Methods for computing lower bounds to eigenvalues of self-adjoint operators

Summary. New approaches for computing tight lower bounds to the eigenvalues of a class of semibounded self-adjoint operators are presented that require comparatively little a priori spectral information and permit the effective use of (among others) finite-element trial functions. A variant of the method of intermediate problems making use of operator decompositions having the form is reviewed and then developed into a new framework based on recent inertia results in the Weinstein-Aronszajn theory. This framework provides greater flexibility in analysis and permits the formulation of a final computational task involving sparse, well-structured matrices. Although our derivation is based on an intermediate problem formulation, our results may be specialized to obtain either the Temple-Lehmann method or Weinberger's matrix method. Received December 12, 1992 / Revised version received October 5, 1994     

Single-photon detection mechanism in a quantum dot transistor

We study the transport mechanisms in a quantum dot MODFET by tuning the localization induced by charge stored on the quantum dots with light. The temperature dependence of the resistivity of a macroscopic sample reveals a hopping transport when the dots contain an excess of electrons. The resistance of a mesoscopic sample however, which is capable of detecting single photons, exhibits a much weaker dependence upon temperature. This points towards source-drain tunnelling as a transport mechanism and is confirmed by a statistical analysis of the single-photon-induced conductance steps. The complexity of the conducting paths increases as the average hopping length reduces.     

Lifting of Nichols algebras of typeB 2

We compute liftings of the Nichols algebra of a Yetter-Drinfeld module of Cartan typeB ₂ subject to the small restriction that the diagnonal elements of the braiding matrix are primitiventh roots of 1 with oddn≠5. As well, we compute the liftings of a Nichols algebra of Cartan typeA ₂ if the diagonal elements of the braiding matrix are cube roots of 1; this case was not completely covered in previous work of Andruskiewitsch and Schneider. We study the problem of when the liftings of a given Nichols algebra are quasi-isomorphic. The Appendix (with I. Rutherford) contains a generalization of the quantum binomial formula. This formula was used in the computation of liftings of typeB ₂ but is also of interest independent of these results. With an appendix “A generalization of theq-binomial theorem” with Ian Rutherford, Department of Mathematics and Computer Science, Mount Allison University, Sackville, N.B., Canada E4L 1E6. Research partially supported by NSERC. A visit to University of Bucharest in 1999 was partially supported by CNCSIS, Grant C12. She would like to thank the department for their warm hospitality. Received partial support from CNCSIS, Grants C12 and 199. Thanks to Mount Allison University for their hospitality in June 1999.     

Synthesis and surface structure of thymine-functionalized, self-assembled monolayer-protected gold nanoparticles

Thymine-functionalized SAM-protected gold nanoparticles with diameters of 2.2 +/- 0.3 nm and 7.0 +/- 1.0 nm were prepared via a modified two-phase transfer method. UV-vis spectra showed that particle size and solvent type, as well as surface charge, influenced the gold surface plasmon band absorption, along with the interaction between thymine terminal groups in the solution. Although the bulky thymine end groups interacted strongly on the particle surface, a well-ordered monolayer of thyminethiol derivatives with a long hydrocarbon chain was formed on the particle surface, exhibiting an ordered, all-trans conformation of the methylene backbone, similar to those of corresponding self-assembled monolayers (SAMs) generated from normal alkanethiols. A larger particle size and a longer reaction time facilitated the formation of more ordered thymine-terminated thiol SAMs. Thermal analysis indicated that reorientation of the SAMs during heat treatment occurred by two processes, caused possibly by the separate recrystallization of the hydrocarbon long chains and thymine units. More ordered SAMs with a higher thermal stability were formed on the larger particle surfaces when compared with those on the smaller ones. A greater density of molecular packing was found on the smaller particle surfaces. However, SAMs formed on the larger gold particles resembled 2D SAMs on the smooth, flat gold surfaces. XPS results confirmed the thymine structure as well as the chemical bond between gold and sulfur. One type of adsorbed sulfur species was observed for the smaller particles and two for the larger ones, but a slightly higher binding energy of thiolate was found for the smaller ones.     

