Complete partitions of graphs

A complete partition of a graph G is a partition of its vertex set in which any two distinct classes are connected by an edge. Let cp(G) denote the maximum number of classes in a complete partition of G. This measure was defined in 1969 by Gupta [19], and is known to be NP-hard to compute for several classes of graphs. We obtain essentially tight lower and upper bounds on the approximability of this problem. We show that there is a randomized polynomial-time algorithm that given a graph G with n vertices, produces a complete partition of size Ω(cp(G)/√lgn). This algorithm can be derandomized. We show that the upper bound is essentially tight: there is a constant C > 1, such that if there is a randomized polynomial-time algorithm that for all large n, when given a graph G with n vertices produces a complete partition into at least C·cp(G)/√lgn classes, then NP ⊆ RTime(n ^{O(lg lg n)}). The problem of finding a complete partition of a graph is thus the first natural problem whose approximation threshold has been determined to be of the form Θ((lgn) ^c ) for some constant c strictly between 0 and 1. The work reported here is a merger of the results reported in [30] and [21].     

Triplet-sensitized photolysis of alkoxycarbonyl azides in solution and matrices

Photolysis of azides 1–4 in methanol, which have a built-in intramolecular triplet sensitizer, yields mainly carbamates 5–8. Laser flash photolysis of 1–4 shows formation of their triplet-excited ketone, which decays by intramolecular energy transfer to form triplet nitrenes 1n–4n. Irradiating 1–3 in matrices yields isocyanic acid, whereas photolysis of 4 forms isocyanate 4i. The depletion rate of the azide bands between 2100 and 2200 cm^?1 is different than the rate of formation for the isocyanic acid bands at ～2265 cm^?1; thus, the formation of isocyanic acid is a stepwise process. Irradiating 1 in matrices produces an absorption band due to nitrene 1n (λ_max ～ 343 nm), which is depleted upon further irradiation, whereas the absorption due to 4-acetyl benzaldehyde (λ_max ～ 280 nm) increases with prolonged irradiation. We propose that formation of isocyanic acid in matrices must come from secondary photolysis of nitrenes 1n–3n. This mechanism is further supported by calculation, which show that the estimated transition state for 1n–4n to fall apart to yield alkoxy and cyanato radicals is only ～34 kcal/mol above the ground state of the triplet nitrenes and thus the cleavage can take place photochemically. Thus, nitrenes 1n–4n can be formed selectively, but these intermediates are highly photosensitive and undergo secondary photolysis in matrices.     

Average distance in graphs and eigenvalues

Brendan McKay gave the following formula relating the average distance between pairs of vertices in a tree T and the eigenvalues of its Laplacian:

     

Synthesis of oxalate doped polyaniline and its corrosion protection performance

It is known that dopants present in polyaniline (PANI) play an important role in corrosion protection of mild steel since the dopant ions form a secondary layer with iron. Since oxalate ions form a stable iron oxalate layer on mild steel, a study has been made on the corrosion protection performance of steel by vinyl coating containing oxalate doped PANI in acid and neutral media. Electrochemical impedance spectroscopy (EIS) studies have shown that the oxalate doped PANI is able to protect mild steel in sodium chloride solution since the impedance values are maintained at 10¹⁰ Ω cm² even after 100 days of exposure.     

Some studies on the extraction of plutonium from phosphate containing nitric acid solutions using DBDECMP as extractant

Extraction studies have been carried out to explore the feasibility of separation of Pu(IV) from phosphate containing analytical wastes generated in the laboratory. Distribution data on the extraction of Pu(IV) from DBDECMP (di-butyl, N,N-diethylcarbamoyl methyl phosphonate) in xylene from an aqueous nitric acid and its mixture with sulfuric as well as with sulfuric and phosphoric acids were obtained. Based on the data obtained, the conditions for the recovery of plutonium from such waste solutions are suggested.     

Toxicity assessment of nickel using Aspergillus niger and its removal from an industrial effluent

Chemical analysis of electroplating effluent revealed the presence of very high concentrations of nickel (393 ppm) in the effluent. Bioassay was carried out to test the toxicity of nickel chloride to Aspergillus niger. In contrast to 50% conidial inhibition at 1.7 mM nickel, hyphal extension was affected even at a lower concentration (0.4 mM), suggesting that hyphae are more sensitive than conidia to nickel. An increase in nickel concentration resulted in a proportionate decrease in the hyphal extension. Nickel (II)-resistant mutants of A. niger M1, M2, and M3, were obtained using direct selection, stepwise adaptation, and ultraviolet mutation techniques. Biosorption of Ni (II) by the mutant M3 was 50% more than that of its parent strain.     

High pressure pyrolysis of toluene. 1. Experiments and modeling of toluene decomposition

The pyrolysis of toluene, the simplest methyl-substituted aromatic molecule, has been studied behind reflected shock waves using a single pulse shock tube. Experiments were performed at nominal high pressures of 27 and 45 bar and spanning a wide temperature range from 1200 to 1900 K. A variety of stable species, ranging from small hydrocarbons to single ring aromatics (principal soot precursors such as phenylacetylene and indene) were sampled from the shock tube and analyzed using standard gas chromatographic techniques. A detailed chemical kinetic model with 262 reactions and 87 species was assembled to simulate the stable species profiles (specifically toluene, benzene and methane) from the current high-pressure pyrolysis data sets and shock tube-atomic resonance absorption spectrometry (ARAS) H atom profiles obtained from prior toluene pyrolysis experiments performed under similar high-temperature conditions and lower pressures from 1.5 to 8 bar. The primary steps in toluene pyrolysis represent the most sensitive and dominant reactions in the model. Consequently, in the absence of unambiguous direct experimental measurements, we have utilized recent high level theoretical estimates of the barrierless association rate coefficients for these primary reactions, C6H5 + CH3 --> C6H5CH3 (1a) and C6H5CH2 + H --> C6H5CH3 (1b) in the detailed chemical kinetic model. The available data sets can be successfully reconciled with revised values for deltaH0f(298K)(C6H5CH2) = 51.5 +/- 1.0 kcal/mol and deltaH0f(298K)(C6H5) = 78.6 +/- 1.0 kcal/mol that translate to primary dissociation rate constants, reverse of 1a and 1b, represented by k(-1a,infinity) = (4.62 x 10(25))T(-2.53)exp[-104.5 x 10(3)/RT] s(-1) and k(-1b,infinity) = (1.524 x 10(16))T(-0.04)exp[-93.5 x 10(3)/RT] s(-1) (R in units of cal/(mol K)). These high-pressure limiting rate constants suggest high-temperature branching ratios for the primary steps that vary from 0.39 to 0.52 over the temperature range 1200-1800 K.     

Differential capacitance of liquid/liquid interfaces--a lattice gas model approach

A lattice gas model formalism under mean field approximation is developed for the analysis of differential capacitance pertaining to liquid/liquid interfaces. The interfacial profiles for the two solvent mole fractions are chosen and ionic charge densities are estimated by minimizing the Helmholtz free energy. The dependence of the differential capacitance on various interaction energies, electrolyte concentrations and dielectric constants is indicated. The influence of the solvent density profile is analyzed and deviations from the predictions of Gouy-Chapman theory are pointed out.     

Aromatic polyethers,polysulfones, and polyketones as laminating resins. II

1,3-Bis(p-phenoxybenzenesulfonyl)benzene and 4,4′-bis(p-phenoxybenzenesulfonyl)-diphenyl ether were polymerized with isophthaloyl and terephthaloyl chloride in Friedel-Crafts type polymerizations. These polymers had 5-cyanoisophthaloyl units in the backbone, obtained by using 5-cyanoisophthaloyl chloride as part of the acid chloride monomer. A number of catalysts were screened to effect the trimerization of the pendant nitrile groups in the polymer to the triazines. Model reactions were carried out for each polymer. Physical and thermal properties of the laminates obtained from these polymers are discussed.