Identification and intensities of the “forbidden” 3ν23 band of 12C16O2

Lines of the 3ν₂³ “forbidden” band of ¹²C¹⁶O₂ have been identified in the 2000-cm^?1 region of a long-path, 0.01-cm^?1 resolution laboratory absorption spectrum. This band has detectable intensity due to Δl = 2 Fermi interactions between the upper level and the nearby ν₁ + ν₂ and 3ν₂¹ levels. Intensities of 18 lines of this band have been measured using a nonlinear least-squares spectral fitting technique. The intensities are enhanced at high J and an expression for the intensity distribution as derived by Toth [Appl. Opt.23, 1825–1834 (1984)] is used for the analysis. In terms of the total sample pressure, the vibrational band intensity is 0.194 ± 0.008 × 10^?30 cm^?1/molecule-cm^?2 at 296 K. The coefficient in the F factor is analogous to the Coriolis coefficient ξ and has been determined to be ?0.0413 ± 0.0015. As expected by theory, its value is very close to that of ξ for the related ν₁ + ν₂ band.     

The numerical analysis of water and solute movement in scale heterogeneous profiles

A computer based numerical method is presented for the analysis of water and solute movement in unsaturated heterogeneous porous materials. Such a method is necessary since, for those field studies where solute movement is of concern, the soil profiles under consideration are invariably heterogeneous. The numerical analysis is based on a general one-dimensional finite difference soil water flow model which includes a numerical technique combining the concepts of scale heterogeneity with an interpolative soil water hysteresis model. An explicit finite difference solute movement subroutine is incorporated into the unsaturated flow model to describe the transport of nonreactive solutes. A velocity dependent longitudinal dispersion coefficient is used in the solution of the hydrodynamic dispersion equation. The resulting hysteretic scale heterogeneous solute movement model permits the study of solute dynamics during infiltrating and redistribution in realistically complex spatially varying soil profiles. Results are presented for the leaching of both coarse grading to fine and fine grading to coarse sand profiles. Both vertical and horizontal profiles are studied using either a constant flux or a constant concentration input boundary condition. The four cases studied demonstrate the versatility of the numerical method and emphasise the substantial differences in transport behavior that can arise between heterogeneous and homogeneous profiles.Now with BHP Petroleum Pty. Ltd., GPO Box 1911R, Melbourne, Vic. 3001, Australia.     

Contractive projections and operator spaces

Parallel to the study of finite-dimensional Banach spaces, there is a growing interest in the corresponding local theory of operator spaces. We define a family of Hilbertian operator spaces , , generalizing the row and column Hilbert spaces and , and we show that an atomic subspace that is the range of a contractive projection on is isometrically completely contractive to an -sum of the and Cartan factors of types 1 to 4. In particular, for finite-dimensional , this answers a question posed by Oikhberg and Rosenthal. Explicit in the proof is a classification up to complete isometry of atomic w-closed -triples without an infinite-dimensional rank 1 w-closed ideal.

     

Billiards and Teichmüller curves on Hilbert modular surfaces

This paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of Riemann surfaces of genus two. These Teichmüller curves lie on Hilbert modular surfaces parameterizing Abelian varieties with real multiplication. Explicit examples, constructed from L-shaped polygons, give billiard tables with optimal dynamical properties.

     

Exceptional congruences for the coefficients of certain eta-product newforms

Let F(z)=∑_n=1^∞a(n)qⁿ denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that

     

Partition Lattice q-Analogs Related to q-Stirling Numbers

We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be constructed using an interpretation of Milne [9] for S[n, k] as sequences of lines in a vector space over the Galois field F _q. Another member is constructed so as to mirror the partial order in the subspace lattice.     

Opposed type double stage cell for Mbar pressure experiment with large sample volume

ABSTRACT

A new opposed type double-stage large volume cell has been developed to compress large volume samples to more than 100?GPa (Mbar) pressure. A pair of second-stage diamond anvils is introduced into the first-stage Paris–Edinburgh press. The double-stage large volume cell allows the generation of ultrahigh pressures using a large culet diameter of the second-stage diamond anvils (diameters of 0.5–1.2?mm). Pressure generation up to 131?GPa has been achieved by using the culet diameter of 0.5?mm. Sample volume of the double-stage large volume cell can be more than ～100 times larger than that of conventional Mbar experiment using a diamond anvil cell. The double-stage large volume cell has a large opening in the horizontal plane for X-ray measurements, which is particularly suited for the multi-angle energy dispersive X-ray diffraction measurement, thus opening a new way of in situ structural determinations of amorphous materials at Mbar pressures.