A note on the connectivity of 2-regular digraphs

Let D ₂(n) be the probability space of 2-regular digraphs on n vertices with the uniform measure. As n tends to infinity, the probability that the digraphs are 2-connected tends to 1. © 1993 John Wiley & Sons, Inc.     

Expert consensus in solo voice performance evaluation

Experts were interviewed to identify criteria for evaluation of vocal performance. A scale was then constructed and inter- and intrajudge reliability assessed. Experts listened to 19 different performances, plus 6 presented a second time. Interjudge reliability for one judge was modest, but increased dramatically as the size of the judge panel increased. The most reliable items were overall score and intonation accuracy. Diction was less reliable than other items. Intrajudge reliability was higher for overall score than for any other item. A factor analysis on the test items yielded factors labelled intrinsic quality, execution, and diction. Another factor analysis, using the experts as variables, revealed two underlying evaluative dimensions. It was found that 13 experts were primarily influenced by execution, and that 8 were mainly affected by intrinsic quality. Interjudge and intrajudge reliabilities of these two groups differed.     

Random multiblock poly(ester amide)s containing poly(L‐lactide) and cycloaliphatic amide segments: Synthesis and biodegradation studies

Novel multiblock poly(ester amide)s containing poly(L ‐lactide) and cycloaliphatic amide segments were synthesized from telechelic oligomer of α,ω‐hydroxyl terminated poly(L ‐lactide), 1,3‐cyclohexylbis(methylamine), and sebacoylchloride by the “two‐step” interfacial polycondensation method. The blocky nature of PEAs was established by FTIR and ¹H NMR spectroscopies. The effect of relative content of ester and amide segments on the crystallization nature of PEAs was investigated by WAXD and DSC analyses. PEAs having lower content of PLLA, PEA 1 and PEA 2, showed a crystallization pattern analogous to polyamides, whereas PEA 3, having higher content of PLLA, showed two crystalline phases characterized by polyester and polyamide segments. Random nature of PEAs was observed from single T_g values. Biodegradation studies using the enzyme lipase from Candida Cylindracea showed higher degradation rate for PEA 3 than that for PEA 1 and PEA 2. FTIR, ¹H NMR, and DSC analyses of the degraded products indicated the involvement of ester linkages in the degradation process. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3250–3260, 2006     

When maths really is rocket science

Two problems in projectiles are discussed which generate interestingloci.     

One cannot hear orbifold isotropy type

We show that the isotropy types of the singularities of Riemannian orbifolds are not determined by the Laplace spectrum. Indeed, we construct arbitrarily large families of mutually isospectral orbifolds with different isotropy types. Finally, we show that the corresponding singular strata of two isospectral orbifolds may not be homeomorphic. Received: 6 October 2005     

Crystal and molecular structure of crenatine carbonate

The crystal and molecular structure of 1-ethyl-4-methoxy-9H-pyrido[3,4b]indole (crenatine) carbonate C₁₄H₁₄N₂O·H₂CO₃, (MS, m/z 226)M _R 288.3, a-carboline alkaloid, has been determined from X-ray diffraction data. The compound crystallizes in the space group Pbca with cell parameters:a=11.616(4),b=18.450(8),c=12.992(5)Å,V=2784(2)ų,Z=8,D _calc=1.375 g cm^–3, (MoK)=0.71069Å,(Mo K)=0.94 cm^–1,F(000)=1216,R/R _w =8.2/10.3% for 1099 reflections. The ring system of the-carboline nucleus is planar. The title compound shows a two center hydrogen bond between the indole N-H group and the oxygen atom of a carbonate group. The structure does not display hydrogen bonding between-carboline groups but rather a bonding network involving the carbonate group.