Stability and Synchronization of a Ring of Identical Cells with Delayed Coupling

We consider a ring of identical elements with time delayed, nearest neighbour coupling. The individual elements are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. The linear stability of the trivial solution is completely analyzed and illustrated in the parameter space of the coupling strength and the coupling delay. Conditions for global stability of the trivial solution are also given. The bifurcation and stability of nontrivial synchronous solutions from the trivial solution is analyzed using a centre manifold construction.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

Ozone-induced dissociation on a modified tandem linear ion-trap: Observations of different reactivity for isomeric lipids

Ozone-induced dissociation (OzID) exploits the gas-phase reaction between mass-selected lipid ions and ozone vapor to determine the position(s) of unsaturation. In this contribution, we describe the modification of a tandem linear ion-trap mass spectrometer specifically for OzID analyses wherein ozone vapor is supplied to the collision cell. This instrumental configuration provides spatial separation between mass-selection, the ozonolysis reaction, and mass-analysis steps in the OzID process and thus delivers significant enhancements in speed and sensitivity (ca. 30-fold). These improvements allow spectra revealing the double-bond position(s) within unsaturated lipids to be acquired within 1 s: significantly enhancing the utility of OzID in high-throughput lipidomic protocols. The stable ozone concentration afforded by this modified instrument also allows direct comparison of relative reactivity of isomeric lipids and reveals reactivity trends related to (1) double-bond position, (2) substitution position on the glycerol backbone, and (3) stereochemistry. For cis- and trans-isomers, differences were also observed in the branching ratio of product ions arising from the gas-phase ozonolysis reaction, suggesting that relative ion abundances could be exploited as markers for double-bond geometry. Additional activation energy applied to mass-selected lipid ions during injection into the collision cell (with ozone present) was found to yield spectra containing both OzID and classical-CID fragment ions. This combination CID-OzID acquisition on an ostensibly simple monounsaturated phosphatidylcholine within a cow brain lipid extract provided evidence for up to four structurally distinct phospholipids differing in both double-bond position and sn-substitution.     

Using a dual inlet atmospheric pressure ionization source as a dynamic reaction vessel

Atmospheric pressure ionization (API) sources have the ability to serve as dynamic 'reaction vessels' and this capability has been rapidly evolving over the past few years. With API sources, many different reagents and source conditions can be rapidly explored with minimal carryover or contamination of the mass spectrometer. While most API applications involve the simple protonation/deprotonation of analyte molecules, a great deal of flexibility and utility is available in almost any API source, provided the reagents and ionization conditions are judiciously selected. Here, the generation of a unique and useful class of reagent ions at atmospheric pressure is demonstrated for the first time. Within the AP gas-phase environment of a dual inlet ion source, the gas-phase synthesis of substituted N-phenylpyridinium cations is demonstrated by establishing conditions favorable to the nucleophilic substitution reaction required for their formation. The flexibility of this API source as a reaction vessel is also demonstrated.     

Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link

We have created a long-lived (≈40 s) persistent current in a toroidal Bose-Einstein condensate held in an all-optical trap. A repulsive optical barrier across one side of the torus creates a tunable weak link in the condensate circuit, which can affect the current around the loop. Superflow stops abruptly at a barrier strength such that the local flow velocity at the barrier exceeds a critical velocity. The measured critical velocity is consistent with dissipation due to the creation of vortex-antivortex pairs. This system is the first realization of an elementary closed-loop atom circuit.     

The mathematical knowledge and beliefs of elementary mathematics specialist-coaches

This paper reports on one aspect of a larger research project conducted in the United States that designed and implemented an elementary mathematics, specialist-coach preparation program and evaluated the effect of qualified specialist-coaches on student achievement. The paper discusses a conceptual framework for coaching in which a specialist-coach is to serve as a “more knowledgeable other” for a community of practice in a school, and ultimately to impact both the knowledge and professional practice of teachers and the school’s mathematics program as a whole. Specialist-coaches have unique opportunities and challenges in this daunting task, and the paper discusses one program designed to prepare well-respected teachers for the transition to the role and responsibilities of a specialist-coach. The reported analyses document changes in specialist-coaches’ mathematical content knowledge, mathematical knowledge for teaching, and beliefs regarding mathematics teaching and learning over the preparation program and during the specialist-coaches’ first years of service in a school. These specialist-coaches’ mathematical content knowledge grew and their beliefs became more aligned with a Making Sense perspective during the preparation program, and their changed state persisted throughout 2–3 years of service as specialist-coaches. Evidence addressing the specialist-coaches’ mathematical knowledge for teaching was mixed, but suggested that growth occurred both during the preparation program and in their first year of coaching, stabilizing in the years following.     

Reaction of acetylated carbohydrates with trimethylaluminum: concise synthesis of 1,2-O-isopropylidene d-ribofuranose

Treatment of β-d-ribose tetraacetate with trimethylaluminum gives α-3,5-O-acetyl-1,2-O-isopropylidene-d-ribofuranoside in excellent yield. This reaction allows for efficient and high-yielding installation of the 1,2-isopropylidene acetal (acetonide), which is difficult to prepare using more traditional acid-catalyzed methods. The reaction of trimethylaluminum with other per-acetylated carbohydrates is also described.