Real meromorphic functions and linear differential polynomials

We determine all real meromorphic functions f in the plane such that f has finitely many zeros, the poles of f have bounded multiplicities, and f and F have finitely many non-real zeros, where F is a linear differential polynomial given by F = f (k) +Σk-1j=0ajf(j) , in which k≥2 and the coefficients aj are real numbers with a0≠0.     

Organocatalytic kinetic resolution cascade reactions: new mechanistic and stereochemical manifold in diphenyl prolinol silyl ether catalysis

A new cascade reaction involving an iminium-catalyzed intramolecular oxa-Michael addition followed by an enamine-catalyzed intermolecular Michael addition is reported herein. This cascade reaction generates enantiopure, highly functionalized tetrahydropyrans and tetrahydrofurans in a one-pot reaction and in up to 89?% combined yield and up to 99?% ee. This cascade reaction is catalyzed by diaryl prolinol silyl ethers, which are a privileged class of catalysts. The stereochemical outcome of these cascade reactions is unprecedented. Computational studies indicate that this stereochemical outcome arises from nonclassical hydrogen-bonding interactions between the electrophile and the substrate, and from entropic considerations of preorganization. The unprecedented configurations of the cascade products, combined with the computational models, reveal for the first time that asymmetric induction by diaryl prolinol silyl ether catalysts is not always exclusively reagent controlled. The stereochemical outcome also arises from a kinetic resolution or dynamic kinetic resolution of the β-stereocenter through an enamine-catalyzed intermolecular reaction. This unprecedented organocascade reaction mechanism may be adaptable to diaryl prolinol silyl ether-catalyzed cascade reactions, in which both the iminium- and enamine-catalyzed steps are intermolecular, an underdeveloped type of cascade reaction.     

Space-charge driven emittance growth in a 3D mismatched anisotropic beam

We investigate the phenomenon of space-charge driven emittance growth in a three-dimensional mismatched anisotropic charged particle beam with relevance to high-intensity linear accelerators. The final emittance growth can be understood as a superposition of the contributions from the mismatch-induced halo formation and from the anisotropy-induced energy exchange. The averaged emittance growth per degree of freedom is bounded from above by the so-called "free energy limit" extended by the contributions from energy exchange. The partition of the growth into longitudinal or transverse is, however, a strong function of the tune ratio including the possibility that an initially equipartitioned beam is even driven substantially away from equipartition. The growth of the beam halo extent is dominated by the effect of mismatch, whereas anisotropy itself generates practically no halo.     

Purity assessment of single-wall carbon nanotubes, using optical absorption spectroscopy

A demand currently exists for a method of assessing the purity of single-wall carbon nanotubes (SWNTs), which will allow for meaningful material comparisons. An established metric and protocol will enable accurate and reproducible purity claims to be substantiated. In the present work, the ability to accurately quantify the mass fraction of SWNTs in the carbonaceous portion of a given sample is demonstrated, using optical absorption spectroscopy on both laser and arc discharge-generated SWNT-N,N-dimethylacetamide (DMA) dispersions. Verification of purity assessment protocols is based upon constructed sample sets comprising designed mass fractions of purified SWNTs and representative carbonaceous synthesis byproducts. Application of a previously reported method based on a ratio of the areal absorbance from linear subtractions of the second interband electronic transitions of semiconducting SWNTs ((S)E(22)) has shown a severe overestimation of SWNT purity (average error >24%). Instead, the development of a nonlinear pi-plasmon model, which considers overlap of electronic transitions and peak broadening, has dramatically improved the purity assessment accuracy (average error <7%), derived from a strong correlation to the constructed sample sets. This approach has enabled corroboration of rapid assessment procedures, such as absorbance peak maxima ratio and Beer's law analysis, directed at purification monitoring and synthesis sample screening. Specifically, a simple protocol for purity assessment of laser and arc-discharge SWNTs has been established that can be extended to other synthetic types (i.e. CVD, HiPco, etc.) and diameter distributions.     

Existence of extraordinary zero-curvature slowness curve in anisotropic elastic media

Acoustic wave propagation in elastic media is characterized by the slowness surface. The slowness surface consists of three sheets associated with three modes of wave propagation and the two outer sheets can have zero-curvature locally. It is shown that the outmost sheet can admit extraordinary zero-curvature and the slowness curve can appear as a straight line locally. Using the perturbation method, the conditions for the extraordinary zero-curvature are derived analytically without violating the thermodynamic condition for elastic media. The results can be applied to crystals with higher symmetry and to the study of phonon focusing and surface waves.     

Particle filtering for chaotic dynamical systems using future right-singular vectors

Nonlinear Dynamics - In this paper, we combine tools from the study of chaotic dynamical systems with nonlinear non-Gaussian data assimilation algorithms to produce novel particle filtering...     

Sorption of inorganic nanoparticles in woven cellulose fabrics

Titanium dioxide was deposited from aqueous suspension onto cellulosic surfaces.Titania was sourced from Degussa (P25TM,70:30 anatase:rutile).Dry uptake of particles was shown to be rapid and dominant with one-third of the deposition occurring in less than 30 s and over one-half in the first minute.Isotherms were recorded to compare the rate of titanium deposition on dry and pre-wetted cotton.In the dry case uptake reached a maximum in 30 min whereas in the pre-wetted case the uptake was seen to continue beyond 180 min.A broad trend of higher deposition occurring at lower pH was seen,corresponding to the region where surface charges were opposite and thus attractive.Dry pickup was less significant at high pH.The response to varying ionic strength was complex and was attributed to the combined effect of charge screening,particle aggregation and consequent particle entrapment or occlusion.Titania deposition into the interstices of woven cotton sheets resulted in the formation of inorganic,nanoparticulate skeletons which could be isolated by controlled combustion of the cellulose and thus cotton was suggested to have potential for the templated synthesis of high surface area semiconductor materials.     

Syntheses and reactions of some fluorinated dienes,cyclobutenes and furans

There are many reports¹ of the pyrolysis of fluorinated organic compounds, including the defluorination of cyclic fluorocarbons over iron to give aromatic compounds. Extending this technique we have investigated the flow pyrolysis of some readily accessible unsaturated fluorocarbons, such as I, II, and III, and found these to be synthetically

useful routes to fluorinated dienes, cyclobutenes, and furans. Pyrolyses were carried out using a nitrogen flow over platinum, iron or caesium fluoride heated at 430–700°. The various products can all be rationalized in terms of intermediate allylic radicals, and the solid substrate influences which allylic radicals are formed.We are also investigating the chemistry of those now accessible compounds, such as IV, V, and VI, and some of the preliminary results are described.

For example the fluoride ion induced dimerisation of IV gave two major products VII and VIII via a particular interesting mechanism.