Dimension of gradient measures

We prove that if pure derivatives with respect to all coordinates of a function on $\mathbb{R}^n$ are signed measures, then their lower Hausdorff dimension is at least $n-1$. The derivatives with respect to different coordinates may be of different order.Comment: 8 page

Scarcity of female mates predicts regional variation in men’s and women’s sociosexual orientation across US states

Previous studies have linked regional variation in willingness to engage in uncommitted sexual relationships (i.e., sociosexual orientation) to many different socio-ecological measures, such as adult sex ratio, life expectancy, and gross domestic product. However, these studies share a number of potentially serious limitations, including reliance on a single dataset of responses aggregated by country and a failure to properly consider intercorrelations among different socio-ecological measures. We address these limitations by (1) collecting a new dataset of 4,453 American men’s and women’s sociosexual orientation scores, (2) using multilevel analyses to avoid aggregation, and (3) deriving orthogonal factors reflecting US state-level differences in the scarcity of female mates, environmental demands, and wealth. Analyses showed that the scarcity of female mates factor, but not the environmental demand or wealth factors, predicted men’s and women’s sociosexual orientation. Participants reported being less willing to engage in uncommitted sexual relationships when female mates were scarce. These results highlight the importance of scarcity of female mates for regional differences in men’s and women’s mating strategies. They also suggest that effects of wealth-related measures and environmental demands reported in previous research may be artifacts of intercorrelations among socio-ecological measures or, alternatively, do not necessarily generalize well to new datasets

Differential invariants of generic hyperbolic Monge--Amp\`ere equations

In this paper basic differential invariants of generic hyperbolic Monge--Amp\`ere equations with respect to contact transformations are constructed and the equivalence problem for these equations is solved.Comment: 25 page

Precipitation strengthened high strength, high conductivity Cu-Cr-Nb alloys produced by chill block melt spinning

A series of Cu-based alloys containing 2 to 10 a/o Cr and 1 to 5 a/o Nb were produced by chill block melt spinning (CBMS). The melt spun ribbons were consolidated and hot rolled to sheet to produce a supersaturated Cu-Cr-Nb solid solution from which the high melting point intermetallic compound Cr2Nb could be precipitated to strengthen the Cu matrix. The results show that the materials possess electrical conductivities in excess of 90 percent that of pure Cu at 200 C and above. The strengths of the Cu-Cr-Nb alloys were much greater than Cu, Cu-0.6 Cr, NARloy-A, and NARloy-Z in the as-melt spun condition. The strengths of the consolidated materials were less than Cu-Cr and Cu-Cr-Zr below 500 C and 600 C respectively, but were significantly better above these temperatures. The strengths of the consolidated materials were greater than NARloy-Z, at all temperatures. The GLIDCOP possessed similar strength levels up to 750 C when the strength of the Cu-Cr-Nb alloys begins to degrade. The long term stability of the Cu-Cr-Nb alloys was measured by the microhardness of aged samples and the growth of precipitates. The microhardness measurements indicate that the alloys overage rapidly, but do not suffer much loss in strength between 10 and 100 hours which confirms the results of the electrical resistivity measurements taken during the aging of the alloys at 500 C. The loss in strength from peak strength levels is significant, but the strength remains exceptionally good. Transmission electron microscopy (TEM) of the as-melt spun samples revealed that Cr2Nb precipitates formed in the liquid Cu during the chill block melt spinning, indicating a very strong driving force for the formation of the precipitates. The TEM of the aged and consolidated materials indicates that the precipitates coarsen considerably, but remain in the submicron range