Monomials, binomials and Riemann–Roch

The Riemann–Roch theorem on a graph G is related to Alexander duality in combinatorial commutative algebra. We study the lattice ideal given by chip firing on G and the initial ideal whose standard monomials are the G-parking functions. When G is a saturated graph, these ideals are generic and the Scarf complex is a minimal free resolution. Otherwise, syzygies are obtained by degeneration. We also develop a self-contained Riemann–Roch theory for Artinian monomial ideals.     

Binding of the ionic liquid cation 1-alkyl-3-methylimidazolium to p-tetranitrocalix[4]arene probed by fluorescent indicator displacement

Acridine orange (AO) was used as a fluorescent probe molecule to study the encapsulation of an alkylimidazolium cation from a water-soluble ionic liquid (IL) within two cavitand species, p-tetranitrocalix[4]arene (1) and calix[4]resorcinarene (2), both in alkaline aqueous media. The addition of IL to the preformed [1·AO] adduct resulted in significantly increased fluorescence due to the expulsion of AO from the inclusion complex to the aqueous phase by competitive recognition of the 1-alkyl-3-methylimidazolium cation ([C(n)mim](+), n = 4 and 6) by 1. Conversely, the fluorescence signal dropped upon the addition of IL to the [2·AO] host-guest complex due to unfavorable binding between [C(n)mim](+) and 2. The formation of these postulated adducts is corroborated using ab initio calculations, which also provide evidence for the location of [bmim](+) at the lower external rim of [2·AO], providing an explanation for the observed luminescence quenching in the latter case. These results point to a number of different paths for exploration, ranging from the fluorescence monitoring of IL contamination in groundwater to the "daisy chaining" of macrocyles toward supramolecular ionic networks. They also broadly encourage the exploration of ILs in host-guest-based optical and mass spectrometric sensory systems.     

Crystal and Molecular Structure Studies of 1′-Benzyl-8-(4-fluorobenzyl)-8-azaspiro[bicyclo-[3.2.1]octane-3,4′-imidazolodine]-2′,5′-dione

Abstract  

The title compound, C₂₃H₂₃FN₃O₂ has been synthesized and the structure was investigated by X-ray diffraction studies. The compound crystallizes in the triclinic crystal class in the space group P[`1]P\overline{1} with cell parameters a = 9.345(2) ?, b = 10.940(3) ?, c = 11.986(4) ?, α = 72.349(6)°, β = 68.106(18)°, γ = 66.867(5)°, Z = 2 and V = 1027.8(5) ?³. The hydantoin ring adopts a planar conformation and is affected by the π conjugation. The pyrrolidine and piperidine rings in the bicyclo octane moiety adopt envelope and chair conformations respectively. The structure exhibits both inter and intramolecular hydrogen bonds of the type N–H···O, C–H···O and C–H···N. One of the oxygen atoms attached to the hydantoin ring simultaneously accepts two hydrogen bonds to form a three centered hydrogen bonding pattern.     

Effect of orientation on the reversible discharge capacity of electrodeposited Cu2O coatings as lithium-ion battery anodes

Journal of Solid State Electrochemistry - Electrodeposited Cu2O coatings with 111 out-of-plane orientation were found to have the lowest reversible discharge capacity as anodes for Li-ion cells....     

Analysis of isotopic radium in thorium mill effluents

A simple and rapid method has been developed for the determination of isotopic radium, based on gamma-ray spectrometry. (228)Ra and (224)Ra are assayed by measuring the intensities of the photo-peaks in the 0.94 and the 2.62 MeV regions of the gamma-spectrum. The interference in these measurements, arising from the presence of the (226)Ra(210)Pb chain in the sample, is obviated by the almost complete expulsion of (222)Rn from the system. The precision of the method is +/-2% and +/-3 % in the determination of (228)Ra and (224)Ra respectively, the absolute sensitivities being 2 and 0.5 nCi. The method has been applied to evaluate the distribution of these isotopes in the various products of the Indian Rare-Earths Factory, Alwaye.     

Adsorption of carbon monoxide and oxygen on transition metal surfaces: A comparative study of the results from electron spectroscopy and theoretical calculations

Results of investigations on the adsorption of CO andO ₂ on transition metal surfaces by employinguv and x-ray photoelectron spectroscopy and electron energy loss spectroscopy (eels) are presented. Results of molecular orbital calculations on adsorbed CO and O₂ are also discussed. Some of the interesting aspects discussed are, satellites in the O(ls) region due to adsorbed CO, vibrationaleels of adsorbed O₂ and dissociation energy profiles of adsorbed O₂ on clean surfaces as well as surfaces covered with potassium or presorbed atomic oxygen. Contribution No 245 from the Solid State and Structural Chemistry Unit.     

CURE CHARACTERISTICS OF HYDROXYL TERMINATED POLYBUTADIENE PREPOLYMER WITH BLOCKED TOLUENE DIISOCYANATE-Ⅱ

Cure characteristics of hydroxyl terminated polybutadiene (HTPB) prepolymer with avariety of blocked toluene diisocyanate (TDI) in the presence of triethylamine (TEA) andchloroacetic acid catalyst are reported. Phenol, thiophenol, p-chloropheno1, p-nitrophenol,p-cresol, resorcinol, naphthols, caprolactam and butylated-hydroxytoluene were used as blockingagents. Viscosity measurements have been carried out using a mixture of HTPB and blocked TDIin cyclohexanone in the presence of the catalysts at 50℃ and 60℃ using Haake rotational vis-cometer. Viscosity measurements have also been carried out with 50% solids such as ammonium sulphate along with HTPB and TDI adduct.     

Neighborhood contraction in graphs

Let G be a graph and v be any vertex of G. Then the neighborhood contracted graphG_v of G, with respect to the vertex v, is the graph with vertex set V ? N(v), where two vertices u,w ∈ V ? N(v) are adjacent in G_v if either w = v and u is adjacent to any vertex of N(v) in G or u,w ? N[v] and u,w are adjacent in G. The properties of the neighborhood contracted graphs are discussed in this paper. The neighborhood contraction in some special class of graphs, the domination in a graph and the neighborhood contracted graphs are discussed in the paper.