Some determinants of path generating functions

We evaluate four families of determinants of matrices, where the entries are sums or differences of generating functions for paths consisting of up-steps, down-steps and level steps. By specialisation, these determinant evaluations have numerous corollaries. In particular, they cover numerous determinant evaluations of combinatorial numbers - most notably of Catalan, ballot, and of Motzkin numbers - that appeared previously in the literature.Comment: 35 pages, AmS-TeX; minor corrections; final version to appear in Adv. Appl. Mat

Automatic holographic droplet analysis for liquid fuel sprays

The basic scheme for automated holographic analysis involves an optical system for reconstruction of the three dimensional real image of the droplet field, a spatial scanning system to transport a digitizing X-y image sensor through the real image, and processing algorithms for droplet recognition which establish the droplet sizes and positions. The hardware for system demonstrated includes the expanded and collimated beam from a 5 mW helium-neon laser for hologram reconstruction, an imaging lens for magnification of the real image field, and a video camera and digitizer providing 512-by-512 pixel resolution with 8-bit digitization. A mechanical stage is used to scan the hologram in three dimensional space, maintaining constant image magnification. A test droplet hologram is used for development and testing of the image processing algorithms

Mode coupling and multiquantum vibrational excitations in Feshbach-resonant positron annihilation in molecules

The dominant mechanism of low-energy positron annihilation in polyatomic molecules is through positron capture in vibrational Feshbach resonances (VFR). In this paper we investigate theoretically the effect of anharmonic terms in the vibrational Hamiltonian on the positron annihilation rates. Such interactions enable positron capture in VFRs associated with multiquantum vibrational excitations, leading to enhanced annihilation. Mode coupling can also lead to faster depopulation of VFRs, thereby reducing their contribution to the annihlation rates. To analyze this complex picture, we use coupled-cluster methods to calculate the anharmonic vibrational spectra and dipole transition amplitudes for chloroform, chloroform-$d_1$, 1,1-dichloroethylene, and methanol, and use these data to compute positron resonant annihilation rates for these molecules. Theoretical predictions are compared with the annihilation rates measured as a function of incident positron energy. The results demonstrate the importance of mode coupling in both enhancement and suppression of the VFR. There is also experimental evidence for the direct excitation of multimode VFR. Their contribution is analyzed using a statistical approach, with an outlook towards more accurate treatment of this phenomenon.Comment: 16 pages, 10 figures, submitted to Phys. Rev.

Nucleotide polymorphisms and an improved PCR-based mtDNA diagnostic for parthenogenetic root-knot nematodes (Meloidogyne spp.)

L'analyse de séquences de 2212 paires de bases provenant de six ADN mitochondriaux haplotypes très voisins de #Meloidogyne (Hugall et al., 1994) a permis de mettre en évidence douze sites nucléotidiens polymorphiques et une délétion. En dépit de cette faible diversité, il existe assez de sites différents d'enzymes de restriction parmi ces séquences pour fournir des tests de diagnostic. En utilisant un choix de ces sites, il a été mis au point un test diagnostique multiplex fondé sur l'amplification en chaîne par polymérase (PCR), test amplifiant simultanément deux étroites régions du génome mitochondrial, et digérant ensuite le produit par HinfI ou MnlI. Ce test diagnostique permet d'identifier les haplotypes - même en mélange - présents chez #M. arenaria, #M. incognita, #M. javanica et #M. hispanica, ainsi que chez #M. hapla et #M. chitwoodi. Ce nouveau test représente une amélioration par rapport aux tests PCR sur DNA mitochondrial appliqués aux #Meloidogyne en ce sens qu'il permet la discrimination entre un plus grand nombre d'espèces et de races (par ex. : races de #M. arenaria vis-à-vis de #M. javanica) ; de plus, des produits plus réduits étant amplifiés, ce test est de ce fait plus robuste. Ont été également mis au point des amorces amplifiant une région de 63 paires de bases en nombre variable de répétitions en tandem. Les schémas de zonation qui en résultent permettent de différencier les isolats à l'intérieur des haplotypes d'enzymes de restriction et peuvent être utilisés pour vérifier l'identité des isolats de nématodes maintenus en élevage. (Résumé d'auteur

Task analysis for error identification: Theory, method and validation

This paper presents the underlying theory of Task Analysis for Error Identification. The aim is to illustrate the development of a method that has been proposed for the evaluation of prototypical designs from the perspective of predicting human error. The paper presents the method applied to representative examples. The methodology is considered in terms of the various validation studies that have been conducted, and is discussed in the light of a specific case study