Asymptotics for Euclidean minimal spanning trees on random points

Summary Asymptotic results for the Euclidean minimal spanning tree onn random vertices inR ^d can be obtained from consideration of a limiting infinite forest whose vertices form a Poisson process in allR ^d. In particular we prove a conjecture of Robert Bland: the sum of thed'th powers of the edge-lengths of the minimal spanning tree of a random sample ofn points from the uniform distribution in the unit cube ofR ^d tends to a constant asn.Whether the limit forest is in fact a single tree is a hard open problem, relating to continuum percolation.Research supported by N.S.F. Grants MCS87-11426 and MCS 90-01710Research supported in part by N.S.F. Grant DMS88-12868, A.F.O.S.R. Grant 89-0301, ARO Grant DAAL03-89-G-0092 and NSA Grant MDA-904-H-2034     

The zeolate ligand; zeolite encapsulated semiconductor nanomaterials

Consolidation of the results of structural, spectroscopic and kinetic studies of a range of intrazeolite guests and their reactions have led to the development of the “crown ether-zeolite ligand analogy” and the concept of the “zeolate” as a macrospheroidal or macrocylindrical multidentate anionic ligand. This view of a zeolite cavity or channel as a collection of interconnected aluminosilicate crown ether-like building blocks, permits a coordination chemistry approach to the understanding of metal-ligand bonding (capping, anchoring, complexing, stabilizing and structure-directing phenomena) in a variety of zeolite guest-host inclusion systems. In this paper we focus attention on the role that the zeolate ligand plays in the organization of semiconductor precursors and their assembly to semiconductor nanoclusters with particular reference to II-VI nanomaterials.     

Flame spectroscopy of TiO: Radiative lifetimes and oscillator strengths of the α (C3Δ-X3Δ) system

Lifetimes of the C³Δ state of TiO have been measured for vibrational levels v′ = 0 to 2 from the decay of photoluminescence excited in a chemiluminescent flame by a short-pulsed (5 nsec) tunable dye laser. Radiative lifetimes of τ_v′=0 = 37 ± 9 nsec, τ_v′=1 = 29 ± 7 nsec, τ_v′=2 = 28 ± 7 nsec were obtained and were used to estimate oscillator strengths which were found to be in good agreement with earlier values based on intensity measurements.     

Two-dimensional supramolecular assembly of phenylmercury(II) and cadmium(II) complexes with a tridentate thiohydrazone NNS donor ligand: Synthesis,coordination behavior and crystal structure

The reaction of phenylmercury(II) acetate and cadmium(II) acetate with a refluxed solution of diacetylmonoxime and morpholine N-thiohydrazide formed a novel phenylmercury(II) complex, [PhHg(Hdammthiol)] (1) and a cadmium(II) complex, [Cd(Hdammthiol)₂] (2), respectively (where H₂dammthiol is the thiol form of diacetylmonoximemorpholine N-thiohydrazone (Hdammth) formed by the condensation of diacetylmonoxime and morpholine N-thiohydrazide in the presence of phenylmercury(II) and cadmium(II) ions). The complexes were characterised by elemental analyses and spectral data (electronic, infrared and ¹H NMR) and also by X-ray crystal structure analysis. The X-ray crystallography shows that the phenylmercury(II) complex attained a tricoordinated distorted T-shaped structure, while the cadmium(II) complex attained a trapezoidal bipyramidal geometry. The phenylmercury(II) complex forms a two-dimensional sheet via C–H?O and O–H?N hydrogen bonding and also forms a two-dimensional supramolecular dimer, having C–H?π synthons. Intermolecular C–H?O and O–H?O hydrogen bonding of the cadmium(II) complex forms a two-dimensional supramolecular sheet along the bc plane and posses an impressively short intermolecular C(sp³)?O(sp³) contact.     

Infrared spectrum of benzene in bromine and carbon tetrachloride solutions

The benzene—bromine complex at room temperature has been re-studied by infrared with bromine in excess of benzene. Solutions of 0.225 M benzene in bromine—carbon tetrachloride mixtures were studied. Under this condition, the spectral changes of measurable benzene absorption bands were observed more clearly than previously. The out-of-plane vibrations of benzene were observed to shift to higher frequencies. The equilibrium constant was found to be 0.11 ? mole^?1. The accord with the equilibrium constant derived from benzene rich systems supports the concept of a specific interaction. A C_6V symmetry is favoured for the geometry of the complex.     

