Nowhere-zero 6-flows

We prove that every graph with no isthmus has a nowhere-zero 6-flow, that is, a circulation in which the value of the flow through each edge is one of ±1, ±2,…, ±5. This improves Jaeger's 8-flow theorem, and approaches Tutte's 5-flow conjecture.     

A note on convergence of the multigrid V-cycle

Several recent papers have discussed the convergence of the multigrid V-cycle. In particular there are several results for the symmetric case: where the numbers of smoothings before the fine-to-coarse transfer and after the coarse-to-fine transfer are the same. In most instances, the smoother H=I?E^-1A has been limited to the case where E is positive definite and the eigenvalues h of H satisfy 0?h?1. In this note we extend these results to asymmetric V-cycles and the case where -b?h?1 with 0<b<1.     

Packing nearly-disjoint sets

De Bruijn and Erdős proved that ifA ₁, ...,A _k are distinct subsets of a set of cardinalityn, and |A _i ∩A _j |≦1 for 1≦i<j ≦k, andk>n, then some two ofA ₁, ...,A _k have empty intersection. We prove a strengthening, that at leastk /n ofA ₁, ...,A _k are pairwise disjoint. This is motivated by a well-known conjecture of Erdőds, Faber and Lovász of which it is a corollary. Partially supported by N. S. F. grant No. MCS—8103440     

Cycles in dense digraphs

Let G be a digraph (without parallel edges) such that every directed cycle has length at least four; let β(G) denote the size of the smallest subset X ? E(G) such that G?X has no directed cycles, and let γ(G) be the number of unordered pairs {u, v} of vertices such that u, v are nonadjacent in G. It is easy to see that if γ(G) = 0 then β(G) = 0; what can we say about β(G) if γ(G) is bounded?

We prove that in general β(G) ≤ γ(G). We conjecture that in fact β(G) ≤ ½γ(G) (this would be best possible if true), and prove this conjecture in two special cases:

• when V(G) is the union of two cliques
• when the vertices of G can be arranged in a circle such that if distinct u, v, w are in clockwise order and uw is a (directed) edge, then so are both uv, vw.

     

Alternating and Random Copolymers of Vinyl Acetate and Maleic Anhydride

Alternating copolymers of vinyl acetate (VAc) and maleic anhydride (MA) are produced preferentially when VAc and MA are copolymerized at moderate temperatures while random copolymers are produced at temperatures above 90°C. A charge-transfer complex (CTC) of VAc/MA exists at moderate temperatures but does not exist at temperatures above 90°C.     

Electron super-rich radicals in the gas phase. A neutralization-reionization mass spectrometric and ab initio/RRKM study of diaminohydroxymethyl and triaminomethyl radicals

Diaminohydroxymethyl (1) and triaminomethyl (2) radicals were generated by femtosecond collisional electron transfer to their corresponding cations (1+ and 2+, respectively) and characterized by neutralization-reionization mass spectrometry and ab initio/RRKM calculations at correlated levels of theory up to CCSD(T)/aug-cc-pVTZ. Ion 1+ was generated by gas-phase protonation of urea which was predicted to occur preferentially at the carbonyl oxygen with the 298 K proton affinity that was calculated as PA = 875 kJ mol-1. Upon formation, radical 1 gains vibrational excitation through Franck-Condon effects and rapidly dissociates by loss of a hydrogen atom, so that no survivor ions are observed after reionization. Two conformers of 1, syn-1 and anti-1, were found computationally as local energy minima that interconverted rapidly by inversion at one of the amine groups with a <7 kJ mol-1 barrier. The lowest energy dissociation of radical 1 was loss of the hydroxyl hydrogen atom from anti-1 with ETS = 65 kJ mol-1. The other dissociation pathways of 1 were a hydroxyl hydrogen migration to an amine group followed by dissociation to H2N-C=O* and NH3. Ion 2+ was generated by protonation of gas-phase guanidine with a PA = 985 kJ mol-1. Electron transfer to 2+ was accompanied by large Franck-Condon effects that caused complete dissociation of radical 2 by loss of an H atom on the experimental time scale of 4 mus. Radicals 1 and 2 were calculated to have extremely low ionization energies, 4.75 and 4.29 eV, respectively, which belong to the lowest among organic molecules and bracket the ionization energy of atomic potassium (4.34 eV). The stabilities of amino group containing methyl radicals, *CH2NH2, *CH(NH2)2, and 2, were calculated from isodesmic hydrogen atom exchange with methane. The pi-donating NH2 groups were found to increase the stability of the substituted methyl radicals, but the stabilities did not correlate with the radical ionization energies.     

Development and applications of an on-line thermal neutron prompt-gamma element analysis system

This paper introduces the principles, instrumentation, implementation, and industrial applications of an on-line thermal neutron prompt-gamma element analysis system (using a²⁵²Cf neutron source, Am–Be neutron source, or neutron generator). The energy resolution of the system at the H prompt-gamma full-energy photopeak (2.22325 MeV) is 3.6 keV. The concentration measurement error of Al₂O₃, FeO₃, CaO, and SiO₂ is ±0.3%, ±0.1%, ±0.4%, and ±0.4%, respectively. The system has been tested on-site at both the Shandong and the Zhengzhou Aluminium Works. Our preliminary on-site measurements confirm that the stability, reliability, measurement range, and accuracy of the system can meet the requirements of the aluminium production process. Facilitation of this measurement at aluminium plants is expected to reduce plant costs by over 3 million dollars annually through reduced energy consumption, more rapid qualification of pulps being mixed during the production process, and in reduced labor costs.Other participants of Shandong and Zhenghou Aluminium Works are: Wang Aili, Zengshen, Dei Jianguo and Lu Jinnan, Wang Deyu, Jin Hequan.