A variational characterization of calibrated submanifolds

Let $M$ be a fixed compact oriented embedded submanifold of a manifold $\overline{M}$. Consider the volume $\mathcal{V} (\overline{g}) = \int_M \mathsf{vol}_{(M, g)}$ as a functional of the ambient metric $\overline{g}$ on $\overline{M}$, where $g = \overline{g}|_M$. We show that $\overline{g}$ is a critical point of $\mathcal{V}$ with respect to a special class of variations of $\overline{g}$, obtained by varying a calibration $\mu$ on $\overline{M}$ in a particular way, if and only if $M$ is calibrated by $\mu$. We do not assume that the calibration is closed. We prove this for almost complex, associative, coassociative, and Cayley calibrations, generalizing earlier work of Arezzo-Sun in the almost K\"ahler case. The Cayley case turns out to be particularly interesting, as it behaves quite differently from the others. We also apply these results to obtain a variational characterization of Smith maps.Comment: 35 pages, comments welcom

Replication Attack Detection in Mobile Wireless Sensor Network with LEACH-ME Routing Protocol

Because the Wireless Sensor Network (WSN) nodes are low-cost devices, attackers may capture some nodes in this network and then duplicate these nodes to eavesdrop the transmitted messages or even control the network gradually without difficulty. This is the so-called node replication attack. This type of attacks could cause the huge threat to information security of WSNs. Therefore, in this paper, we would like to suggest a detection approach which can offer good performance but with higher energy consumption. Hence, it can provide an alternative solution for some specific applications that need better precision but do not care energy or lifespan too much

(1E)-6-Meth­oxy-3,4-dihydro­naphthalen-1(2H)-one oxime

In the crystal structure of the title compound, C11H13NO2, the mol­ecules are paired into centrosymmetric dimers via inter­molecular O—H⋯N hydrogen bonds

A large aberrant stem ichthyosauriform indicating early rise and demise of ichthyosauromorphs in the wake of the end-Permian extinction

Contrary to the fast radiation of most metazoans after the end-Permian mass extinction, it is believed that early marine reptiles evolved slowly during the same time interval. However, emerging discoveries of Early Triassic marine reptiles are questioning this traditional view. Here we present an aberrant basal ichthyosauriform with a hitherto unknown body design that suggests a fast radiation of early marine reptiles. The new species is larger than coeval marine reptiles and has an extremely small head and a long tail without a fluke. Its heavily-built body bears flattened and overlapping gastral elements reminiscent of hupehsuchians. A phylogenetic analysis places the new species at the base of ichthyosauriforms, as the sister taxon of Cartorhynchus with which it shares a short snout with rostrally extended nasals. It now appears that ichthyosauriforms evolved rapidly within the first one million years of their evolution, in the Spathian (Early Triassic), and their true diversity has yet to be fully uncovered. Early ichthyosauromorphs quickly became extinct near the Early-Middle Triassic boundary, during the last large environmental perturbation after the end-Permian extinction involving redox fluctuations, sea level changes and volcanism. Marine reptile faunas shifted from ichthyosauromorph-dominated to sauropterygian-dominated composition after the perturbation