Generalized Catalan Numbers, Weyl Groups and Arrangements of Hyperplanes

For an irreducible, crystallographic root system in a Euclideanspace V and a positive integer m, the arrangement of hyperplanesin V given by the affine equations (, x) = k, for and k =0, 1, ..., m, is denoted here by . The characteristic polynomial of is related in the paper to that of the Coxeter arrangement A(corresponding to m = 0), and the number of regions into whichthe fundamental chamber of A is dissected by the hyperplanesof is deduced to be equal to the product , where e₁,e₂, ..., e_l are the exponents of and h is the Coxeter number.A similar formula for the number of bounded regions follows.Applications to the enumeration of antichains in the root posetof are included. 2000 Mathematics Subject Classification 20F55(primary), 05A15, 52C35 (secondary).     

Adsorption of cobalt ions on the "electrolytic solution/gamma-alumina" interface studied by diffuse reflectance spectroscopy (DRS)

Diffuse reflectance spectroscopy was used for the first time to investigate the adsorption of the [Co(H2O)6]2+ ions on the interface developed between the surface of the gamma-alumina particles and the electrolytic aqueous solutions used for the preparation of cobalt-supported gamma-alumina catalysts by equilibrium deposition filtration. The formation of inner-sphere Co(II) surface complexes in which Co(II) is in octahedral symmetry was confirmed. A deconvolution peak centered at approximately 585 nm was attributed to the exchange of one aqua ligand with one AlxOHy (x = 1, 2, or 3; y = 0 or 1) negatively charged surface group resulting in the formation of mononuclear monosubstituted inner-sphere Co(II) complexes at a Co(II) surface concentration equal to 0.02 micromol of Co(II)/m2. It was inferred that as the surface Co(II) concentration increases the formation of disubstituted and/or trisubstituted surface complexes is favored with respect to the formation of monosubstituted Co(II) surface complexes. A deconvolution peak centered at approximately 640 nm was attributed to the exchange of one or more aqua ligands with bridging hydroxo ligands (Co-O-H). The relative magnitude of this peak increases with the Co(II) surface concentration, reflecting the increasing formation of binuclear, oligonuclear, and multinuclear Co(II) surface complexes and then the formation of the Co(II) surface precipitate.     

Lanthanide transport in stabilized zirconias: interrelation between ionic radius and diffusion coefficient

The diffusion of all stable lanthanides was measured both in calcia stabilized zirconia (CSZ) and in yttria stabilized zirconia (YSZ) in the temperature range between 1,286 and 1,600 degrees C. The lanthanide diffusion coefficients obtained increase with increasing ionic radius. The experimental activation enthalpy of diffusion is near 6 eV for CSZ and between 4 and 5 eV for YSZ and is not strongly affected by the type of lanthanide. The results were correlated with defect energy calculations of the lanthanide diffusion enthalpy using the Mott-Littleton approach. An association enthalpy of cation vacancies with oxygen vacancies of about 1 eV (96 kJ/mol) was deduced in the case of CSZ, while there is no association in the case of YSZ. Furthermore, the change in diffusion coefficients can be correlated to the interaction parameter for the interaction between the lanthanide oxide with zirconia: The higher the interaction parameter, the higher the lanthanide diffusion coefficient.     

Preparation of hydroxyapatite via microemulsion route

Hydroxyapatite (HAp) was prepared using a microemulsion route in combination with the pH-shock wave method. The samples as received consisted of amorphous aggregated particles, which had remarkable mesoporosity with a narrow pore size distribution. After being heated at 650 degrees C, the A-type carbonate hydroxyapatite was crystallized at 635 degrees C in particles of similar size (40--120 nm) with no internal porosity. At a higher temperature (900 degrees C) a sintering process took place, resulting in network of a larger particles, consisting of HAp and beta-tricalcium phosphate (beta-TCP). The crystallization of HAp occurs at 635 degrees C with an activation energy of 62.7--72.2 kcalmol(-1).     

Wide compositional and structural diversity in the system Tl/Bi/P/Q (Q=S, Se) and observation of vicinal P-Tl J coupling in the solid state

The compounds alpha-TlBiP2Se6 (I), beta-TlBiP2Se6 (II), TlBiP2S6 (III), Tl3Bi3(PS4)4 (IV), TlBiP2S7 (V), and Tl3Bi(PS4)2 (VI) were synthesized, and the structures of I-V were determined by single-crystal X-ray diffraction analysis. The structure of I features infinite chains. Those of compounds II, III, and V are layered. The structure of IV features a three-dimensional framework. Tl4Bi2(PS4)2(P2S6) (VII) was also prepared for comparison to the title compounds. The band gaps of each compound are 1.23, 1.27, 1.81, 1.88, 2.06, 1.98, and 1.97 eV for I-VII, respectively. Compounds I, III, IV, and VI melt congruently at 544, 595, 495, and 563 degrees C, respectively, and compounds II, V, and VII melt incongruently at 544, 509, and 600 degrees C, respectively. Solid-state 31P NMR spectroscopy of the reported compounds demonstrates chemical shifts and chemical shift anisotropies in line with related chalcophosphate materials. Evidence for two-bond P-Tl J coupling was observed in 31P NMR spectra (J=481-1781 Hz), and to the best of our knowledge, this is the first example of two-bond P-Tl J coupling and the first example of P-Tl coupling in the solid state. It was possible to assign chemical shifts of inequivalent 31P atoms from the same [PxQy]z- anion type based on different modes of metal ion coordination to the chalcogen. These assignments provide information about the vicinal metal ion contribution to the 31P chemical shift.     

Self-induced transparency in diblock copolymer dispersions

We report on the versatile effect of weak red laser light impinging on diblock copolymer [poly(isoprene-b-styrene)] dispersions in two selective solvents for each block. In the strongly scattering but transparent micellar solutions in hexane (a good solvent for polyisoprene), higher refractive index copolymer-rich fibers were formed. In the turbid dispersions of the same copolymer in ethyl acetate (a good solvent for polystyrene), the effect of self-induced transparency was observed. A two-step patterning mechanism caused the generation of a transparent microchannel, increasing light transmission. The analogy between the current effect and that observed in homopolymer polyisoprene solutions in different solvents is discussed toward an understanding of the unanticipated light-soft-matter interaction.     

Signature files: An integrated access method for text and attributes,suitable for optical disk storage

We design and analyze integrated ways of applying the signature file approach for text and attributes simultaneously. In traditional signature file methods, the records are stored sequentially in the main file; for every record, a hash-coded abstraction of it (record signature) is created and stored in the signature file (usually, sequentially). To resolve a query, the signature file is scanned; the signatures retrieved correspond to all the qualifying records, plus some false drops.Here, we extend some signature file methods, namely superimposed coding and disjoint coding, to handle text and attributes. We develop a mathematical model and derive formulas for the optimal choice of parameters. The proposed methods achieve significant performance improvements, because they can take advantage of the skewed distribution of the queries. Depending on the query frequencies, the false drop probability can be reduced 40–45 times ( 97% savings), for the same overhead.Also with the University of Maryland Institute for Advanced Computer Studies (U.M.I.A.C.S.). This research was sponsored partially by the National Science Foundation under the grant DCR-86-16833.     

Changes of gross gamma-ray intensity in a submarine spring system due to a distant earthquake event on 30th of March 2019 at Itea,Greece

Journal of Radioanalytical and Nuclear Chemistry - A medium resolution underwater in-situ gamma-ray spectrometer (GeoMAREA) was deployed in the submarine spring (Kiveri) for continuous monitoring...