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

Reaction layer formation at the graphite/copper-chromium alloy interface

Sessile drop tests were used to obtain information about copper chromium alloys that suitably wet graphite. Characterization of graphite/copper-chromium alloy interfaces subjected to elevated temperatures were conducted using scanning electron micrography, energy dispersive spectroscopy, auger electron spectroscopy, and x ray diffraction analyses. These analyses indicate that during sessile drop tests conducted at 1130 C for one hour, copper alloys containing greater than 0.98 percent chromium form continuous reaction layers of approximately 10 micron thickness. The reaction layers adhere to the graphite surface. The copper wets the reaction layer to form a contact angle of 60 degrees or less. X ray diffraction results indicate that the reaction layer is chromium carbide. The kinetics of reaction layer formation were modelled in terms of bulk diffusion mechanisms. Reaction layer thickness is controlled initially by the diffusion of Cr out of Cu alloy and later by the diffusion of C through chromium carbide

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