A stability result for purely radiative spacetimes

An existence and stability result for a class of purely radiative vacuum spacetimes arising from hyperboloidal data is given. This result generalises semiglobal existence results for Minkowski-like spacetimes to the case where the reference solution contains gravitational radiation. The analysis makes use of the extended conformal field equations and a gauge based on conformal geodesics so that the location and structure of the conformal boundary of the perturbed solutions is known a priori.Comment: 25 pages, 4 figure

A C3(H20) recycling pathway is a component of the intracellular complement system

An intracellular complement system (ICS) has recently been described in immune and nonimmune human cells. This system can be activated in a convertase-independent manner from intracellular stores of the complement component C3. The source of these stores has not been rigorously investigated. In the present study, Western blotting identified a band corresponding to C3 in freshly isolated human peripheral blood cells that was absent in corresponding cell lines. One difference between native cells and cell lines was the time absent from a fluid-phase complement source; therefore, we hypothesized that loading C3 from plasma was a route of establishing intracellular C3 stores. We found that many types of human cells specifically internalized C3(H(2)O), the hydrolytic product of C3, and not native C3, from the extracellular milieu. Uptake was rapid, saturable, and sensitive to competition with unlabeled C3(H(2)O), indicating a specific mechanism of loading. Under steady-state conditions, approximately 80% of incorporated C3(H(2)O) was returned to the extracellular space. These studies identify an ICS recycling pathway for C3(H(2)O). The loaded C3(H(2)O) represents a source of C3a, and its uptake altered the cytokine profile of activated CD4(+) T cells. Importantly, these results indicate that the impact of soluble plasma factors should be considered when performing in vitro studies assessing cellular immune function

A Dirac type result on Hamilton cycles in oriented graphs

We show that for each \alpha>0 every sufficiently large oriented graph G with \delta^+(G),\delta^-(G)\ge 3|G|/8+ \alpha |G| contains a Hamilton cycle. This gives an approximate solution to a problem of Thomassen. In fact, we prove the stronger result that G is still Hamiltonian if \delta(G)+\delta^+(G)+\delta^-(G)\geq 3|G|/2 + \alpha |G|. Up to the term \alpha |G| this confirms a conjecture of H\"aggkvist. We also prove an Ore-type theorem for oriented graphs.Comment: Added an Ore-type resul

An existence result for a nonlinear transmission problems

Let $\Omega^o$ and $\Omega^i$ be open bounded subsets of $\mathbb{R}^n$ of class $C^{1,\alpha}$ such that the closure of $\Omega^i$ is contained in $\Omega^o$. Let $f^o$ be a function in $C^{1,\alpha}(\partial\Omega^o)$ and let $F$ and $G$ be continuous functions from $\partial\Omega^i\times\mathbb{R}$ to $\mathbb{R}$. By exploiting an argument based on potential theory and on the Leray-Schauder principle we show that under suitable and completely explicit conditions on $F$ and $G$ there exists at least one pair of continuous functions $(u^o, u^i)$ such that $$\left\{ \begin{array}{ll} \Delta u^o=0&\text{in }\Omega^o\setminus\mathrm{cl}\Omega^i\,,\\ \Delta u^i=0&\text{in }\Omega^i\,,\\ u^o(x)=f^o(x)&\text{for all }x\in\partial\Omega^o\,,\\ u^o(x)=F(x,u^i(x))&\text{for all }x\in\partial\Omega^i\,,\\ \nu_{\Omega^i}\cdot\nabla u^o(x)-\nu_{\Omega^i}\cdot\nabla u^i(x)=G(x,u^i(x))&\text{for all }x\in\partial\Omega^i\,, \end{array} \right.$$ where the last equality is attained in certain weak sense. In a simple example we show that such a pair of functions $(u^o, u^i)$ is in general neither unique nor local unique. If instead the fourth condition of the problem is obtained by a small nonlinear perturbation of a homogeneous linear condition, then we can prove the existence of at least one classical solution which is in addition locally unique