Complexation of the triply-bonded dirhenium(II) complex Re(2)Cl(4)(mu-dppm)(2) (dppm = Ph(2)PCH(2)PPh(2)) by up to three acetylene molecules

The triply bonded dirhenium(II) synthons Re(2)X(4)(mu-dppm)(2) (X = Cl, Br; dppm = Ph(2)PCH(2)PPh(2)) react with acetylene at room temperature in CH(2)Cl(2) and acetone to afford the bis(acetylene) complexes Re(2)X(4)(mu-dppm)(2)(mu:eta(2),eta(2)-HCCH)(eta(2)-HCCH) (X = Cl (3), Br(4)). Compound 3 has been derivatized by reaction with RNC ligands in the presence of TlPF(6) to give unsymmetrical complexes of the type [Re(2)Cl(3)(mu-dppm)(2)(mu:eta(2),eta(2)-HCCH)(eta(2)-HCCH)(CNR)]PF(6) (R = Xyl (5), Mes (6), t-Bu (7)), in which the RCN ligand has displaced the chloride ligand cis to the eta(2)-HCCH ligand. The reaction of 3 with an additional 1 equiv of acetylene in the presence of TlPF(6) gives the symmetrical all-cis isomer of [Re(2)Cl(3)(mu-dppm)(2)(mu:eta(2),eta(2)-HCCH)(eta(2)-HCCH)(2)]PF(6) (8). The two terminal eta(2)-HCCH ligands in 8 are very labile and can be displaced by CO and XylNC to give the complexes [Re(2)Cl(3)(mu-dppm)(2)(mu:eta(2),eta(2)-HCCH)(L)(2)]Y (L = CO when Y = PF(6) (9); L = CO when Y = (PF(6))(0.5)/(H(2)PO(4))(0.5) (10); L = XylNC when Y = PF(6) (11)). These substitution reactions proceed with retention of the all-cis stereochemistry. Single-crystal X-ray structure determinations have been carried out on complexes 3, 5, 8, 10, and 11. In no instance have we found that the acetylene ligands undergo reductive coupling reactions.     

Resource pooling in congested networks: proportional fairness and product form

We review two areas of recent research linking proportional fairness with product form networks. The areas concern, respectively, the heavy traffic and the large deviations limiting regimes for the stationary distribution of a flow model, where the flow model is a stochastic process representing the randomly varying number of document transfers present in a network sharing capacity according to the proportional fairness criterion. In these two regimes we postulate the limiting form of the stationary distribution, by comparison with several variants of the fairness criterion. We outline how product form results can help provide insight into the performance consequences of resource pooling.     

Fusion multiplicities as polytope volumes: -point and higher-genus su(2) fusion

We present the first polytope volume formulas for the multiplicities of affine fusion, the fusion in Wess–Zumino–Witten conformal field theories, for example. Thus, we characterise fusion multiplicities as discretised volumes of certain convex polytopes, and write them explicitly as multiple sums measuring those volumes. We focus on su(2), but discuss higher-point ( ) and higher-genus fusion in a general way. The method follows that of our previous work on tensor product multiplicities, and so is based on the concepts of generalised Berenstein–Zelevinsky diagrams, and virtual couplings. As a by-product, we also determine necessary and sufficient conditions for non-vanishing higher-point fusion multiplicities. In the limit of large level, these inequalities reduce to very simple non-vanishing conditions for the corresponding tensor product multiplicities. Finally, we find the minimum level at which the higher-point fusion and tensor product multiplicities coincide.     

A Statewide Implementation of the Critical Features of Professional Development: Impact on Teacher Outcomes

This study is focused on a statewide implementation of the core conceptual framework for effective professional development in the United States. and associated impact on teacher quality and attitudes. The framework included content focus, active learning, coherence, duration, and collective participation. There were 252 participants in the study, who were involved in one of the five science or six mathematics programs. Findings indicated a significant impact on teacher quality for all participating programs. Teacher attitudes were positive at the baseline, and remained positive with some improvement at the end of the program. However, teacher perceived preparedness increased significantly across the duration of the program. Discussion of the findings and implications for professional development programs internationally are shared.     

Existence of solutions for the anti-plane stress for a new class of “strain-limiting” elastic bodies

The main purpose of this study is to establish the existence of a weak solution to the anti-plane stress problem on V-notch domains for a class of recently proposed new models that could describe elastic materials in which the stress can increase unboundedly while the strain yet remains small. We shall also investigate the qualitative properties of the solution that is established. Although the equations governing the deformation that are being considered share certain similarities with the minimal surface problem, the boundary conditions and the presence of an additional model parameter that appears in the equation and its specific range makes the problem, as well as the result, different from those associated with the minimal surface problem.     

The relative detectability for mice of gaps having different ramp durations at their onset and offset boundaries

The effect on gap detectability of varying noise fall time (FT) and rise time (RT) of the gap boundary ramps was examined in mice using reflex modification audiometry, measuring inhibition of acoustic startle reflexes by variously shaped gaps just preceding reflex expression. In experiment 1 (n = 12) inhibition increased up to near-asymptotic values with longer FT (0, 1, 2, 3, 5, or 10 ms) and QT (quiet time, 0 to 13 ms), with a 2:1 trade-off between FT and QT. In experiment 2 (n = 24) inhibition increased for any RT above 0 ms (2, 3, 5, or 7 ms) if QT= 1 ms, but diminished with increased RT when QT = 3 or 8 ms. Enhanced detectability for subthreshold gaps by longer ramps results from their extending the apparent gap duration. The negative effect of increased RT for threshold gaps suggests the importance for gap detection of the stronger neural responses to sharp edges at the end of the gap shown previously in the mouse inferior colliculus. These effects are specific to gaps: inhibition for fixed (70-dB SPL) or varied level pulses (30 to 60 dB) was unaffected by varying the ramped edges (experiments 3 and 4, n = 9).     

The numerical solution of the matrix equationXA+AY=F

An iterative method for solving the matrix equationXA+AY=F is discussed Algorithms and techniques for accelerating convergence are outlined. The method compares favourably with existing techniques.     

Visualization of the hinge flow in a 5:1 scaled model of the medtronic parallel bileaflet heart valve prosthesis

 In this work, a flow visualization experiment was performed to elucidate features of the retrograde hinge flow through a 5 : 1 scaled model of the Medtronic Parallel bileaflet heart valve. It was hypothesized that this model would provide detailed flow information facilitating identification of flow structures associated with thrombus formation in this valve. The experimental protocol was designed to ensure fluid dynamic similarity between the model and prototype heart valves. Flow was visualized using dye injection. The detailed flow structures observed showed the hinge’s inflow channel was the most suspect region for thrombus formation. Here a complex helical structure was observed. Received: 27 October 1997/Accepted: 1 May 1998