Correlations of Length Spectra for Negatively Curved Manifolds

In this paper we obtain asymptotic estimates for pairs of closed geodesics on negatively curved manifolds, the differences of whose lengths lie in a prescribed family of shrinking intervals, where the geodesics are ordered with respect to a discrete length. In certain cases, this discrete length can be taken to be the word length with respect to a set of generators for the fundamental group.     

Investigating the consistency of woodwind instrument manufacturing by comparing five nominally identical oboes

For large-scale woodwind instrument makers, producing instruments with exactly the same playing characteristics is a constant aim. This paper explores manufacturing consistency by comparing five Howarth S10 student model oboes. Psychophysical testing involving nine musicians is carried out to investigate perceived differences in the playing properties of the two Howarth oboes believed to be most dissimilar. Further testing, involving one musician and combinations of the five oboes, provides information regarding the relative playabilities of the instruments at specific pitches. Meanwhile, input impedance measurements are made on the five oboes for fingerings throughout the playing range and their bore profiles are measured. The main findings are (1) the two instruments used in the preliminary psychophysical testing are perceived as identical by most of the musicians, although differences are identified by two players when playing the note F6 and by one player when playing in the lowest register, (2) a variation in the playability of F6 across the five oboes is due to differences in the elevation of the C key, and (3) variations in the playing properties in the lowest register are related to input impedance differences,which, in turn, appear to be at least partly due to bore profile differences.     

Untersuchung von Milch

Ohne Zusammenfassung     

The elusive 16-electron Cp*M(NO)Me(2)(M = Mo, W) complexes and their spontaneous conversions to Cp*M(NMe)(O)Me isomers.

Treatment of [Cp*Mo(NO)Cl(mu-Cl)](2) with magnesium (Me(2)Mg.dioxane, MeMgCl) or aluminum (Me(3)Al) methylating reagents affords the known compound [Cp*Mo(NO)Me(mu-Cl)](2) (1). Similar treatment of the dichloro precursor with MeLi in ethereal solvents generates an equimolar mixture of 1 and the trimethyl "ate" complex, Cp*MoMe(3)(NO-Li(OEt(2)(n)), (2-Et(2)O). Reaction of 2-Et(2)O with a source of [Me](+) forms Cp*MoMe(3)(=N-OMe)(3), a rare terminal alkoxylimido complex. Metathesis of the chloro ligands of [Cp*Mo(NO)Cl(mu-Cl)](2) by MeLi in toluene at low temperatures produces the target dimethyl complex, Cp*Mo(NO)Me(2) (4), in 75% isolated yield. In solution, 4 is predominantly a monomeric species, whereas in the solid state it adopts a dimeric or oligomeric structure containing isonitrosyl bridges as indicated by IR and (15)N/(13)C NMR spectroscopies. Hydrolysis of 4 affords meso- and rac-[Cp*Mo(NO)Me](2)(mu-O) (5), and the reactions of 4 with a range of Lewis bases, L, to form the 18e adducts Cp*Mo(NO)(L)Me(2) (e.g., Cp*Mo(NO)(PMe(3))Me(2) (7)), have established it to be the most electrophilic complex of its family. Acidolysis of the methyl groups of 4 is also facile. Most notably, 4 is thermally unstable in solution and undergoes isomerization via nitrosyl N-O bond cleavage to its oxo(imido) form, Cp*Mo(NMe)(O)Me (11), which is isolable from the final reaction mixture as the mu-oxo-bridged adduct formed by 4 and 11, i.e., Cp*Mo(NO)Me(2)(mu-O)Cp*Mo(NMe)Me (4 <-- 11). The rate of this isomerization is significantly faster for the tungsten dimethyl complex; hence, Cp*W(NO)Me(2) (12) is not isolable free of a supporting donor interaction and can only be isolated as Cp*W(NO)Me(2)(mu-O)Cp*W(NMe)Me (12 <-- 13) or Cp*W(NO)Me(2)(PMe(3)) (14) adducts.     

A conservative formulation for plasticity

In this paper we propose a fully conservative form for the continuum equations governing rate-dependent and rate-independent plastic flow in metals. The conservation laws are valid for discontinuous as well as smooth solutions. In the rate-dependent case, the evolution equations are in divergence form, with the plastic strain being passively convected and augmented by source terms. In the rate-independent case, the conservation laws involve a Lagrange multiplier that is determined by a set of constraints; we show that Riemann problems for this system admit scale-invariant solutions.     

Focused cryogenic trapping for dynamic headspace and pyrolytic analysis of polymers on a fused silica capillary column

Focused cryogenic trapping has been used to maximize the high resolution capabilities of fused silica capillary columns during dynamic headspace and pyrolytic polymer analyses. Mass spectrometric detection with data system recording/processing provide sensitive, selective, and rapid results. The techniques described herein demonstrate the power of both dynamic headspace and pyrolytic analyses for troubleshooting applications with complex industrial polymer products.