On Series of Ordinals and Combinatorics

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑_bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑_bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑_β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic.     

Synthesis of bioactive indolocarbazoles: synthesis, nucleophilic ring-opening and chiral base desymmetrisation of a cyclic sulfate intermediate

A number of new functionalised bridged indolocarbazole systems have been prepared by ring-opening reactions of a key cyclic sulfate intermediate, prepared from the corresponding diol by the action of sulfuryl diimidazole and DBU. The same cyclic sulfate also undergoes an unprecedented asymmetric rearrangement to a chiral ketone, on treatment with a chiral lithium amide base.     

Contemplating Criteria for Science Education Reform: The Case of the Olympia School District

Proposals for current reform in science education elaborate national standards and a plethora of state-level interpretations commonly labeled as curriculum or learning frameworks. The purpose of this case study was to examine the dynamics of the science curriculum reform process in one of the first school districts to use the Georgia Framework for Learning Mathematics and Science as a basis for their reform initiative. The paper describes the ways in which members of the Olympia School District's Science Curriculum Committee participated in the science curriculum reform process, as well as their personal beliefs about the criteria needed for reform to take place. The results highlight the nature of metaphors guiding reform efforts; the influence of social, historical, economic, and political forces on the reform process; the use of local and professional languages as discourses for communicating about reform; and the complex power relations that influence the micropolitics of reform in the Olympia School District. This study has important implications for other teachers and school districts engaged in standards-based science curriculum reform. It points to the need for reform to include reflection and analysis of the role of teachers in the reform process and consideration of the purpose of science education reform in society.     

Synthesis of substituted 5-aminomethyl tetrahydro-isoquinolines and dihydro-isoindoles

The synthesis of ten substituted aminomethylene tetrahydro-isoquinolines is described, proceeding in eight steps from 5-hydroxyisoquinoline via reductive amination of N-Boc tetrahydro-isoquinoline 5-carboxaldehyde. Likewise, reductive amination was used to prepare four substituted dihydro-isoindoles from the corresponding aldehyde. The dihydro-isoindole ring system was conveniently accessed via a 2+2+2 cycloaddition reaction.     

An integrated console for capsule-based,automated organic synthesis

The current laboratory practices of organic synthesis are labor intensive, impose safety and environmental hazards, and hamper the implementation of artificial intelligence guided drug discovery. Using a combination of reagent design, hardware engineering, and a simple operating system we provide an instrument capable of executing complex organic reactions with prepacked capsules. The machine conducts coupling reactions and delivers the purified products with minimal user involvement. Two desirable reaction classes – the synthesis of saturated N-heterocycles and reductive amination – were implemented, along with multi-step sequences that provide drug-like organic molecules in a fully automated manner. We envision that this system will serve as a console for developers to provide synthetic methods as integrated, user-friendly packages for conducting organic synthesis in a safe and convenient fashion.

Using a combination of reagent design, hardware engineering, and a simple operating system we provide an instrument capable of executing complex organic reactions using prepacked capsules with minimal user involvement.     

Moisture induced solid phase degradation of l-ascorbic acid part 2, separation and characterization of the major degradation products

The influence of moisture in the presence and absence of air on the solid state degradation of l-ascorbic acid has been investigated previously [1]. Reaction kinetics were studied using tristimulus colorimetry and a quantitative high performance liquid chromatographic assay for both total l-ascorbic acid and dehydroascorbic acid. The degradation gave rise to a discolouration of the samples, the most severely degraded samples were almost black in appearance although over 68% w/w of the l-ascorbic acid remained. The samples were analyzed for the presence of carbonyl compounds, furan related compounds, compounds responsible for the discolouration and evolution of carbon dioxide. No 2,4-dinitrophenylhydrazine (2,4-DNP) derivatives of carbonyl compounds or furan related compounds were detected by HPLC. An HPLC screening procedure was developed which was used to monitor for compounds responsible for the discolouration, at least eight unknown compounds were resolved and a relative response factor of 5.47 was assigned to them with respect to l-ascorbic acid at 280 nm. One mole of carbon dioxide was evolved per mole of l-ascorbic acid. This paper describes the investigation into the identity of the degradation products.     

Unusual solid-state behavior in a neutral [2]catenane bearing a hydrolyzable component

A template-directed strategy to forming a bis(diimide) macrocycle through an intermediate asymmetric [2]catenane is reported. Saponification of the ester linkages within the crown ether component is much slower in the mechanically interlocked structure when compared to the free crown. The predominance of a single translational isomer leads to a dimeric structure, resulting in the generation of infinite channels within the crystal lattice. [structure: see text]     

High-energy (neodymium) laser pyrolysis of U.S. coals

As part of a study exploring conditions that influence coal pyrolysis, the effects of neodymium laser heating upon five different rank coals have been studied. Gaseous products from neodymium-laser pyrolysis of all coal types can be explained by condensation reactions during the cooling of high-temperature systems. The use of neutral or reducing atmospheres (helium, hydrogen or deuterium at two atmospheres) does not significantly alter the product distributions, although some deuteration of products was observed. High-speed photography was used to determine the dynamics of the laser interactions.     

An FTIR study of the surface chemistry of the dynamic Si(100) surface during etching in alkaline solution

In situ FTIR spectroscopy has been used in the attenuated total reflectance (ATR) mode to investigate the surface chemistry of etching Si(100) surfaces in aqueous KOH. The effect of solution concentration and electrode potential on the Si-H vibrations has been explored and the experimental results compared with density functional theory calculations. In addition. the kinetics of surface passivation of n-Si(100) has been investigated using FTIR spectroscopy.