Recent developments in algebraic combinatorics

We survey three recent developments in algebraic combinatorics. The first is the theory of cluster algebras and the Laurent phenomenon of Sergey Fomin and Andrei Zelevinsky. The second is the construction of toric Schur functions and their application to computing three-point Gromov-Witten invariants, by Alexander Postnikov. The third development is the construction of intersection cohomology for nonrational fans by Paul Bressler and Valery Lunts and its application by Kalle Karu to the torich-vector of a nonrational polytope. We also briefly discuss the “half hard Lefschetz theorem” of Ed Swartz and its application to matroid complexes. Partially supported by NSF grant #DMS-9988459.     

Measurements: developments in the USA

Summary Sales and use of analytical instruments have expanded in the United States over the past two years, despite the recessionary nature of the economy. Interest in increasing the quality of analytical measurements seems to be undiminished, if not growing. Trends in several measurement areas, including health, environment, manufacturing, and commerce, are described as they bear on this growth of interest in reliably accurate measurements. The paper also considers trends in the development of reference materials and accreditation of laboratories in the USA. United States of America participation in efforts of the International Organization for Standardization, and a study by the International Bureau of Weights and Measures of how to provide for international traceability for analytical chemical measurements are mentioned.     

Quantitative analysis of imazamox herbicide in environmental water samples by capillary electrophoresis electrospray ionization mass spectrometry

Capillary electrophoresis-mass spectrometry (CE-MS) with an electrospray ionization interface was applied for the quantitative analysis of imazamox pesticide in well water, potable water, and pond water. The detector response for imazamox was determined to be linear over the concentration range of 50-1 ng/ml. The limits of quantitation and detection of the method were determined to be 200 and 20 ng/l for imazamox compound in each type of water sample, respectively. The total sample preparation and CE-MS analysis time was under 2 h.     

Hydrothermal synthesis of potassium molybdenum oxide bronzes: structure-inheriting solid-state route to blue bronze and dissolution/deposition route to red bronze

The hydrothermal syntheses of the alkali metal molybdenum bronzes from starting solids (H_xMoO₃) with structural affinities to the desired products were investigated. Single-phase potassium blue and red bronzes were prepared by the hydrothermal treatments at around 430 K, and characterized by powder X-ray diffraction, IR spectroscopy, and SEM. The formation processes of these two bronzes during the hydrothermal treatments were found to differ. The blue bronze was formed by a structure-inheriting solid-state route from H_xMoO₃ with x<0.3, whereas the red bronze was formed for x>0.3 through a solution dissolution/deposition route via the formation of MoO₃+MoO₂.     

Vibration frequencies of Ca3Fe2Si3O12 andradite: an ab initio study with the CRYSTAL code

The vibrational spectrum of Ca3Fe2Si3O12 andradite is calculated at the Gamma point by using the periodic ab initio CRYSTAL program that adopts an all-electron Gaussian-type basis set and the B3LYP Hamiltonian. The full set of frequencies (17 IR active, 25 Raman active, and 55 inactive modes) is calculated. The effect of the basis set on the calculated frequencies is discussed. The modes are characterized by direct inspection of the eigenvectors and isotopic substitution. The present calculations permit us to clarify some of the assignment problems raised by experiments. The mean absolute differences of the various modes with respect to the available experimental IR and Raman data are as small as 9 and 5 cm(-1), respectively.     

The katoite hydrogarnet Si-free Ca3Al2([OH]4)3: a periodic Hartree-Fock and B3-LYP study

The structure of the Si-free katoite hydrogarnet (116 atoms in the unit cell) has been investigated at the periodic ab initio quantum mechanical level with the CRYSTAL program, by using a Gaussian type basis set and both the HF and the hybrid B3-LYP Hamiltonians. The structure has been fully optimized at various pressures in the 0-46 GPa range; the modifications of the structure, and in particular of the (OH)4 group, as a function of pressure are analyzed. At the B3-LYP level and P greater than 15 GPa, a O-H...O interaction of increasing strength appears, with important modifications in the local geometry of the tetrahedral site. The calculated omega01(O-H) fundamental vibrational frequency at zero pressure is in excellent agreement with experiment (3674 and 3663 cm(-1), respectively); the omega01(O-H) stretching frequency remains essentially constant in the 0-15 GPa interval, whereas it dramatically decreases at higher pressures with a corresponding anharmonicity increase, as a consequence of the formation of a strong hydrogen bond. The hydration energy of grossular and the formation energy of Si-free katoite have also been computed, and the B3-LYP results are in quite good agreement with experiment.