Highly edge‐connected detachments of graphs and digraphs

Let G = (V,E) be a graph or digraph and r : V → Z₊. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν₁,…,ν_r(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003     

Hydrogen migrations in mass spectrometry. VI—the chemical ionization mass spectra of substituted benzoic acids and benzyl alcohols

The H₂ and CH₄ chemical ionization mass spectra of a series of series of substituted benzoic acids and substituted benzyl alcohols have been determined. For the benzoic acids the major fragmentation reactions of the protonated molecule involve elimination of H₂O or elimination of CO₂, the latter reaction involving migration of the carboxylic hydrogen to the aromatic ring. For the benzyl alcohols the major fragmentation reactions of [MH]⁺ involve loss of H₂O or CH₂O, analogous to the CO₂ elimination reaction for the benzoic acids. It is shown that the CO₂ and CH₂O elimination reactions occur only when a conjugated aromatic ring system is present, and that for the carboxylic acid systems, methyl groups and, to a lesser extent, phenyl groups are capable of migrating. The only discernible effect of substituents on the fragmentation of [MH]⁺ is an enhancement of the H₂O loss reaction in the benzoic acid system when an amino, hydroxyl, or halogen substituent is ortho to the carboxyl function. This ‘ortho’ effect, which differs in scope from that observed in electron impact mass spectra, is attributed to an intramolecular catalysis by the ortho substituent of the 1,3 hydrogen migration in the carbonyl protonated acid followed by H₂O elimination. Apparently, this route is favoured over the direct elimination of H₂O from the carbonyl protonated acid, since the latter has a high activation energy barrier because of unfavourable orbital symmetry restrictions.     

Transitions between disordered phases in supercooled liquid silicon

We have investigated the transitions between disordered phases in supercooled liquid silicon using computer simulations. The thermodynamic properties were directly obtained from the free energy, which was computed using the recently proposed reversible scaling method. The calculated free energies of the crystalline and liquid phases of silicon at zero pressure, obtained using the environment dependent interatomic potential, are in excellent agreement with the available experimental data. The results show that, at zero pressure, a weak first-order liquid-liquid transition occurs at 1135 K and a continuous liquid-amorphous transition takes place at 843 K. These results are consistent with the existence of a second critical point for the liquid-liquid transition at a negative pressure.     

Bispectral KP solutions and linearization of Calogero-Moser particle systems

Rational and soliton solutions of the KP hierarchy in the subgrassmannianGr ₁ are studied within the context of finite dimensional dual grassmannians. In the rational case, properties of the tau function, , which are equivalent to bispectrality of the associated wave function, , are identified. In particular, it is shown that there exists a bound on the degree of all time, variables in if and only if is a rank one bispectral wave function. The action of the bispectral involution, , in the generic rational case is determined explicitly in terms of dual grassmannian parameters. Using the correspondence between rational solutions, and particle systems, it is demonstrated that is a linearizing map of the Calogero-Moser particle system and is essentially the map introduced by Airault, McKean and Moser in 1977 [2].Research supported by NSA Grant MDA904-92-H-3032     

Chiral induction in self-assembled helicates: CHIRAGEN type ligands with ferrocene bridging units

The aim of this work was the preparation of enantiomerically pure bis(pinene-bipyridine) ligands containing the ferrocenyl moiety. Several such ligands (1-3) were synthesized and completely characterized. These molecules can be diastereoselectively deprotonated at the acidic methylene group of the pinene moiety using a strong and sterically hindered base such as LDA. Subsequent reaction of the formed anion with alkyl halides yield the family of C(2)-symmetric enantiopure compounds (1a-c). Copper(I), silver(I), or zinc(II) complexes with several ligands (C1-C8) were prepared and structurally characterized in the solid state and in solution. Self-assembled helical species are formed in several cases. It became evident that the chiral groups present in the ligand do not completely determined the helical configuration of the assemblages. Diastereoselectivity is thus not complete with this type of ligands, contrary to other, similar ligands studied before.     

