled as a scalar density field, which is advected and diffused through turbulence in the gas flow field. The model is tested against empirical predictions for two test cases, a slug of granular material dropped from a set height and air flow over a granular stockpile. Both give good agreement to the empirical relations, showing that the model can accurately predict the production and subsequent dispersal of dust from a dynamic granular bed. Copyright © 2012 John Wiley & Sons, Ltd.