Dynamics of a monolayer of nitrogen physisorbed on graphite

The dynamics of a crystalline monolayer of molecular nitrogen physisorbed on the basal plane of graphite, which was assumed to be rigid, has been studied by means of lattice and molecular dynamics. The study focusses mainly on the registered solid in which the centres of mass adopt the √3 × √3 R30° structure, but some results are also reported for denser monlayers, including one where the centre-of-mass lattice is non-triangular. Harmonic dispersion curves are reported for two models of the N₂-N₂ interaction combined with Steele's representation of the molecule-surface interaction. The one-phonon density of states is given for one of the models. Molecular dynamics results for the same model at two temperatures, 5 and 17 K, are analysed in terms of the dynamical structure factor, and one-phonon approximation to it, and the out-of-plane motions are treated in a manner similar to the one-phonon approximation. In-plane and out-of-plane motions are largely decoupled in all cases studied, and the in-plane motions show evidence of marked anharmonicity. The out-of-plane motions appear to exhibit Fermi-Pasta-Ulam type recurrences, although this is not analysed in detail.     

A symmetry problem in polymer calculations

It is shown by a symmetry argument that the band gap in a symmetric polyene must be zero in the restricted single determinant approximation. Spurious band gaps can arise in SCF calculations when the symmetry of the lattice is not reflected in the lattice sums. The consequences of this symmetry problem are discussed.     

State reduction in quantum mechanics: A calculational example

The question is posed as to the role of the state reduction hypothesis in the passage of a molecular beam through a Stern-Gerlach apparatus of the ordinary sort, and of the sort proposed by Wigner, in which the beam is rejoined at the end of the apparatus. The effect of the magnetic field is calculated, as is the effect of a “detector” atom placed asymmetrically in the apparatus, and sensitive to the passage of the molecular beam nearby. It is shown that in the absence of the detector atom the rejoined beam is represented by a pure case density matrix. However, when the detector is present in one arm of our Stern-Gerlach apparatus, the beam is found to be in a statistical mixture approximating “reduction”, even if we never “look” at the detector atom. It is also seen that the beam density matrix is reduced to diagonal form even though it is not physically affected by the detector.     

Stepping into iSMART: Understanding Science–Mathematics Integration for Middle School Science and Mathematics Teachers

This paper is based on an online graduate program for middle school science and mathematics teachers in Texas titled Integration of Science, Mathematics and Reflective Teaching (iSMART). Launching the program for its first cohort in fall 2010, the authors attempted to answer the following two questions in this paper: (a) How do the members of the iSMART design team and the first cohort of teacher participants define science and mathematics integration with similar and different emphases? and (b) How would these definitions and concerns impact the ongoing design of the program? The iSMART design team members and the participating cohort teachers had a shared view regarding the importance of integration and its possible impact on student motivation. The findings also revealed that the two groups showed some different points of emphasis in their definitions of integration. These issues will be addressed in the ongoing design of the program in the following three areas: (a) design of the second summer meeting activities, (b) greater emphasis on teacher as researcher and action research, and (c) administrative support for teacher collaboration.     

Conservative and Semismooth Derivatives are Equivalent for Semialgebraic Maps

Set-Valued and Variational Analysis - Subgradient and Newton algorithms for nonsmooth optimization require generalized derivatives to satisfy subtle approximation properties: conservativity for the...     

Glyceride‐Mimetic Prodrugs Incorporating Self‐Immolative Spacers Promote Lymphatic Transport,Avoid First‐Pass Metabolism,and Enhance Oral Bioavailability

First‐pass hepatic metabolism can significantly limit oral drug bioavailability. Drug transport from the intestine through the lymphatic system, rather than the portal vein, circumvents first‐pass metabolism. However, the majority of drugs do not have the requisite physicochemical properties to facilitate lymphatic access. Herein, we describe a prodrug strategy that promotes selective transport through the intestinal lymph vessels and subsequent release of drug in the systemic circulation, thereby enhancing oral bioavailability. Using testosterone (TST) as a model high first‐pass drug, glyceride‐mimetic prodrugs incorporating self‐immolative (SI) spacers, resulted in remarkable increases (up to 90‐fold) in TST plasma exposure when compared to the current commercial product testosterone undecanoate (TU). This approach opens new opportunities for the effective development of drugs where oral delivery is limited by first‐pass metabolism and provides a new avenue to enhance drug targeting to intestinal lymphoid tissue.     

Levels and sublevels of composition algebras over \mathfrak{p}-adic function fields

In [7], the level and sublevel of composition algebras are studied, wherein these quantities are determined for those algebras defined over local fields. In this paper, the level and sublevel of composition algebras, of dimension 4 and 8 over rational function fields over local non-dyadic fields, are determined completely in terms of the local ramification data of the algebras. The proofs are based on the “classification” of quadratic forms over such fields, as is given in [8]. The first author gratefully acknowledges financial support provided through the European Community’s Human Potential Programme, under contract HPRN-CT-2002-00287 KTAGS, which made possible an enjoyable stay at Ghent University.     

A sol-gel derived pH-responsive bovine serum albumin molecularly imprinted poly(ionic liquids) on the surface of multiwall carbon nanotubes

A pH-responsive surface molecularly imprinted poly(ionic liquids) (MIPILs) was prepared on the surface of multiwall carbon nanotubes (MWCNTs) by a sol-gel technique. The material was synthesized using a 3-aminopropyl triethoxysilane modified multiwall carbon nanotube (MWCNT-APTES) as the substrate, bovine serum albumin (BSA) as the template molecule, an alkoxy-functionalized IL 1-(3-trimethoxysilyl propyl)-3-methyl imidazolium chloride ([TMSPMIM]Cl) as both the functional monomer and the sol-gel catalyst, and tetraethoxysilane (TEOS) as the crosslinking agent. The molecular interaction between BSA and [TMSPMIM]Cl was quantitatively evaluated by UV–vis spectroscopy prior to polymerization so as to identify an optimal template/monomer ratio and the most suitable pH value for the preparation of the MWCNTs@BSA-MIPILs. This strategy was found to be effective to overcome the problems of trial-and-error protocol in molecular imprinting. The optimum synthesis conditions were as follows: template/monomer ratio 7:20, crosslinking agent content 2.0–2.5 mL, temperature 4 °C and pH 8.9 Tris–HCl buffer. The influence of incubation pH on adsorption was also studied. The result showed that the imprinting effect and selectivity improved significantly with increasing incubation pH from 7.7 to 9.9. This is mainly because the non-specific binding from electrostatic and hydrogen bonding interactions decreased greatly with the increase of pH value, which made the specific binding affinity from shape selectivity strengthened instead. The polymers synthesized under the optimal conditions were then characterized by BET surface area measurement, FTIR, thermogravimetric analysis (TGA) and scanning electron microscopy (SEM). The adsorption capacity, imprinting effect, selective recognition and reusability were also evaluated. The as-prepared MWCNTs@BSA-MIPILs were also found to have a number of advantages including high surface area (134.2 m² g⁻¹), high adsorption capacity (55.52 mg g⁻¹), excellent imprinting effect (imprinting factor of up to 5.84), strong selectivity (selectivity factor of 2.61 and 5.63 for human serum albumin and bovine hemoglobin, respectively), and good reusability.