Expansion solution for subsonic compressible flow

An expansion solution in the physical plane is developed for subsonic compressible fluid flow past an obstacle. Assuming that the stream is inviscid, isentropic, irrotational and steady, it is shown that the velocity potential may be expressed as a series of homogeneous Heun functions and radial distance terms. The basis of this analysis is Ludford's formal discussion of corresponding singularities in Bergman's Linear Integral Operator Method. A modification of these results permits reduction of the governing nonlinear partial differential equation to an ordinary, nonhomogeneous, linear differential equation. The expansion solution is compared with the Rayleigh-Janzen method and the Prandtl-Glauert theory. The comparison indicates that this expansion gives better results than other methods currently used. The simplicity and economy of this expansion solution facilitates direct practical application.     

The isomorphism theorem for relatively finitely determined Z n -actions

Any two ergodic Z ⁿ -actions which are finitely determined relative to a common factor are isomorphic if and only if they have the same entropy. This work supported in part by N.S.F. Grant DMS-85-04701.     

Multiply Abundant Numbers

A multiply abundant number N of order r is a number for which the sum of the proper divisors, S(N), is greater than r times N. The authors explore abundant, double abundant, and triple abundant numbers as well as abundant numbers of higher orders. They also consider odd abundant numbers of orders greater than 1. They present a proof that abundant numbers of every order r exist. Readers are encouraged to use the included computer code to explore abundant numbers for themselves, look for patterns in the output, and consider further questions about these fascinating numbers.     

Disjoint hamiltonian cycles in bipartite graphs

Let G=(X,Y) be a bipartite graph and define . Moon and Moser [J. Moon, L. Moser, On Hamiltonian bipartite graphs, Israel J. Math. 1 (1963) 163-165. MR 28 # 4540] showed that if G is a bipartite graph on 2n vertices such that , then G is hamiltonian, sharpening a classical result of Ore [O. Ore, A note on Hamilton circuits, Amer. Math. Monthly 67 (1960) 55] for bipartite graphs. Here we prove that if G is a bipartite graph on 2n vertices such that , then G contains k edge-disjoint hamiltonian cycles. This extends the result of Moon and Moser and a result of R. Faudree et al. [R. Faudree, C. Rousseau, R. Schelp, Edge-disjoint Hamiltonian cycles, Graph Theory Appl. Algorithms Comput. Sci. (1984) 231-249].     

Identification of speaker sex from one vowel across a range of fundamental frequencies

To identify a speaker's sex, listeners may rely on sex-based differences in average fundamental frequency (F0), but overlap in male and female F0 ranges undermines such judgments. To test accuracy of sex-identification throughout the F0 range, listeners were asked to judge sex based on audio recordings of /ɑ/ spoken on a number of overlapping steady F0s by 10 male and 10 female English speakers. In general, listeners performed above chance (71.6% correct). However, near range extrema, listeners followed an apparent bias toward hearing high F0s as female and low as male; confidence was high when accuracy was high and vice-versa. At mid-range, listeners identified sex fairly accurately but were not very confident in their judgments. In a forced-choice task, vowels close in F0 (but beyond the difference limen) were presented in male-female or female-male pairs. Listeners weakly identified speaker sex (63.3% correct). Identification of the male voice was considerably above chance only when the male had the lower F0 of the pair. Reliance on stereotypes of speaking F0 may bias listeners to hear low F0s as male and high F0s as female, perhaps with a contribution from vocal-tract length information. No strong evidence for a contribution of voice quality obtained.     

Covariates of corticotropin-releasing hormone (CRH) concentrations in cerebrospinal fluid (CSF) from healthy humans

Background  

Define covariates of cerebrospinal corticotropin-releasing hormone (CRH) levels in normal humans. CRH_CSF was measured in 9 normal subjects as part of an intensive study of physiological responses stressors in chronic pain and fatigue states. CRH_CSF was first correlated with demographic, vital sign, HPA axis, validated questionnaire domains, baseline and maximal responses to pain, exercise and other stressors. Significant factors were used for linear regression modeling.     

Beta-delayed proton emitter kr

The nucleide ⁷³Kr has been identified by on-line mass separation as a precursor of β-delayed proton emission. The proton branch is (6.8 ±1.2) × 10⁻³ proton/decay. The protons populate the ground state and also the first excited 2⁺ state at 866 keV in ⁷²Se with a relative intensity of (35±9) %. The value of Q_EC−B_p, where B_p is the proton separation energy for the nucleus ⁷³Br, is found to be 4.85 ±0.30 MeV based on the fraction of proton events preceded by positron decay.