Moments of a Thue–Morse generating function

We study the moments of even order of the generating function

$$\prod\limits_{0 \leqslant r \leqslant n} {(1 - e({2^r}x))} $$

of the Thue–Morse sequence and present several conjectures related to these moments.

     

Fabrication and characterization of poly(methylmethacrylate) microfluidic devices bonded using surface modifications and solvents

The fabrication of polymer microchips allows inexpensive, durable, high-throughput and disposable devices to be made. Poly(methylmethacrylate) (PMMA) microchips have been fabricated by hot embossing microstructures into the substrate followed by bonding a cover plate. Different surface modifications have been examined to enhance substrate and cover plate adhesion, including: air plasma treatment, and both acid catalyzed hydrolysis and aminolysis of the acrylate to yield carboxyl and amine-terminated PMMA surfaces. Unmodified PMMA surfaces were also studied. The substrate and cover plate adhesion strengths were found to increase with the hydrophilicity of the PMMA surface and reached a peak at 600 kN m(-2) for plasma treated PMMA. A solvent assisted system has also been designed to soften less than 50 nm of the surface of PMMA during bonding, while still maintaining microchannel integrity. The extent to which both surface modifications and solvent treatment affected the adhesion of the substrate to the cover plate was examined using nanoindentation methods. The solvent bonding system greatly increased the adhesion strengths for both unmodified and modified PMMA, with a maximum adhesion force of 5500 kN m(-2) achieved for unmodified PMMA substrates. The bond strength decreased with increasing surface hydrophilicity after solvent bonding, a trend that was opposite to what was observed for non-solvent thermal bonding.     

In-depth study into the interaction of single walled carbon nanotubes with anthracene and p-terphenyl

Solubilization of single walled carbon nanotubes (SWNT) in the presence of polycyclic aromatic hydrocarbons (PAHs) such as p-terphenyl and anthracene has been shown. The suspensions formed are stable for periods greater than 48 months but to date experimental research is scarce regarding the interactions that are taking place. Spectroscopic analysis such as Raman and fluorescence are used to probe the interactions occurring between the PAHs and the SWNT over a wide concentration range. Previous studies show the fluorescence of the PAHs is quenched on interaction with SWNT and in the case of p-terphenyl, the spectrum is red shifted. This result prompted a study of a large range of concentrations to quantify the degree of interaction between the SWNT and PAHs. It was found at high concentrations that both the PAHs and SWNT formed aggregates and at lower concentrations it was found that free PAHs and isolated SWNT were interacting. The radial breathing modes (RBMs) in Raman spectroscopy gave detail as to how diameter selective the PAH samples are when compared to the pristine SWNT modes. An increase in the wavenumber of the RBMs for both composite spectra was observed and it is believed that such a result is due to the debundling of the SWNT on interaction with the PAHs. It was also found that anthracene and p-terphenyl selectively interact with SWNT and the selected SWNT were found to be within a distinct diameter range and possessed unique physical properties.     

Phosphine dissociation and diffusion on Si(001) observed at the atomic scale

A detailed atomic-resolution scanning tunneling microscopy (STM) and density functional theory study of the adsorption, dissociation, and surface diffusion of phosphine (PH(3)) on Si(001) is presented. Adsorbate coverages from approximately 0.01 monolayer to saturation are investigated, and adsorption is performed at room temperature and 120 K. It is shown that PH(3) dissociates upon adsorption to Si(001) at room temperature to produce both PH(2) + H and PH + 2H. These appear in atomic-resolution STM images as features asymmetric-about and centered-upon the dimer rows, respectively. The ratio of PH(2) to PH is a function of both dose rate and temperature, and the dissociation of PH(2) to PH occurs on a time scale of minutes at room temperature. Time-resolved in situ STM observations of these adsorbates show the surface diffusion of PH(2) adsorbates (mediated by its lone pair electrons) and the dissociation of PH(2) to PH. The surface diffusion of PH(2) results in the formation of hemihydride dimers on low-dosed Si(001) surfaces and the ordering of PH molecules along dimer rows at saturation coverages. The observations presented here have important implications for the fabrication of atomic-scale P dopant structures in Si, and the methodology is applicable to other emerging areas of nanotechnology, such as molecular electronics, where unambiguous molecular identification using STM is necessary.     

Undergraduate Projects in the Application of Artificial Intelligence to Chemistry. I. Background

The potential of Artificial Intelligence (AI) in the development of intelligent machines is widely recognized. It is less widely appreciated that the methods which computer scientists use in their work on AI are also applicable to the solution of numerous problems in science. In many cases, AI methods are preferable to more conventional approaches, being superior in terms of time, quality of solution, or both. Most AI tools are comparatively simple to understand, despite their power, and computer programs to implement them can be written by anyone with average programming skills. This series of papers will demonstrate how AI methods are of value in science, why they work, and how they can be introduced into the syllabus as undergraduate research projects; suggestions of projects, illustrative programs and Java source code will be provided. This paper introduces the topic of AI and explains some of the ways in which an AI program differs from a conventional program.     

(–)‐Gibberic acid: hydrogen‐bonding pattern of the monohydrate of a non‐­racemic tetracyclic δ‐keto acid derivative of gibberellin A3

In the the title compound, 1,7‐di­methyl‐8‐oxo‐4bα,7α‐gibba‐1,3,4a(10a)‐triene‐10β‐carboxyl­ic acid monohydrate, C₁₈H₂₀O₃·H₂O, the water of hydration accepts a hydrogen bond from the carboxyl and donates hydrogen bonds to the carboxyl carbonyl and the ketone in two different screw‐related neighbors, which are mutually translational, yielding a complex three‐dimensional hydrogen‐bonding array.     

Separation of Flavonoids from the Leaves of Oroxylum indicum by HSCCC

A high-speed counter-current chromatography system (HPCCC) capable of rapid processing has been employed to separate seven flavonoids from a methanolic extract of the leaves of Oroxylum indicum by a one-step isocratic elution using a chloroform–methanol–water (9.5:10:5) two-phase system. LC, MS and NMR have identified the components from the extract as chrysin, baicalein, baicalein-7-O-glucoside, baicalein-7-O-diglucoside, chrysin-7-O-glucuronide, baicalein-7-O-glucuronide, and a chrysin-diglucoside. Baicalein-7-O-glucuronide and chrysin-7-O-glucuronide have been separated from this plant by HSCCC for the first time. The present study also reports a new chrysin-diglucoside from the leaf extract. The results demonstrate that HSCCC is a powerful separation tool and can contribute to identifying and quantifying plant ingredients.

     

Meshfree First-order System Least Squares

We prove convergence for a meshfree first-order system least squares （FOSLS） partition of unity finite element method （PUFEM）. Essentially, by virtue of the partition of unity, local approximation gives rise to global approximation in H（div）∩H（curl）. The FOSLS formulation yields local a posteriori error estimates to guide the judicious allotment of new degrees of freedom to enrich the initial point set in a meshfree discretization. Preliminary numerical results are provided and remaining challenges are discussed.