Direct attachment of well-aligned single-walled carbon nanotube architectures to silicon (100) surfaces: a simple approach for device assembly

A new approach for the attachment of vertically-aligned shortened carbon nanotube architectures to a silicon (100) substrate by chemical anchoring directly to the surface has been demonstrated for the first time. The ordered assembly of single-walled carbon nanotubes (SWCNTs) was accomplished by hydroxylating the silicon surface followed by a condensation reaction with carboxylic acid functionalised SWCNTs. This new nanostructure has been characterised by X-ray photoelectron, Raman and Fourier transform infrared (FTIR) spectroscopy as well as scanning electron and atomic force microscopy. The assembly behaviour of SWCNTs onto the silicon surface shows a fast initial step producing isolated functionalised carbon nanotubes or nanotube bundles anchored to the silicon surface followed by a slower step where the adsorbed nanotubes grow into larger aggregates via van der Waals interactions between adsorbed and solvated nanotubes. The electrochemical and optical properties of the SWCNTs directly attached to silicon have also been investigated. These new nanostructures are excellent electrochemical electrodes. They also fluoresce in the wavelength range 650-800 nm. The successful attachment of the SWCNTs directly to silicon provides a simple, new avenue for fabrication and development of silicon-based nanoelectronic, nano-optoelectronic and sensing devices. Compared to existing techniques, this new approach has several advantages including low operating temperature, low cost and the possibility of further modification.     

From the Bench to the Field in Low‐Cost Diagnostics: Two Case Studies

Despite the growth of research in universities on point‐of‐care (POC) diagnostics for global health, most devices never leave the laboratory. The processes that move diagnostic technology from the laboratory to the field—the processes intended to evaluate operation and performance under realistic conditions—are more complicated than they might seem. Two case studies illustrate this process: the development of a paper‐based device to measure liver function, and the development of a device to identify sickle cell disease based on aqueous multiphase systems (AMPS) and differences in the densities of normal and sickled cells. Details of developing these devices provide strategies for forming partnerships, prototyping devices, designing studies, and evaluating POC diagnostics. Technical and procedural lessons drawn from these experiences may be useful to those designing diagnostic tests for developing countries, and more generally, technologies for use in resource‐limited environments.     

The discovery of 3-(1-aminoethylidene)quinoline-2, 4(1H,3H)-dione derivatives as novel PSII electron transport inhibitors

Based on the structures of the 4-hydroxyphenylpyruvate dioxygenase inhibitor mesotrione and natural product fischerellin A, a series of imine derivatives of ( $E$ )-3-acyl-quinoline-2,4(1H,3H)-dione (6, 12 and 16) were designed, synthesized and systematically evaluated for their herbicidal activity. The bioassay results indicated that most of the synthesized compounds displayed good to excellent herbicidal activity, of which 6e, 6g, 6h, 6q and 6t exhibited more than 50 % inhibition against Brassica napus L., Amaranthus retroflexu or Digitaria adscendens at a dosage of $94\,\hbox {g}\,\hbox {ha}^{-1}$ or lower. The symptom of injured leaves in vivo, the high Hill reaction inhibitory activity of 6h in vitro ( $\hbox {IC}_{50}\,0.1\, \upmu \hbox {g}\,\hbox {mL}^{-1})$ and the computer-based binding model of compound 6h with D1 protein in photosystem II (PSII) reaction centre suggest this novel structure to likely be a new type of PSII electron transport inhibitor. Thus, we have found a novel type of diketone enamine structure targeted at the PSII reaction centre.     

The role of mineral surface chemistry in modified dextrin adsorption

The adsorption of two modified dextrins (phenyl succinate dextrin--PS Dextrin; styrene oxide dextrin--SO Dextrin) on four different mineral surfaces has been studied using X-ray photoelectron spectroscopy (XPS), in situ atomic force microscopy (AFM) imaging, and captive bubble contact angle measurements. The four surfaces include highly orientated pyrolytic graphite (HOPG), freshly cleaved synthetic sphalerite (ZnS), and two surfaces produced through surface reactions of sphalerite: one oxidized in alkaline solution (pH 9, 1 h immersion); and one subjected to metal ion exchange between copper and zinc (i.e. copper activation: exposed to 1×10(-3) M CuSO(4) solution for 1 h). XPS measurements indicate that the different sphalerite surfaces contain varying amounts of sulfur, zinc, oxygen, and copper, producing substrates for polymer adsorption with a range of possible binding sites. AFM imaging has shown that the two polymers adsorb to a similar extent on HOPG, and that the two polymers display very different propensities for adsorption on the three sphalerite surface types, with freshly cleaved sphalerite encouraging the least adsorption, and copper activated and oxidized sphalerite encouraging significantly more adsorption. Contact angle measurements of the four surfaces indicate that synthetic sphalerite has a low contact angle upon fracture, and that oxidation on the timescale of one hour substantially alters the hydrophobicity. HOPG and copper-activated sphalerite were the most hydrophobic, as expected due to the carbon and di/poly-sulfide rich surfaces of the two samples, respectively. SO Dextrin is seen to have a significant impact on the wettability of HOPG and the surface reacted sphalerite samples, highlighting the difficulty in selectively separating sphalerite from carbonaceous unwanted minerals in flotation. PS Dextrin has the least effect on the hydrophobicity of the reacted sphalerite surfaces, whilst still significantly increasing the wettability of graphite, and thus has more potential for use as a polymer depressant in this separation.