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

Linear semigroups with coarsely dense orbits

Let $S$ be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional real or complex vector space $V$. We show that every coarsely dense orbit of $S$ is actually dense in $V$. More generally, if the orbit contains a coarsely dense subset of some open cone $C$ in $V$ then the closure of the orbit contains the closure of $C$. In the complex case the orbit is then actually dense in $V$. For the real case we give precise information about the possible cases for the closure of the orbit.Comment: We added comments and remarks at various places. 14 page

Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model recently developed by Abels, Garcke, and Gr\"un for fluids with different densities, which leads to a solenoidal velocity field. The model is given by a non-homogeneous Navier-Stokes system with a modified convective term coupled to a Cahn-Hilliard system. The density of the mixture depends on an order parameter.Comment: 33 page

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

Peptide Presentation Is the Key to Immunotherapeutical Success

Positive and negative selection in the thymus relies on T-cell receptor recognition of peptides presented by HLA molecules and determines the repertoire of T cells. Immune competent T-lymphocytes target cells display nonself or pathogenic peptides in complex with their cognate HLA molecule. A peptide passes several selection processes before being presented in the peptide binding groove of an HLA molecule; here the sequence of the HLA molecule’s heavy chain determines the mode of peptide recruitment. During inflammatory processes, the presentable peptide repertoire is obviously altered compared to the healthy state, while the peptide loading pathway undergoes modifications as well. The presented peptides dictate the fate of the HLA expressing cell through their (1) sequence, (2) topology, (3) origin (self/nonself). Therefore, the knowledge about peptide competition and presentation in the context of alloreactivity, infection or pathogenic invasion is of enormous significance. Since in adoptive cellular therapies transferred cells should exclusively target peptide-HLA complexes they are primed for, one of the most crucial questions remains at what stage of viral infection viral peptides are presented preferentially over self-peptides. The systematic analyzation of peptide profiles under healthy or pathogenic conditions is the key to immunological success in terms of personalized therapeutics

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

Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo