Some Properties of Distal Actions on Locally Compact Groups

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We also show that a compactly generated locally compact group of polynomial growth has a compact normal subgroup $K$ such that $G/K$ is distal and the conjugacy action of $G$ on $K$ is ergodic; moreover, if $G$ itself is (pointwise) distal then $G$ is Lie projective. We prove a decomposition theorem for contraction groups of an automorphism under certain conditions. We give a necessary and sufficient condition for distality of an automorphism in terms of its contraction group. We compare classes of (pointwise) distal groups and groups whose closed subgroups are unimodular. In particular, we study relations between distality, unimodularity and contraction subgroups.Comment: 27 pages, main results are revised and improved, some preliminary results are removed and some new results are added, some proofs are revised and some are made shorte

Coercivity and stability results for an extended Navier-Stokes system

In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of controlling the nonlinear terms. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Even in two space dimensions, global existence is open in general, and remains so, primarily due to the lack of a self-contained $L^2$ energy estimate. However, through use of new $H^1$ coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure

Overexpression of melanoma inhibitory activity (MIA) enhances extravasation and metastasis of A-mel 3 melanoma cells in vivo

The secreted MIA protein is strongly expressed by advanced primary and metastatic melanomas but not in normal melanocytes. Previous studies have shown that MIA serum levels correlate with clinical tumour progression in melanoma patients. To provide direct evidence that MIA plays a role in metastasis of malignant melanomas, A-mel 3 hamster melanoma cells were transfected with sense- and antisense rhMIA cDNA and analysed subsequently for changes in their tumorigenic and metastatic potential. Enforced expression of MIA in A-mel 3 cells significantly increased their metastatic potential without affecting primary tumour growth, cell proliferation or apoptosis rate in hamsters, compared with control or antisense transfected cells. Additionally, MIA overexpressing transfectants showed a higher rate of both tumour cell invasion and extravasation. Cells transfected with MIA antisense generally exerted an opposite response. The above changes in function attributed to the expression of MIA may underlie the contribution of MIA to the malignant phenotype. © 2000 Cancer Research Campaig

The Global Stratotype Section and Point (GSSP) of the Serravallian Stage (Middle Miocene)

The Global Stratotype Section and Point (GSSP) for the Base of the Serravallian Stage (Middle Miocene) is defined in the Ras il Pellegrin section located in the coastal cliffs along the Fomm Ir-Rih Bay on the west coast of Malta (35°54'50"N, 14°20'10"E). The GSSP is at the base of the Blue Clay Formation (i.e., top of the transitional bed of the uppermost Globigerina Limestone). This boundary between the Langhian and Serravallian stages coincides with the end of the major Mi-3b global cooling step in the oxygen isotopes and reflects a major increase in Antarctic ice volume, marking the end of the Middle Miocene climate transition and the Earth's transformation into an "Icehouse" climate state. The associated major glacio-eustatic sea-level drop corresponds with sequence boundary Ser1 of Hardenbol et al. (1998) and supposedly with the TB2.5 sequence boundary of Haq et al (1987). This event is slightly older than the last common and/or continuous occurrence of the calcareous nannofossil Sphenolithus heteromorphus, previously considered as guiding criterion for the boundary, and is projected to fall within the younger half of Chron C5ACn. The GSSP level is in full agreement with the definitions of the Langhian and Serravallian in their respective historical stratotype sections in northern Italy and has an astronomical age of 13.82 Ma

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments

The Baum-Connes Conjecture via Localisation of Categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant homology theories, not just for the K-theory of the crossed product. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting

Well posedness of an isothermal diffusive model for binary mixtures of incompressible fluids

We consider a model describing the behavior of a mixture of two incompressible fluids with the same density in isothermal conditions. The model consists of three balance equations: continuity equation, Navier-Stokes equation for the mean velocity of the mixture, and diffusion equation (Cahn-Hilliard equation). We assume that the chemical potential depends upon the velocity of the mixture in such a way that an increase of the velocity improves the miscibility of the mixture. We examine the thermodynamic consistence of the model which leads to the introduction of an additional constitutive force in the motion equation. Then, we prove existence and uniqueness of the solution of the resulting differential problem