Toward understanding the ionization of biomarkers from micrometer particles by bio-aerosol mass spectrometry

The appearance of informative signals in the mass spectra of laser-ablated bio-aerosol particles depends on the effective ionization probabilities (EIP) of individual components during the laser ionization process. This study investigates how bio-aerosol chemical composition governs the EIP values of specific components and the overall features of the spectra from the bio-aerosol mass spectrometry (BAMS). EIP values were determined for a series of amino acid, dipicolinic acid, and peptide aerosol particles to determine what chemical features aid in ionization. The spectra of individual amino acids and dipicolinic acid, as well as mixtures, were examined for extent of fragmentation and the presence of molecular ion dimers, which are indicative of ionization conditions. Standard mixtures yielded information with respect to the significance of secondary ion plume reactions on observed spectra. A greater understanding of how these parameters affect EIP and spectra characteristics of bio-aerosols will aid in the intelligent selection of viable future biomarkers for the identification of bio-terrorism agents.     

The structural and spectroscopic characterisation of three actinyl complexes with coordinated and uncoordinated perrhenate: [UO2(ReO4)2(TPPO)3], [[(UO2)(TPPO)3]2(mu2-O2)][ReO4]2 and [NpO2(TPPO)4][ReO4

The first structural characterization of an actinide complex with coordinated perrhenate is reported, [UO2(ReO4)2(TPPO)3] (1). In this [UO2]2+ complex two [ReO4]- anions and three TPPO (triphenylphosphine oxide) P=O donor ligands are coordinated in the equatorial plane in a cisoid arrangement. This bonding arrangement, and apparent strain observed in the equatorially bonded ligands, is attributed to the solid state packing in adjacent molecules in which hydrophobic TPPO ligands form an effective "shell" around a hydrophilic core of two UO2(ReO4)2 moieties. Solid state vibrational spectroscopy (infrared and Raman), 31P CP MAS NMR and elemental analysis are also consistent with the formula of 1. Solution state vibrational spectroscopy and 31P NMR measurements in EtOH indicate the lability of the TPPO and [ReO4]- groups. The photolytic generation of peroxide in EtOH solutions of 1 leads to the formation of trace quantities of [[(UO2)(TPPO)3]2(mu2-O2)][ReO4]2, 2, in which the coordinated [ReO4]- groups of 1 have been displaced by bridging O2(2-), derived from atmospheric O2. Finally, attempts to synthesise a [NpO2]+ analogue of have resulted only in the formation of [NpO2(TPPO)4][ReO4], 3, in which [ReO4]- acts solely as a counter anion. From these results it can be concluded that [ReO4]- will bond to [UO2]2+, but will be readily displaced by a more strongly coordinating ligand (e.g. peroxide) and will not coordinate to an actinyl cation with a lower charge, [NpO2]+, under the same reaction conditions.     

Rapid conversion of cellulose to 5-hydroxymethylfurfural using single and combined metal chloride catalysts in ionic liquid

Direct conversion of cellulose into 5-hydroxymethylfurfural(HMF) was performed by using single or combined metal chloride catalysts in 1-ethyl-3-methylimidazolium chloride(Cl) ionic liquid.Our study demonstrated formation of 2-furyl hydroxymethyl ketone(FHMK),and furfural(FF) simultaneously with the formation of HMF.Various reaction parameters were addressed to optimize yields of furan derivatives produced from cellulose by varying reaction temperature,time,and the type of metal chloride catalyst.Catalytic reaction by using FeCl3 resulted in 59.9% total yield of furan derivatives(HMF,FHMK,and FF) from cellulose.CrCl3 was the most effective catalyst for selective conversion of cellulose into HMF(35.6%) with less concentrations of FHMK,and FF.Improving the yields of furans produced from cellulose could be achieved via reactions catalyzed by different combinations of two metal chlorides.Further optimization was carried out to produce total furans yield 75.9% by using FeCl3/CuCl2 combination.CrCl3/CuCl2 was the most selective combination to convert cellulose into HMF(39.9%) with total yield(63.8%) of furans produced from the reaction.The temperature and time of the catalytic reaction played an important role in cellulose conversion,and the yields of products.Increasing the reaction temperature could enhance the cellulose conversion and HMF yield for short reaction time intervals(5~20 min).