Weak convergence of random <Emphasis Type="Bold">p</Emphasis>-mappings and the exploration process of inhomogeneous continuum random trees

We study the asymptotics of the p-mapping model of random mappings on [n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of “attracting points” to emerge.Research supported by NSF Grant DMS-0203062.Research supported by NSF Grant DMS-0071468.     

Causal Algebras on Chain Event Graphs with Informed Missingness for System Failure

Graph-based causal inference has recently been successfully applied to explore system reliability and to predict failures in order to improve systems. One popular causal analysis following Pearl and Spirtes et al. to study causal relationships embedded in a system is to use a Bayesian network (BN). However, certain causal constructions that are particularly pertinent to the study of reliability are difficult to express fully through a BN. Our recent work demonstrated the flexibility of using a Chain Event Graph (CEG) instead to capture causal reasoning embedded within engineers’ reports. We demonstrated that an event tree rather than a BN could provide an alternative framework that could capture most of the causal concepts needed within this domain. In particular, a causal calculus for a specific type of intervention, called a remedial intervention, was devised on this tree-like graph. In this paper, we extend the use of this framework to show that not only remedial maintenance interventions but also interventions associated with routine maintenance can be well-defined using this alternative class of graphical model. We also show that the complexity in making inference about the potential relationships between causes and failures in a missing data situation in the domain of system reliability can be elegantly addressed using this new methodology. Causal modelling using a CEG is illustrated through examples drawn from the study of reliability of an energy distribution network.     

The Arveson Extension Theorem and coanalytic models

We develop techniques which allow one to describe in simple terms the set of operators on Hilbert space of the form M^{* ()} |M, where M is multiplication by z on a Hilbert space of analytic functions satisfying certain technical assumptions, M^{* ()} is the direct sum of a countably infinite number of copies of M^*, andM is invariant for M^{* ()}. One of the main ingredients in our technique is the Arveson Extension Theorem and this paper illustrates the great power and tractability of that theorem in a concrete setting.Research partially supported by NSF grant MCS 81-02518     

Optical properties of Cu nanocomposite glass obtained via CuO and SnO co-doping

Prospective applications of plasmonic nanocomposites in photonic and optoelectronic devices demand innovative means of material syntheses, as well as a comprehensive understanding of the influence of material composition and processing on resulting properties. In this work, it is shown that a phosphate glass matrix prepared with stoichiometric amounts of CuO and SnO dopants by the melting technique may well be effective for the precipitation of Cu nanoparticles (NPs) upon heat treatment (HT). Optical absorption and photoluminescence (PL) spectroscopy, including emission decay dynamics, are employed in the characterization of the melt-quenched glass, and for investigating the influence of HT on material optical properties. The as-prepared material appeared highly luminescent; the data suggests contributions from both twofold-coordinated tin centers and Cu⁺ ions to light emission. The PL depends strongly on excitation wavelength; e.g. excitation at 260 nm shows a blue–white emission for which a significant contribution from tin is indicated, whereas excitation at 360 nm produces an orange emission in association with Cu⁺ ions. Thermal processing results in the chemical reduction of ionic copper via Sn²⁺ ultimately producing Cu NPs in the matrix, as evidenced by the appearance of the surface plasmon resonance around 574 nm. As a result, Cu⁺ PL decreases and the emission band shows a dip due to reabsorption by Cu NPs in resonance.     

The enumerative geometry of surfaces and modular forms

Let be a surface, and let be a holomorphic curve in representing a primitive homology class. We count the number of curves of geometric genus with nodes passing through generic points in in the linear system for any and satisfying .

When , this coincides with the enumerative problem studied by Yau and Zaslow who obtained a conjectural generating function for the numbers. Recently, Göttsche has generalized their conjecture to arbitrary in terms of quasi-modular forms. We prove these formulas using Gromov-Witten invariants for families, a degeneration argument, and an obstruction bundle computation. Our methods also apply to blown up at 9 points where we show that the ordinary Gromov-Witten invariants of genus constrained to points are also given in terms of quasi-modular forms.     

PROMETHEE: an extension through fuzzy mathematical programming

PROMETHEE multi-criteria methods are based on fuzzy evaluations of the differences between pairs of alternatives for each criterion. PROMETHEE II associates a crisp number to each action. PROMETHEE III associates an interval to each action and two actions are considered indifferent when they are very close to each other. PROMETHEE V applies Integer Linear Programming in order to select the subset of alternatives that maximizes the sum of PROMETHEE II scorings, subject to a set of constraints. In order to make the model more realistic, this paper proposes that some constraints are soft and some coefficients are estimated by fuzzy numbers. Fuzzy Integer Linear Programming is applied, using the PROMETHEE III scorings as objective function coefficients, in order to find the subsets of non-outranked alternatives that best satisfy the soft constraints. The new model is more realistic and fits better the fuzzy philosophy of PROMETHEE. The method is illustrated with an example.     

Simultaneous spectrofluorimetric determination of europium, dysprosium, gadolinium and terbium using chemometric methods

A spectrofluorimetric method for the simultaneous determination of dysprosium, europium, gadolinium and terbium in ternary and quaternary mixtures by the use of pyridine-2,6-dicarboxylic acid as a chelating agent was developed. The influence of chemical variables affecting the analytical reaction was evaluated. A partial least-squares procedure and PC Quant software were used to assess data obtained from a variable number of calibration solutions and wavelengths. The ensuing method was validated by applying it to the analysis of synthetic ternary (Eu-Dy-Tb) and quaternary mixtures (Eu-Dy-Gd-Tb) over the concentration ranges 60-550 mug Eu l(-1), 30-400 mug Dy l(-1) and 30-400 mug Tb l(-1) in the former, and 20-220 mug Eu l(-1), 20-235 mug Dy l(-1), 25-230 mug Gd l(-1) and 75-230 mug Tb l(-1) in the latter. The results obtained by using the two quantitation procedures are compared. The relative errors in the determinations were less than 8% in most cases.     

Dynamics of Atomic and Molecular Hydrogen Elimination from Hydrocarbons at VUV Excitation

Elimination of atomic hydrogen (H) and molecular hydrogen (H₂) are important elementary chemical processes in photochemistry and combustion chemistry. Recently, unique and sensitive detection techniques for atomic and molecular hydrogen detection were developed in our laboratory. Using the advanced molecular beam methods, we have studied the photodissociation of a few typical hydrocarbons at 157 nm excitation, especially their atomic and molecular hydrogen elimination processes. In this report, we will briefly describe the results from photodissociation of propane, ethylene, propyne and methanol at 157 nm excitation. These molecules represent different classes of hydrocarbons such as alkane, alkene, alkyne and alcohol. Through careful studies on differently deuterated compounds, clear pictures of selective atomic and molecular hydrogen elimination processes can be constructed for all of the above compounds. These results will help us to understand the dissociation dynamics of the small hydrocarbon molecules.     

Determination of rotenone residues in raw honey by solid-phase extraction and high-performance liquid chromatography

A method for determining residues of the insecticide rotenone in raw-honey by high-performance liquid chromatography (HPLC) is described. To extract the residues, organic solvents such as ethyl acetate, n-hexane/dichloromethane and solid-phase extraction with octadecylsilane cartridges or Florisil packed columns were tested. Determination was carried out by reversed-phase HPLC using acetonitrile-buffer phosphate (pH 7) (60:40, v/v) as mobile phase and detection at 210 nm. Although the data showed that the two extraction methods were able to isolate the pesticide residues, the extraction on octadecylsilane cartridges was preferred due to its simplicity and higher recovery. Recoveries depended strongly on the fortification level for the two extraction procedures. Practical determination limits of 0.015 mg/kg were obtained. In the analysis of honeys, from beehives treated with rotenone at therapeutical doses for 1 month, residual amounts below 0.2 mg/kg were found.     

Temperature Dependence of the Solubility of Acetaminophen in Propylene Glycol + Ethanol Mixtures

The thermodynamic functions Gibbs energy, enthalpy and entropy of solution, mixing and solvation of acetaminophen in propylene glycol (PG) + ethanol (EtOH) cosolvent mixtures were evaluated from solubility data measured at several temperatures, using the van't Hoff and Gibbs equations. The solubility was greater at 50% m/m of PG at 20.0^C, while it was greater at 80% of PG at 40.0 ^C where m/m refers to mass percent. The solvation of this drug is appreciably greater in the mixtures than in the pure solvents. By means of an enthalpy–entropy compensation analysis, complex behavior was found for the solution. From 0 up to 20% of PG and from 60 up to 100% of PG the solution process is enthalpy driven, whereas from 20 up to 60% of PG it is entropy driven. These facts can be explained in terms of a decrease in the energy required for cavity formation in the solvent for mixtures containing 20–60% of PG.