Does alpha-fluorination affect the structural trans-influence and kinetic trans-effect of an alkyl ligand? Molecular structures of Pd(TMEDA)(CH(3))(R(F)) and a kinetic study of the trans to cis isomerization of Pt(TMEDA)(CH(3))(2)I(R(F)) [R(F) = CF(2)CF(3), CFHCF(3), CH(2)CF(3)

Reaction of Pd(TMEDA)(CH(3))(2) [TMEDA = tetramethylethylenediamine] with fluoroalkyl iodides R(F)I affords a series of square planar Pd(II) complexes Pd(TMEDA)(CH(3))(R(F)) [R(F) = CF(2)CF(3) (9), CFHCF(3) (10), CH(2)CF(3) (11)], presumably by oxidative addition followed by reductive elimination of CH(3)I. The solid-state structures of each compound have been determined by single crystal X-ray diffraction studies, allowing the effect of increasing alpha-fluorination on the structural trans-influence of alkyl ligands to be examined. In these compounds there is no significant difference observed in the trans-influence of the three fluorinated alkyl ligands toward the trans-N atom, although a significant cis-influence on the neighboring methyl ligand is apparent. Oxidative addition of the same series of fluoroalkyl ligands to the corresponding Pt(TMEDA)(CH(3))(2) affords octahedral Pt(IV) complexes trans-Pt(TMEDA)(CH(3))(2)(R(F))I [R(F) = CF(2)CF(3) (12), CFHCF(3) (13), CH(2)CF(3) (14)] as the kinetic products. In each case, subsequent isomerization to the corresponding all cis-isomers is observed; in the case of 13, the stereocenter at the alpha-carbon results in two diastereomeric cis-isomers, which are formed at different rates. The molecular structures of 13 and its more stable all cis-isomer 16b have been crystallographically determined. Kinetic studies of the trans-cis isomerization reactions show the mechanism to involve a polar transition state, presumably involving iodide dissociation, followed by rearrangement of the cation, and iodide recombination. High dielectric solvents increase the rate, but solvent coordinating ability has no effect. Dissolved salts (LiI, LiOTf) show normal accelerative salt effects, with no inhibition in the case of added iodide, consistent with the formation of an intimate ion pair intermediate. The kinetic parameters show that the trans-effects of fluoroalkyl ligands in these compounds follow the order expected from the relative sigma-donor properties of the ligands, with CF(2)CF(3) < CFHCF(3) < CH(2)CF(3).     

Unrestricted perfect pairing: the simplest wave-function-based model chemistry beyond mean field

The perfect pairing (PP) approximation from generalized valence bond theory is formulated in an unrestricted fashion for both closed- and open-shell systems using a coupled cluster ansatz. In the model chemistry proposed here, active electron pairs are correlated, but the unpaired or radical electrons remain uncorrelated, leading to a linear number of decoupled cluster amplitudes which can be solved for analytically. The alpha and beta spatial orbitals are variationally optimized independently. This minimal treatment of electron-electron correlation noticeably improves upon symmetry-breaking problems and other pathologies in Hartree-Fock (HF) theory and may be computed using the resolution of the identity approximation at only a factor of several times more effort than HF itself. PP also generally predicts improved molecular structures over HF. This compact, correlated wave function potentially provides a useful starting point for dynamical correlation corrections.     

Purification and Characterization of Gum-Derived Polysaccharides of Moringa oleifera and Azadirachta indica and Their Applications as Plant Stimulants and Bio-Pesticidal Agents

Plant gums are bio-organic substances that are derived from the barks of trees. They are biodegradable and non-adverse complex polysaccharides that have been gaining usage in recent years due to a number of advantages they contribute to various applications. In this study, gum was collected from Moringa oleifera and Azadirachta indica trees, then dried and powdered. Characterizations of gum polysaccharides were performed using TLC, GC-MS, NMR, etc., and sugar molecules such as glucose and xylose were found to be present. Effects of the gums on Abelmoschus esculentus growth were observed through root growth, shoot growth, and biomass content. The exposure of the seeds to the plant gums led to bio stimulation in the growth of the plants. Poor quality soil was exposed to the gum polysaccharide, where the polysaccharide was found to improve soil quality, which was observed through soil analysis and SEM analysis of soil porosity and structure. Furthermore, the plant gums were also found to have bio-pesticidal activity against mealybugs, which showed certain interstitial damage evident through histopathological analysis.     

Algebras of Symmetric Holomorphic Functions on lp

The authors study the algebra of uniformly continuous holomorphicsymmetric functions on the ball of l_p, investigating in particularthe spectrum of such algebras. To do so, they examine the algebraof symmetric polynomials on l_p-spaces, as well as finitely generatedsymmetric algebras of holomorphic functions. Such symmetricpolynomials determine the points in l_p up to a permutation.