Computational and dynamic NMR investigation of 2,2-dimesityl-1,1,1,3,3,3-hexamethyltrisilane

The structure and rotational barrier for the mesityl-silicon bond of 2,2-dimesityl-1,1,1,3,3,3-hexamethyltrisilane have been investigated by ¹H- and ¹³C-variable temperature nuclear magnetic resonance (NMR) as well as by density functional theory structural calculations. The calculations show that the lowest energy structure has C₂ symmetry with nonequivalent ortho methyl groups, consistent with the crystal structure and solution NMR. The nonequivalent ortho methyl groups exchange through a C_s transition state with a calculated relative free energy of 11.0 kcal mol⁻¹. The barrier for this rotation found by dynamic NMR is 13.4 ± 0.2 kcal mol⁻¹ at 298 K.     

Packing Non-Zero A-Paths In Group-Labelled Graphs

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊂V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k −2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem. These results were obtained at a workshop on Structural Graph Theory at the PIMS Institute in Vancouver, Canada. This research was partially conducted during the period the first author served as a Clay Mathematics Institute Long-Term Prize Fellow.     

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.     

Extending an edge-coloring

When can a k-edge-coloring of a subgraph K of a graph G be extended to a k-edge-coloring of G? One necessary condition is that for all X ? E(G) - E(K), where μ_i(X) is the maximum cardinality of a subset of X whose union with the set of edges of K colored i is a matching. This condition is not sufficient in general, but is sufficient for graphs of very simple structure. We try to locate the border where sufficiency ends.     

Packing directed circuits fractionally

LetG be a digraph, and letk1, such that no fractional packing of directed circuits ofG has value >k, when every vertex is given capacity 1. We prove there is a set ofO (k logk logk) vertices meeting all directed circuits ofG.     

Organic ions in the gas phase—XXI: Synthesis and mass spectra of deuteriothiophenes

Mass-spectral and n.m.r. analysis of thiophenes labeled by exchange with deuteriosulfuric acid establishes that exchange at the 2 and 5 positions is essentially complete before any deuterium is incorporated at positions 3 and 4. Thus, such exchange is a satisfactory procedure for position-specific labeling. Mass spectra of the labeled thiophenes show that about 60% of the [CHS]⁺ ion yield is derived from molecular ions that have not undergone prior rearrangement. The remaining 40% arises by a path or paths in which the four hydrogen atoms lose position identity. Other decomposition paths contributing to the mass spectrum are characterized by more nearly complete scrambling of hydrogens.