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We characterize some classes of finite soluble groups. In particular, we prove that: a finite group $G$ is supersoluble if and only if $G$ has a normal subgroup $D$ such that $G/D$ is supersoluble and $D$ avoids every chief factor of $G$ between $V^{G}$ and $V_{G}$ for every maximal subgroup $V$ of the generalized Fitting subgroup $F^{*}(G)$ of $G$; a finite soluble group $G$ is a $PST$-group (that is, Sylow permutability is a transitive relation on $G$) if and only if $G$ has a normal subgroup $D$ such that $G/D$ is nilpotent and $D$ avoids every chief factor of $G$ between $V^{G}$ and $V_{G}$ for every subnormal subgroup $A$ of $G$., Comment: 19 pages

The most abundant terrestrial lavas, mid-ocean ridge and ocean island basalt (MORB and OIB), are commonly considered to be derived from a depleted MORB-mantle component and more specific, variably enriched mantle plume sources. However, findings of oceanic lavas and mafic cumulates issued from melts, enriched in chlorine and having a radiogenic Sr ratio, can be attributed to an interaction between the asthenosphere-derived melts and lithospheric peridotite variably hydrated due to penetration of hydrothermal water down to and below Moho level. To constrain mechanisms and rates responsible for the interaction, we report results of experiments of reaction between serpentinite and tholeiitic basaltic melt. Results show that the reaction proceeds via a multi-stage mechanism: (i) transformation of serpentinite into Cr-rich spinel-bearing harzburgite containing pore fluid, (ii) partial melting and dissolution of the harzburgite assemblage with formation of interstitial hydrous melts, and (iii) final assimilation of the Cr-rich spinel-bearing harzburgite/dunite and formation of hybrid basaltic melts with high MgO and elevated Cr and Ni contents. Assimilation of serpentinite by basaltic melt may occur under elevated melt/rock ratios and may lead to chromitite formation. Our experiments provide evidence that MORB and high-Mg-Cr orthopyroxene-rich cumulates depleted in incompatible elements can be produced from common mid-ocean ridge basaltic melts modified by reaction with hydrated lithospheric peridotite. We established that the rate of assimilation of serpentinized peridotite is controlled by silica diffusion in the reacting hydrous basaltic melt., Comment: 6 figures, 6 tables, Frontiers in Earth Science, accepted

Current theories suggest that on Earth and, possibly, on other terrestrial planets early in their history, the first continental crust may has been produced by direct melting of hydrated peridotite. However, the conditions, mechanisms and necessary ingredients of such production remain elusive. To fill this gap, we have conducted experiments of serpentinite melting in the presence of variable proportions of basaltic melt, at typical conditions of the shallow lithosphere and asthenosphere. These experiments revealed formation of silica-rich liquids, which are similar to tonalite-trondhjemite-granodiorite magmas (TTG) identified in modern terrestrial oceanic mantle settings. Our results suggest a new mechanism of aqueous fluid-assisted partial melting of peridotite that may have operated on the early Earth and Mars just after the solidification of an ultramafic-mafic magma ocean, leading to the formation of the first embryos of continental crust. The proposed mechanism of the continental crust formation may have been predominant before the onset of plate tectonics., Comment: 62 pages, 9 figures, submitted to Frontiers in Earth Science

For a non-linear MIMO feedback system, the robustness against uncertain time-variations in the feedback loop is investigated in an input-output framework. A general sufficient condition in terms of a bound on average rates of time-variation for the system to be stable is derived. The condition gives a tolerable limit on infrequent large variations or slow time-variation rate of a non-linear MIMO adaptive switching system., Comment: 12 pages, 10 figures, submitted to IEEE Trans. Automatic Control