Elements of the Lagrangian Whitney trick

We investigate the possibility of a Lagrangian Whitney trick, a process to remove a pair of intersection points of a self-transverse Lagrangian immersion by a homotopy through Lagrangian immersions. There is a model for which a Lagrangian Whitney trick with compact support works assuming the model satisfies an area-capacity condition. Reduction of more general cases to the model, not necessarily fulfilling the area-capacity requirement, is possible if the given pair of double points admits a suitable symplectic disc and a certain Maslov-Viterbo index is 1. We look into an example to see the actualities of the Maslov-Viterbo index and the area-capacity conditions. The authors would like to thank the anonymous referee whose suggestions improved remarkably the exposition of the paper. This work was supported by the grant no.R01-2000-000-00004-0 from Korea Science & Engineering Foundation.     

Robustness of optimal designs for correlated random variables

Suppose that Y = (Y_i) is a normal random vector with mean Xb and covariance σ²I_n, where b is a p-dimensional vector (b_j), X = (X_ij) is an n × p matrix with X_ij ∈ {−1, 1}; this corresponds to a factorial design with −1, 1 representing low or high level respectively, or corresponds to a weighing design with −1, 1 representing an object j with weight b_j placed on the left and right of a chemical balance respectively. E-optimal designs Z are chosen that are robust in the sense that they remain E-optimal when the covariance of Y_i, Y_i′ is ρ > 0 for i ≠ i′. Within a smaller class of designs similar results are obtained with respect to a general class of optimality criteria which include the A- and D-criteria.     

Effect of chain stiffness on the morphology of diblock copolymer melts

The authors have studied the microphase separation of symmetric diblock copolymers with variable block stiffness and different block chain lengths using coarse-grained molecular dynamics simulations. The simulation results show that for symmetric diblock copolymers, a combination of chain length and relative stiffness between the blocks may play the major role in determining the equilibrium morphology of the system. When the variation in stiffness between blocks is small, the equilibrium morphology of the diblock system is found to be lamellar; this is also the case for systems with small chain lengths, regardless of the difference in block stiffness. However, in systems with longer chains with modest variation in stiffness between the blocks, an ordered cylindrical phase is formed in which the stiffer blocks form cylinders completely surrounded by the flexible components. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2556–2565, 2009     

Valence‐to‐core X‐ray emission spectroscopy of titanium compounds using energy dispersive detectors

X‐ray emission spectroscopy (XES) of transition metal compounds is a powerful tool for investigating the spin and oxidation state of the metal centers. Valence‐to‐core (vtc) XES is of special interest, as it contains information on the ligand nature, hybridization, and protonation. To date, most vtc‐XES studies have been performed with high‐brightness sources, such as synchrotrons, due to the weak fluorescence lines from vtc transitions. Here, we present a systematic study of the vtc‐XES for different titanium compounds in a laboratory setting using an X‐ray tube source and energy dispersive microcalorimeter sensors. With a full‐width at half‐maximum energy resolution of approximately 4 eV at the Ti Kβ lines, we measure the XES features of different titanium compounds and compare our results for the vtc line shapes and energies to previously published and newly acquired synchrotron data as well as to new theoretical calculations. Finally, we report simulations of the feasibility of performing time‐resolved vtc‐XES studies with a laser‐based plasma source in a laboratory setting. Our results show that microcalorimeter sensors can already perform high‐quality measurements of vtc‐XES features in a laboratory setting under static conditions and that dynamic measurements will be possible in the future after reasonable technological developments.     

Volume-based thermoelasticity: consequences of the (near) proportionality of isothermal compressibility to formula-unit volume

Groups of structurally related materials, including the alkali halides, exhibit a proportionality of isothermal compressibility to formula-unit volume. The relationship has recently been explored by Glasser and by Recio et al. In this paper, we present the consequences of such proportionality on the relationships of Born-Lande? and Born-Mayer parameters to the formula-unit volume. These relationships have then been tested separately on (i) alkali (excluding cesium) halides and (ii) cesium halides. We conclude that the equations fit the NaCl-type materials satisfactorily, but less well for the CsCl-type materials, and that the Born-Mayer equation is more applicable. These results confirm the conclusion that volume is intimately linked to thermodynamic quantities, as already demonstrated by our development of volume-based thermodynamics (VBT).     

Synthetic UDP-furanoses as potent inhibitors of mycobacterial galactan biogenesis

UDP-galactofuranose (UDP-Galf) is a substrate for two types of enzymes, UDP-galactopyranose mutase and galactofuranosyltransferases, which are present in many pathogenic organisms but absent from mammals. In particular, these enzymes are involved in the biosynthesis of cell wall galactan, a polymer essential for the survival of the causative agent of tuberculosis, Mycobacterium tuberculosis. We describe here the synthesis of derivatives of UDP-Galf modified at C-5 and C-6 using a chemoenzymatic route. In cell-free assays, these compounds prevented the formation of mycobacterial galactan, via the production of short "dead-end" intermediates resulting from their incorporation into the growing oligosaccharide chain. Modified UDP-furanoses thus constitute novel probes for the study of the two classes of enzymes involved in mycobacterial galactan assembly, and studies with these compounds may ultimately facilitate the future development of new therapeutic agents against tuberculosis.     

Saxophonists tune vocal tract resonances in advanced performance techniques

The acoustical impedance spectrum was measured in the mouths of saxophonists while they played. During bugling and while playing in the very high or altissimo range, experienced players tune a strong, but relatively broad, peak in the tract impedance to select which peak in the bore impedance will determine the note. Less experienced players are unable to produce resonances with impedance peaks comparable in magnitude to those of the bore and consequently are unable to play these notes. Experienced players can also tune their tracts to select which combinations of notes are played simultaneously in multiphonics or chords, and to produce pitch bending, a technique in which notes are produced at frequencies far from those of the peak of impedance of the instrument bore. However, in normal playing in the standard range, there is no consistent tuning of the tract resonances. The playing frequency, in all cases, lies close to the peak in the impedance of the reed in parallel with the series combination of the impedances measured in the mouth and the instrument bore on either side of the reed (ZMouth+ZBore)∥ZReed.