Eigenvalues of Hermite and Laguerre ensembles: large beta asymptotics

In this paper we examine the zero and first order eigenvalue fluctuations for the β-Hermite and β-Laguerre ensembles, using tridiagonal matrix models, in the limit as β→∞. We prove that the fluctuations are described by multivariate Gaussians of covariance O(1/β), centered at the roots of a corresponding Hermite (Laguerre) polynomial. The covariance matrix itself is expressed as combinations of Hermite or Laguerre polynomials respectively.We show that the approximations are of real value even for small β; we can use them to approximate the true functions even for the traditional β=1,2,4 values.     

Territories,corridors, and networks: A biological model for the premodern state

When depicted on maps as homogenous territorial wholes, ancient states are visually summarized as static entities in a way that conceals the highly fluid dynamics of polity formation, maintenance, and growth. Models derived from studies of animal behavior show that “territory” does not consist of an undifferentiated use of the landscape. Instead, the concept of territory can be parsed into a series of resource‐rich nodes linked by corridors of access, surrounded by unutilized regions and boundaries marked at points of competition. Ancient human groups also can be analyzed as having perceived and occupied landscapes through strategies of flexible networks in which nodes and corridors were surrounded by unutilized spaces around which boundaries were selectively identified and defended. This strategy is identifiable in human social groups at different levels of complexity ranging from hunter‐gatherers through ancient chiefdoms and states. © 2007 Wiley Periodicals, Inc. Complexity 12: 28–35, 2007     

α-Fe2O3-In2O3 mixed oxide nanoparticles synthesized under hydrothermal supercritical conditions

α-Fe₂O₃-In₂O₃ mixed oxide nanoparticles system has been synthesized by hydrothermal supercritical and postannealing route, starting with (1−x)Fe(NO₃)₃·9H₂O·xIn(NO₃)₃·5H₂O aqueous solution (x=0-1). X-ray diffraction and Mössbauer spectroscopy have been used to study the phase structure and substitutions in the nanosized samples. The concentration regions for the existence of the solid solutions in the α-Fe₂O₃-In₂O₃ nanoparticle system together with the solubility limits of In³⁺ ions in the hematite lattice and of Fe³⁺ ions in the cubic In₂O₃ structure have been evidenced. In general, the substitution level is considerably lower than the nominal concentration x. A justification of the processes leading to the formation of iron and indium phases in the investigated supercritical hydrothermal system has been given.     

Solvent-dependent host–guest complexation of two homologous merocyanines by a water-soluble calix[8]arene: Spectroscopic analysis and structural calculations

The sulfonated calixarene I₈C₁₂ acts as a host for homologous merocyanines Mc1 and Mc2 in organic solvents, exhibiting neither selectivity towards the guest dyes nor solvent dependence of the complexation equilibria. In water, on the contrary, only the lower homologue, Mc1, is solubilized in the presence of the calixarene. A combination of UV–visible and fluorescence spectroscopic and photophysical analysis and MD structural simulation of the calixarene-dye complexes was employed to account for the observations, and suggests that a radical change in the complexation mode occurs upon moving from an organic to an aqueous environment.     

Structure of the asparagine-linked sugar chains of porcine kidney and human urine cerebroside sulfate activator protein

The specific sugar residues and their linkages in the oligosaccharides from pig kidney and human urine cerebroside sulfate activator proteins (saposin B), although previously hypothesized, have been unambiguously characterized. Exhaustive sequential exoglycosidase digestion of the trimethyl-p-aminophenyl derivatives, followed by either matrix-assisted laser desorption/ionization and/or mass spectrometry, was used to define the residues and their linkages. The oligosaccharides were enzymatically released from the proteins by treatment with peptidyl-N-glycosidase F and separated from the proteins by reversed-phase high-performance liquid chromatography (HPLC). Reducing termini were converted to the trimethyl-p-aminophenyl derivative and the samples were further purified by normal-phase HPLC. The derivatized carbohydrates were then treated sequentially with a series of exoglycosidases of defined specificity, and the products of each digestion were examined by mass spectrometry. The pentasaccharides from pig kidney and human urine protein were shown to be of the asparagine-linked complex type composed of mannose-alpha 1-6-mannose-beta 1-4-N-acetylglucosamine-N-acetylglucosamine(alpha 1-6-fucose). This highly degraded structure probably represents the final product of intra-lysosomal exoglycosidase digestion. Oligosaccharide sequencing by specific exoglycosidase degradation coupled with mass spectrometry is more rapid than conventional oligosaccharide sequencing. The procedures developed will be useful for sequencing other oligosaccharides including those from other members of the lipid-binding protein class to which cerebroside sulfate activator belongs. (c) 2000 John Wiley & Sons, Ltd.     

Pyranoxanthones from Calophyllum Inophyllum

Phytochemical investigation of the stem bark of Calophyllum inophyllum resulted in the isolation of a new dipyrenoxanthone, calophinone ( 1 ), together with four related xanthones ( 2–5 ). Identification of the isolated compounds was achieved through intensive studies of their spectral data, especially 2D NMR.     

Lithiation and electrophilic substitution of 8-chlorodibenz[b,f][1,4]-oxazepine-10-tert-butylcarbamate: The preparation of novel fused heterocyclic derivatives of 8-chlorodibenzoxazepine

Lithiation of 8-chlorodibenz[b,f][1,4]oxazepine-10-tert-butylcarbamate ( 1 ) is described. Electrophilic substitution of the resulting N-Boc dibenzoxazepine α- lithioamine 2 with ketones, aldehydes, nitriles, iso-cyanates and imines, followed by an in-situ cyclization, gave fused carbamates 5–26 , fused 2H-imidazol-2-ones 27–29 , fused hydantoins 30–32 , and fused ureas 33–35 , respectively, in 11–66% yield.     

Colourants and opacifiers in seventh and eighth century glass investigated by spectroscopic techniques

Glass fragments dating from the seventh and eighth century AD were excavated in the Crypta Balbi in Rome. They were studied to detect agents involved in colour development and opacification. Reflectance spectra recorded on powdered samples revealed the contribution of Fe(II), Fe(III), Mn(III), Cu(II), and Co(II) ions in determining colour hues. The effect of the Mn/Fe atomic ratio on glass colour is discussed. It is apparent that medieval glassmakers in Italy could obtain a wide range of colours by exploiting the presence of iron and manganese as contaminants of sand and flux and controlling the amount of oxygen let into the furnace. X-ray diffraction and scanning electron microscopy coupled with energy-dispersive X-ray analysis were used to study opaque fragments. The presence of calcium antimonate was detected in white, blue, and blue-green fragments, and elemental copper was detected in a red glass.