A Three-component Extension of the Camassa–Holm Hierarchy

We introduce a bi-Hamiltonian hierarchy on the loop-algebra of endowed with a suitable Poisson pair. It gives rise to the usual Camassa–Holm (CH) hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a three-component extension of the CH equation.     

The impact of polystyrene resins in solid-phase organic synthesis

Summary A major objective of the DIVERSOMER^® technology is to provide pure and characterized compounds for biological testing in order to prevent false negatives in our libraries. On several occasions, analysis of the final products by¹H-NMR and MS, has revealed by-products from the polystyrene solid support. Subsequently, three alternative methods were studied to remove polystyrene by-products; (i) prewashing of the resin prior to execution of the synthesis; (ii) pretreatment of the resin with the cleavage conditions consistent with the solid-phase synthesis reaction scheme; and (iii) parallel purification.     

Exploring Pi Using the Computer in Middle School Mathematics

The National Council of Teachers of Mathematics (NCTM) in its Curriculum and Evaluation Standards for School Mathematics encourages a middle school curriculum that integrates technology. It recommends that students should be able to identify and use functional relationships and make connections among seemingly diverse concepts and topics. In this activity of exploring the derivation of Pi, students take a constructivist role by collecting data and making conjectures. Using the data they construct graphs and tables and discourse about appropriate algebraic representations. The computer is used as an instructional aid enabling the students to view the data in a variety of forms. They are encouraged to communicate about the connections among the various representations.     

A combined transient and steady state approach for robust lifetime spectroscopy with micrometer resolution

We present the combination of two complementary micro‐photoluminescence spectroscopic techniques operating in transient and steady state condition, respectively. Introducing the time domain into the well‐established micro‐photoluminescence mapping approach operating under steady state conditions demonstrates a distinct improvement of the robustness and reliability in the determination of charge carrier lifetime measured with micrometer spatial resolution. Lifetimes from 50 ns to above ms are accessible. We elaborate a calibration procedure and apply the combined all‐photoluminescence setup to high‐performance multicrystalline silicon. A lifetime image obtained from the established photoluminescence imaging technique is reconstructed from the microscopic map by considering lateral diffusion and optical blurring, revealing a more detrimental influence of small angle grain boundaries as well as a higher lifetime within grains as may be deduced from the standard imaging technique. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

A combined crossed molecular beam and quasiclassical trajectory study of the Titan-relevant N(2D) + D2O reaction

Following a recent investigation on the N(²D) + H₂O reaction [Homayoon et al., J. Phys. Chem. Lett. 5, 3508 (2014)], we report on an experimental and theoretical study of the isotopologue N(²D) + D₂O reaction. Crossed molecular beam (CMB) experiments were conducted at a collision energy of 10.3 kcal mol^–1. Quasiclassical trajectory calculations were performed on a recent potential energy surface to derive the centre-of-mass functions necessary to simulate the CMB laboratory distributions. Excellent agreement was found. The importance of the channel leading to HON/DON was confirmed. The inclusion of this channel, in addition to that leading to the isomer HNO/DNO, can affect the models considering the coupling between nitrogen and oxygen chemistry in the upper atmosphere of Titan.     

Vibrations of a timoshenko beam clamped at one end and carrying a finite mass at the other

The present paper deals with an exact solution of the title problem. Modal shapes and natural frequency coefficients are determined for a significant range of the mechanical and geometric parameters that come into play. When the parameter I/AL² (where I is cross-sectional moment of inertia, A is cross-sectional area, and L beam length) approaches zero, the beam dynamic characteristics agree with values already available in the open literature.     

Lineshape analysis of stimulated Raman spectra of the near‐nozzle region of free jet expansions

An anomalous lineshape of stimulated Raman spectra obtained from the region very close to the nozzle of supersonic pulsed expansions of nitrogen is presented. High‐resolution Raman spectra of the Q branch of the fundamental vibration mode of N₂ have been recorded from two different nitrogen expansions at T₀ = 295 K and P₀ = 1.5–3.5 bar, the lasers crossing the jet axis in the range z/D = 0.25–1.25, where D is the effective nozzle diameter. The combination of Doppler shifts and strong gradients of density and temperature in the near‐nozzle region yield an inhomogeneous broadening and a double peak structure of the recorded Raman line profiles. The comparison of the experimental results with the simulation of the Raman spectrum from this region provides valuable information about the near‐nozzle flow field. The lineshape described here is different from another reported previously in the literature, which is based on a depletion of the density of free molecules on the axis due to condensation. Copyright © 2009 John Wiley & Sons, Ltd.